Daily Papers

We propose HOI Transformer to tackle human object interaction (HOI) detection in an end-to-end manner. Current approaches either decouple HOI task into separated stages of object detection and interaction classification or introduce surrogate interaction problem. In contrast, our method, named HOI Transformer, streamlines the HOI pipeline by eliminating the need for many hand-designed components. HOI Transformer reasons about the relations of objects and humans from global image context and directly predicts HOI instances in parallel. A quintuple matching loss is introduced to force HOI predictions in a unified way. Our method is conceptually much simpler and demonstrates improved accuracy. Without bells and whistles, HOI Transformer achieves 26.61% AP on HICO-DET and 52.9% AP_{role} on V-COCO, surpassing previous methods with the advantage of being much simpler. We hope our approach will serve as a simple and effective alternative for HOI tasks. Code is available at https://github.com/bbepoch/HoiTransformer .

Mixed-precision quantization must decide which parts of a model to keep at higher precision. A common premise, shared by sensitivity-based methods such as HAWQ and CoopQ, is that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation. We test this premise at the 4-bit weight-and-activation precisions now being deployed, treating the change in loss f(S) from quantizing a layer set S as a set function on the Boolean cube and analyzing it through two classical changes of basis. This analysis yields two findings. First, across configurations drawn from the deployment distribution, 85--93\% of the variance of f is explained by per-layer effects alone. Second, a monotone transform of a sum of per-layer terms reproduces f's ranking of configurations, misordering at most 2\% of pairs. We propose the coverage model f(S)=cbigl(1-prod_{iin S}(1-a_i)bigr), which reproduces the measured variance profile of f to within a few percent from its L fitted break-rates. This structure supports two predictors of a configuration's loss, each with L+1 parameters. The additive model is the optimal first-order predictor. By Parseval's identity its mean-squared error equals the variance of f left unexplained by per-layer effects, which we measure on full lattices, estimate out of sample at full-network scale, and report with every result as a certificate of how well any additive model can do. The coverage model itself is the second predictor. As allocators at matched memory, they attain the lowest KL divergence among the compared allocators on models from 30B to 355B parameters. Below four bits, the resulting allocations continue to solve code and reasoning tasks at budgets where allocations from gradient sensitivities no longer produce terminating generations.

As large language model inference shifts toward lower precision, post-training quantization (PTQ) becomes increasingly brittle, making quantization-aware training (QAT) essential for preserving model quality. However, QAT computes the loss and surrogate gradients using a lossy reconstruction of latent full-precision weights, while applying updates to the latent weights themselves. This mismatch can lead to suboptimal training trajectories and a higher loss floor. Second-order PTQ methods mitigate a similar gap by minimizing loss-aware reconstruction error, but doing it once for a frozen model can take hours; repeating this process throughout QAT as the weights evolve is impractical. We introduce QUASAR, a QAT method that continuously performs lightweight, loss-aware reconstruction in the training loop to lower the loss floor and improve the resulting low-bit model. At each training step, QUASAR uses the exponential moving average of squared gradients as online saliency estimates, searches over a small set of clipping ranges, and fits affine dequantizers via saliency-weighted least squares. Our analysis shows that the loss-aware reconstruction error is the only reconstruction-dependent term in the QAT convergence bound and controls the loss of the final quantized model, establishing QUASAR's objective as a principled optimization target. QUASAR modifies only the training procedure and supports standard deployment formats, including integer quantization and NVFP4, with no inference-time changes or overhead. Across Qwen3 and Llama-3.1, QUASAR achieves the lowest held-out KL divergence among competitive QAT methods at 2, 3, and 4 bits, reducing KL by at least 10% at 3 and 4 bits and by 29% at 2 bits. At 2 bits, it improves average accuracy across eight tasks by 3.5-4.3 percentage points over strong QAT and PTQ baselines.

Retrieving relevant documents from a corpus is typically based on the semantic similarity between the document content and query text. The inclusion of structural relationship between documents can benefit the retrieval mechanism by addressing semantic gaps. However, incorporating these relationships requires tractable mechanisms that balance structure with semantics and take advantage of the prevalent pre-train/fine-tune paradigm. We propose here a holistic approach to learning document representations by integrating intra-document content with inter-document relations. Our deep metric learning solution analyzes the complex neighborhood structure in the relationship network to efficiently sample similar/dissimilar document pairs and defines a novel quintuplet loss function that simultaneously encourages document pairs that are semantically relevant to be closer and structurally unrelated to be far apart in the representation space. Furthermore, the separation margins between the documents are varied flexibly to encode the heterogeneity in relationship strengths. The model is fully fine-tunable and natively supports query projection during inference. We demonstrate that it outperforms competing methods on multiple datasets for document retrieval tasks.

A common classification task situation is where one has a large amount of data available for training, but only a small portion is annotated with class labels. The goal of semi-supervised training, in this context, is to improve classification accuracy by leverage information not only from labeled data but also from a large amount of unlabeled data. Recent works have developed significant improvements by exploring the consistency constrain between differently augmented labeled and unlabeled data. Following this path, we propose a novel unsupervised objective that focuses on the less studied relationship between the high confidence unlabeled data that are similar to each other. The new proposed Pair Loss minimizes the statistical distance between high confidence pseudo labels with similarity above a certain threshold. Combining the Pair Loss with the techniques developed by the MixMatch family, our proposed SimPLE algorithm shows significant performance gains over previous algorithms on CIFAR-100 and Mini-ImageNet, and is on par with the state-of-the-art methods on CIFAR-10 and SVHN. Furthermore, SimPLE also outperforms the state-of-the-art methods in the transfer learning setting, where models are initialized by the weights pre-trained on ImageNet or DomainNet-Real. The code is available at github.com/zijian-hu/SimPLE.

Nearly all practical neural models for classification are trained using cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiments on multi-class classification problems showing that the squentropy loss outperforms both the pure cross entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can typically be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true "plug-and-play" replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.

Score- and flow-matching models often rely on preference-based reinforcement learning for two purposes: aligning with subjective preferences and, surprisingly, recovering properties such as visual realism and coherent object structure that matching-based training is intended to learn from the data itself. We argue that this reflects a structural mismatch. Matching losses measure ell_2 regression error on the velocity or score field under training-time marginals, a proxy poorly aligned with the visual and semantic properties that determine sample quality at inference. Given a reward aligned with these properties, RL sidesteps the mismatch by evaluating the model on its own samples and following the reward landscape directly. The challenge is to obtain such a reward without relying on human preferences, which are expensive and conflate data realism with annotator inclinations. We propose Discriminator-Guided RL (DRL). DRL trains a discriminator to separate data from base-model samples in a pretrained representation space and uses its logit as the reward in KL-regularized RL. The pretrained space restricts the discriminator to perceptually meaningful directions, and the logit estimates the log-likelihood ratio between data and model, which is the optimal reward for targeting the data distribution. Across SiT, JiT, REPA, and RAE, DRL reduces guidance-free FID (e.g., 9.38 to 2.62 on SiT) and semantic-space FD (e.g., 88.2 to 19.3 on DINOv3 for SiT), with consistent gains across all backbones, and improves human-preference rewards without training on them. It also yields a better Pareto frontier between preference reward and image fidelity under subsequent preference-based post-training, increasing alignment while reducing low-level artifacts such as oversaturation and excessive brightness.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

Emergent misalignment (EM) is a recently discovered phenomenon in LLMs where fine-tuning on a narrow misaligned task, such as writing insecure code, leads to broadly misaligned behaviour on unrelated prompts. Previous work has noted that the severity of EM is highly sensitive to training choices; however, we still lack a systematic characterisation of this sensitivity. We perform a sweep over several Qwen3 models, optimisers, datasets, and batch sizes, and find that the choice of optimiser has the largest effect, producing a 7x spread in misalignment rate. Surprisingly, model size has a negligible effect within the Qwen3 family. An additional sweep over 12 models from three families using Adam confirms that model scale (1B-235B) and family have negligible effects for that optimiser. Analysing the loss-alignment relationship on Qwen3-8B, we find that final log training loss is a strong predictor of alignment, and that stratifying by optimiser captures nearly all the residual variance. Training dynamics reveal that each optimiser follows a different trajectory through loss-alignment space, and that after significant training, the optimiser becomes more important than training loss as a predictor of alignment. Muon, the adaptive optimiser that preserves alignment the best, implicitly regularises for a more uniform distribution of singular values of the LoRA adapter. We evaluate this insight by training with an additional loss term that incentivises a flatter singular value spectrum, and find that this substantially recovers alignment for the more EM-prone adaptive optimisers (Adam and Lion), with negligible cost to training loss. These results identify optimiser choice as a key factor in EM severity, but show that spectral regularisation can substantially mitigate the effects of EM-prone optimisers.

When quantizing neural networks, assigning each floating-point weight to its nearest fixed-point value is the predominant approach. We find that, perhaps surprisingly, this is not the best we can do. In this paper, we propose AdaRound, a better weight-rounding mechanism for post-training quantization that adapts to the data and the task loss. AdaRound is fast, does not require fine-tuning of the network, and only uses a small amount of unlabelled data. We start by theoretically analyzing the rounding problem for a pre-trained neural network. By approximating the task loss with a Taylor series expansion, the rounding task is posed as a quadratic unconstrained binary optimization problem. We simplify this to a layer-wise local loss and propose to optimize this loss with a soft relaxation. AdaRound not only outperforms rounding-to-nearest by a significant margin but also establishes a new state-of-the-art for post-training quantization on several networks and tasks. Without fine-tuning, we can quantize the weights of Resnet18 and Resnet50 to 4 bits while staying within an accuracy loss of 1%.

PTQTP decomposes LLM weight matrices into two ternary (trit) planes with two free per-group scales. Tying the scales to a fixed ratio of three collapses the decomposition into a single uniform nine-level quantizer, a known balanced-ternary identity. To our knowledge, at the time of writing, this work is the first to impose that identity as a constraint inside PTQTP's solver. The two trit planes then fold losslessly into one 4-bit code plane that we make the persistent serving representation: disk bytes, expert-cache bytes, and kernel input are the same 4.0625-bits/weight blocks, consumed in one integer dot pass. For this conjunction (ratio-3 nine-level code, CPU-SIMD kernels, SSD expert streaming, identical persistent bytes) we likewise found no precedent. We apply this to the routed experts of DeepSeek-V4-Flash-0731, a 284B-A13B mixture-of-experts model, quantizing in one shot from the released MXFP4 expert weights and streaming experts from SSD on a 64 GB laptop. Against a 4.5-bit Q4_K baseline, measured one process per fixture with an expert-lossless anchor arm as reference control, the tied model matches the official serving API on 5/5 fixtures at step 0 (Q4_K: 4/5) and 12/14 captured continuation steps (11/14), scores 86 vs. 84 on a 100-item MMLU subset, decodes 6.7% faster in decode phase, and ships 9% smaller files: no detected fidelity difference at these small evaluation sizes, and every fixture-level difference between the arms traces to a single measured near-tie cell. The tied fit nevertheless shows higher weight-reconstruction error and worse perplexity, a measured dissociation between proxy metrics and reference fidelity. A cumulative trunk-ternarization ladder and bitwise-pinned aarch64/x86-64 kernels complete the report. All code, formats, and evaluation artifacts are open source in the fucina inference stack.

Measuring the similarity of the internal representations of deep neural networks is an important and challenging problem. Model stitching has been proposed as a possible approach, where two half-networks are connected by mapping the output of the first half-network to the input of the second one. The representations are considered functionally similar if the resulting stitched network achieves good task-specific performance. The mapping is normally created by training an affine stitching layer on the task at hand while freezing the two half-networks, a method called task loss matching. Here, we argue that task loss matching may be very misleading as a similarity index. For example, it can indicate very high similarity between very distant layers, whose representations are known to have different functional properties. Moreover, it can indicate very distant layers to be more similar than architecturally corresponding layers. Even more surprisingly, when comparing layers within the same network, task loss matching often indicates that some layers are more similar to a layer than itself. We argue that the main reason behind these problems is that task loss matching tends to create out-of-distribution representations to improve task-specific performance. We demonstrate that direct matching (when the mapping minimizes the distance between the stitched representations) does not suffer from these problems. We compare task loss matching, direct matching, and well-known similarity indices such as CCA and CKA. We conclude that direct matching strikes a good balance between the structural and functional requirements for a good similarity index.

We consider whether off-policy experience from a smaller, weaker model can elicit capability in a stronger learner that on-policy RL fine-tuning (e.g., GRPO) does not reach. We find that injecting mathematically wrong drafts from a smaller but more domain-trained model -- mismatched to the current problem -- into a stronger learner's GRPO context consistently outperforms standard on-policy GRPO on held-out MATH-500 and out-of-distribution AIME 2025/2026. Concretely, we use Mathstral-7B as the learner, Qwen2.5-Math-1.5B as the draft model, 8.8K Level 3--5 MATH problems (with MATH-500 held out), and train with Dr. GRPO. Mismatch is an active ingredient: shuffling drafts to mismatched problems while holding everything else constant yields +1.62pp on MATH-500 (greedy pass@1) over the matched-wrong variant (n=10 seeds, p=0.0015, Welch's t). In fact, the mismatched-wrong variant leads all other variants we tested on MATH-500 across both greedy pass@1 and sampling pass@k. On out-of-distribution AIME 2025 and 2026, the mismatched-wrong variant uniquely lifts pass@k above both Mathstral-7B (in its native [INST] format) and the Qwen2.5-Math-1.5B draft model at every sample budget from k=1 to k=1024 across 2 seeds (+14.2pp on 2025 and +9.0pp on 2026 at pass@1024 over Mathstral-7B), and at pass@1024 also leads no-draft, matched-wrong, and mismatched-correct variants on both years. All variants use the same prompt with no draft injection at test time. The recipe -- trained on a single GPU with no SFT, no reward models, no synthesized data, and no produce-critique-revise inner loop -- reaches 71.98% MATH-500 on Mathstral-7B-v0.1, the highest published result on this model to our knowledge, surpassing the heavier WizardMath pipeline at 70.9% on full MATH (SFT + PPO with process/instruction reward models).

Most existing works focus on improving robustness against adversarial attacks bounded by a single l_p norm using adversarial training (AT). However, these AT models' multiple-norm robustness (union accuracy) is still low, which is crucial since in the real-world an adversary is not necessarily bounded by a single norm. The tradeoffs among robustness against multiple l_p perturbations and accuracy/robustness make obtaining good union and clean accuracy challenging. We design a logit pairing loss to improve the union accuracy by analyzing the tradeoffs from the lens of distribution shifts. We connect natural training (NT) with AT via gradient projection, to incorporate useful information from NT into AT, where we empirically and theoretically show it moderates the accuracy/robustness tradeoff. We propose a novel training framework RAMP, to boost the robustness against multiple l_p perturbations. RAMP can be easily adapted for robust fine-tuning and full AT. For robust fine-tuning, RAMP obtains a union accuracy up to 53.3% on CIFAR-10, and 29.1% on ImageNet. For training from scratch, RAMP achieves a union accuracy of 44.6% and good clean accuracy of 81.2% on ResNet-18 against AutoAttack on CIFAR-10. Beyond multi-norm robustness RAMP-trained models achieve superior universal robustness, effectively generalizing against a range of unseen adversaries and natural corruptions.

Neural scaling laws approximate a language model's loss as a power-law function of parameter count N and token count D. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed tokens-per-parameter (TPP) ratio k and set D = kN. We show that this collinear design, combined with the empirically common near-equality of the exponents governing N and D, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the N and D-exponents. The scale coefficients become practically unidentifiable, with confidence intervals inflating by an order of magnitude or more, yielding a ``sloppy'' model whose extrapolations degrade sharply off the training ray. We prove this for four scaling-law formalisms and derive a closed-form TPP-diversity threshold that is necessary and sufficient for well-conditioned estimation. Empirically, non-collinear designs outperform collinear ones on held-out splits with a 97.3\% win rate across four laws, five corpora, multiple floating point precision modes. We further show the degeneracy is rooted in Jacobian geometry and is not an artifact of the loss function: any smooth estimation objective whose curvature involves the Jacobian inherits the same ill-conditioning.

Cross-tokenizer knowledge distillation allows a student model to learn from teachers with incompatible vocabularies. Prior work operates on hidden states or logits; the latter is preferred as a drop-in replacement requiring no auxiliary components. Logit-based methods either use only the correct-token probability, missing the full 'dark knowledge' in the teacher's distribution, or operate on the full output distribution, relying on strict token partitioning and/or unprincipled heuristic ranking. We identify two key shortcomings of full-distribution, logit-based methods: (i) an uncommon-token failure, where critical tokens fall into the unmatched subset (e.g., Llama's 1100 multi-digit numerals under digit-splitting Qwen supervision) and are suppressed during training, reducing GSM8k from 12.89 to 2.56 compared to same-tokenizer KD from a weaker teacher; and (ii) over-conservative matching, where strict 1-to-1 matching excludes near-equivalent tokens across surface forms. These failures require distinct remedies: eliminating the partition when critical tokens are misaligned, and refining it when alignment is reliable. We propose X-Token, an approach with two complementary loss formulations targeting these issues. P-KL removes partitioning and aligns the student's distribution with the teacher's via a sparse projection matrix W (initialized from tokenizer-level string rules) to address the uncommon-token failure. H-KL retains the hybrid form while relaxing matching to align each student token with its top-ranked teacher mapping under W. Both objectives share W and extend naturally to multiple teachers. Empirically, on Llama-3.2-1B, X-Token outperforms the current state of the art GOLD by +3.82 average points with a Qwen3-4B teacher and by +0.5 with a Phi-4-Mini teacher. Further, a two-teacher setup (Phi-4-mini + Llama-3B) improves over single-teacher distillation by +1.3 points.

While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving reasoning over quantities, especially arithmetics. This has particular relevance in scientific datasets where combinations of text and numerical data are abundant. One fundamental limitation is the nature of the CE loss, which assumes a nominal (categorical) scale and thus cannot convey proximity between generated number tokens. As a remedy, we here present two versions of a number token loss. The first is based on an L_p loss between the ground truth token value and the weighted sum of the predicted class probabilities. The second loss minimizes the Wasserstein-1 distance between the distribution of the predicted output probabilities and the ground truth distribution. These regression-like losses can easily be added to any language model and extend the CE objective during training. We compare the proposed schemes on a mathematics dataset against existing tokenization, encoding, and decoding schemes for improving number representation in language models. Our results reveal a significant improvement in numerical accuracy when equipping a standard T5 model with the proposed loss schemes.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

The goal of face recognition (FR) can be viewed as a pair similarity optimization problem, maximizing a similarity set S^p over positive pairs, while minimizing similarity set S^n over negative pairs. Ideally, it is expected that FR models form a well-discriminative feature space (WDFS) that satisfies mathcal{S^p} > mathcal{S^n}. With regard to WDFS, the existing deep feature learning paradigms (i.e., metric and classification losses) can be expressed as a unified perspective on different pair generation (PG) strategies. Unfortunately, in the metric loss (ML), it is infeasible to generate negative pairs taking all classes into account in each iteration because of the limited mini-batch size. In contrast, in classification loss (CL), it is difficult to generate extremely hard negative pairs owing to the convergence of the class weight vectors to their center. This leads to a mismatch between the two similarity distributions of the sampled pairs and all negative pairs. Thus, this paper proposes a unified negative pair generation (UNPG) by combining two PG strategies (i.e., MLPG and CLPG) from a unified perspective to alleviate the mismatch. UNPG introduces useful information about negative pairs using MLPG to overcome the CLPG deficiency. Moreover, it includes filtering the similarities of noisy negative pairs to guarantee reliable convergence and improved performance. Exhaustive experiments show the superiority of UNPG by achieving state-of-the-art performance across recent loss functions on public benchmark datasets. Our code and pretrained models are publicly available.

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates x) of training and testing samples p_tr(x) and p_te(x) are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio p_te(x)/p_tr(x) to weight training samples (reweighted methods) or using the ratio p_tr(x)/p_te(x) to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.

A family of loss functions built on pair-based computation have been proposed in the literature which provide a myriad of solutions for deep metric learning. In this paper, we provide a general weighting framework for understanding recent pair-based loss functions. Our contributions are three-fold: (1) we establish a General Pair Weighting (GPW) framework, which casts the sampling problem of deep metric learning into a unified view of pair weighting through gradient analysis, providing a powerful tool for understanding recent pair-based loss functions; (2) we show that with GPW, various existing pair-based methods can be compared and discussed comprehensively, with clear differences and key limitations identified; (3) we propose a new loss called multi-similarity loss (MS loss) under the GPW, which is implemented in two iterative steps (i.e., mining and weighting). This allows it to fully consider three similarities for pair weighting, providing a more principled approach for collecting and weighting informative pairs. Finally, the proposed MS loss obtains new state-of-the-art performance on four image retrieval benchmarks, where it outperforms the most recent approaches, such as ABEKim_2018_ECCV and HTL by a large margin: 60.6% to 65.7% on CUB200, and 80.9% to 88.0% on In-Shop Clothes Retrieval dataset at Recall@1. Code is available at https://github.com/MalongTech/research-ms-loss.

This paper provides a pair similarity optimization viewpoint on deep feature learning, aiming to maximize the within-class similarity s_p and minimize the between-class similarity s_n. We find a majority of loss functions, including the triplet loss and the softmax plus cross-entropy loss, embed s_n and s_p into similarity pairs and seek to reduce (s_n-s_p). Such an optimization manner is inflexible, because the penalty strength on every single similarity score is restricted to be equal. Our intuition is that if a similarity score deviates far from the optimum, it should be emphasized. To this end, we simply re-weight each similarity to highlight the less-optimized similarity scores. It results in a Circle loss, which is named due to its circular decision boundary. The Circle loss has a unified formula for two elemental deep feature learning approaches, i.e. learning with class-level labels and pair-wise labels. Analytically, we show that the Circle loss offers a more flexible optimization approach towards a more definite convergence target, compared with the loss functions optimizing (s_n-s_p). Experimentally, we demonstrate the superiority of the Circle loss on a variety of deep feature learning tasks. On face recognition, person re-identification, as well as several fine-grained image retrieval datasets, the achieved performance is on par with the state of the art.

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap, an objective that is insufficient for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the correct topology of the segmented structures. However, so far, none of the existing approaches achieve a spatially correct matching between the topological features of ground truth and prediction. In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching. We show how induced matchings guarantee the spatially correct matching between barcodes in a segmentation setting. Furthermore, we propose an efficient algorithm to compute the Betti matching of images. We show that the Betti matching error is an interpretable metric to evaluate the topological correctness of segmentations, which is more sensitive than the well-established Betti number error. Moreover, the differentiability of the Betti matching loss enables its use as a loss function. It improves the topological performance of segmentation networks across six diverse datasets while preserving the volumetric performance. Our code is available in https://github.com/nstucki/Betti-matching.

Post-training quantization (PTQ) enables efficient deployment of large language models by mapping pretrained weights to low-bit formats without retraining, typically using a small calibration set to minimize a layer-wise calibration objective. However, this sequential procedure induces a mismatch: errors from earlier quantized layers alter the inputs received by later layers, causing the activations to deviate from those of the full-precision model. Recent approaches introduce mismatch-aware calibration objectives to compensate for this effect, but leave open how much of the observed mismatch should shift each layer's calibration target. Fully applying this correction can overfit limited calibration data, while scaling the mismatch correction with a fixed coefficient ignores varying reliability of mismatch estimates across layers. To address these limitations, we propose CoreQ, a learning-free PTQ framework that applies a closed-form coefficient for mismatch correction derived from a geometric decomposition of the mismatch. The resulting coefficient adapts the correction across layers, reduces overfitting to finite calibration data, and requires no hyperparameter tuning. Given the corrected target, CoreQ minimizes the induced triangular least-squares objective with an efficient greedy successive-rounding solver and a bounded beam-search extension, K-CoreQ, that trades modest additional compute for improved performance. Across multiple LLM families, scales, bit-widths, and quantization settings, CoreQ improves perplexity and downstream accuracy over strong PTQ baselines.

Quantization-aware training (QAT) is a leading technique for improving the accuracy of quantized neural networks. Previous work has shown that decomposing training into a full-precision (FP) phase followed by a QAT phase yields superior accuracy compared to QAT alone. However, the optimal allocation of compute between the FP and QAT phases remains unclear. We conduct extensive experiments with various compute budgets, QAT bit widths, and model sizes from 86.0M to 2.2B to investigate how different QAT durations impact final performance. We demonstrate that, contrary to previous findings, the loss-optimal ratio of QAT to FP training increases with the total amount of compute. Moreover, the optimal fraction can be accurately predicted for a wide range of model sizes and quantization widths using the tokens-per-parameter-byte statistic. From experimental data, we derive a loss scaling law that predicts both optimal QAT ratios and final model performance across different QAT/FP compute allocation strategies and QAT bit widths. We use the scaling law to make further predictions, which we verify experimentally, including which QAT bit width is optimal under a given memory constraint and how QAT accuracy with different bit widths compares to full-precision model accuracy. Additionally, we propose a novel cooldown and QAT fusion approach that performs learning rate decay jointly with quantization-aware training, eliminating redundant full-precision model updates and achieving significant compute savings. These findings provide practical insights into efficient QAT planning and enable the training of higher-quality quantized models with the same compute budget.

In this report, we present our champion solution for EPIC-KITCHENS-100 Multi-Instance Retrieval Challenge in CVPR 2024. Essentially, this challenge differs from traditional visual-text retrieval tasks by providing a correlation matrix that acts as a set of soft labels for video-text clip combinations. However, existing loss functions have not fully exploited this information. Motivated by this, we propose a novel loss function, Symmetric Multi-Similarity Loss, which offers a more precise learning objective. Together with tricks and ensemble learning, the model achieves 63.76% average mAP and 74.25% average nDCG on the public leaderboard, demonstrating the effectiveness of our approach. Our code will be released at: https://github.com/xqwang14/SMS-Loss/tree/main

Few-shot learning is a challenging area of research that aims to learn new concepts with only a few labeled samples of data. Recent works based on metric-learning approaches leverage the meta-learning approach, which is encompassed by episodic tasks that make use a support (training) and query set (test) with the objective of learning a similarity comparison metric between those sets. Due to the lack of data, the learning process of the embedding network becomes an important part of the few-shot task. Previous works have addressed this problem using metric learning approaches, but the properties of the underlying latent space and the separability of the difference classes on it was not entirely enforced. In this work, we propose two different loss functions which consider the importance of the embedding vectors by looking at the intra-class and inter-class distance between the few data. The first loss function is the Proto-Triplet Loss, which is based on the original triplet loss with the modifications needed to better work on few-shot scenarios. The second loss function, which we dub ICNN loss is based on an inter and intra class nearest neighbors score, which help us to assess the quality of embeddings obtained from the trained network. Our results, obtained from a extensive experimental setup show a significant improvement in accuracy in the miniImagenNet benchmark compared to other metric-based few-shot learning methods by a margin of 2%, demonstrating the capability of these loss functions to allow the network to generalize better to previously unseen classes. In our experiments, we demonstrate competitive generalization capabilities to other domains, such as the Caltech CUB, Dogs and Cars datasets compared with the state of the art.

Post-training quantization (PTQ) has emerged as a widely adopted technique for compressing and accelerating Large Language Models (LLMs). The major challenge in LLM quantization is that uneven and heavy-tailed data distributions can expand the quantization range, thereby reducing bit precision for most values. Recent methods attempt to eliminate outliers and balance inter-channel differences by employing linear transformations; however, they remain heuristic and are often overlook optimizing the data distribution across the entire quantization space.In this paper, we introduce Quantization Space Utilization Rate (QSUR), a novel metric that effectively assesses the quantizability of transformed data by measuring the space utilization of the data in the quantization space. We complement QSUR with mathematical derivations that examine the effects and limitations of various transformations, guiding our development of Orthogonal and Scaling Transformation-based Quantization (OSTQuant). OSQuant employs a learnable equivalent transformation, consisting of an orthogonal transformation and a scaling transformation, to optimize the distributions of weights and activations across the entire quantization space. Futhermore, we propose the KL-Top loss function, designed to mitigate noise during optimization while retaining richer semantic information within the limited calibration data imposed by PTQ. OSTQuant outperforms existing work on various LLMs and benchmarks. In the W4-only setting, it retains 99.5\% of the floating-point accuracy. In the more challenging W4A4KV4 configuration, OSTQuant reduces the performance gap by 32\% on the LLaMA-3-8B model compared to state-of-the-art methods. https://github.com/BrotherHappy/OSTQuant{https://github.com/BrotherHappy/OSTQuant}.

Quantizing the weights of a neural network has two steps: (1) Finding a good low bit-complexity representation for weights (which we call the quantization grid) and (2) Rounding the original weights to values in the quantization grid. In this paper, we study the problem of rounding optimally given any quantization grid. The simplest and most commonly used way to round is Round-to-Nearest (RTN). By rounding in a data-dependent way instead, one can improve the quality of the quantized model significantly. We study the rounding problem from the lens of discrepancy theory, which studies how well we can round a continuous solution to a discrete solution without affecting solution quality too much. We prove that given m=poly(1/ε) samples from the data distribution, we can round all but O(m) model weights such that the expected approximation error of the quantized model on the true data distribution is le ε as long as the space of gradients of the original model is approximately low rank (which we empirically validate). Our proof, which is algorithmic, inspired a simple and practical rounding algorithm called DiscQuant. In our experiments, we demonstrate that DiscQuant significantly improves over the prior state-of-the-art rounding method called GPTQ and the baseline RTN over a range of benchmarks on Phi3mini-3.8B and Llama3.1-8B. For example, rounding Phi3mini-3.8B to a fixed quantization grid with 3.25 bits per parameter using DiscQuant gets 64\% accuracy on the GSM8k dataset, whereas GPTQ achieves 54\% and RTN achieves 31\% (the original model achieves 84\%). We make our code available at https://github.com/jerry-chee/DiscQuant.

We present ITQ3_S (Interleaved Ternary Quantization -- Specialized), a novel 3-bit weight quantization format for LLMs integrating TurboQuant (TQ), a rotation-domain strategy based on the Fast Walsh-Hadamard Transform (FWHT). Conventional 3-bit methods suffer precision loss from heavy-tailed weight distributions and inter-channel outliers. ITQ3_S pre-rotates the weight space via FWHT before quantization, spreading outlier energy across the vector and inducing a near-Gaussian distribution amenable to uniform ternary coding. We derive a rigorous dequantization procedure fusing a 256-point Inverse FWHT into the CUDA shared-memory loading stage, ensuring reconstruction error is bounded exclusively by the ternary quantization grid with no additional error from the transform inversion. For any weight vector w in R^{256}, the reconstruction satisfies |mathbf{w} - w|_2 leq ε_q, strictly smaller than uniform 3-bit baselines that do not exploit rotation-induced distribution normalization. TurboQuant lacks a native CUDA kernel, precluding direct deployment; naively composing TQ with existing weight quantizers introduces domain mismatch errors that accumulate across layers, degrading quality below standard 3-bit baselines. ITQ3_S resolves this by co-designing the FWHT rotation and quantization kernel as a unified pipeline grounded in the IQ3_S weight format, with the inverse transform fused into the CUDA MMQ kernel. Empirically, on the NVIDIA RTX 5090 (Blackwell), ITQ3_S achieves perplexity competitive with FP16 while delivering throughput exceeding 1.5x that of 4-bit alternatives via optimized DP4A and Tensor Core scheduling. Our results establish ITQ3_S as a practical, mathematically grounded solution for high-fidelity LLM deployment on consumer hardware.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

Quantizing neural networks is one of the most effective methods for achieving efficient inference on mobile and embedded devices. In particular, mixed precision quantized (MPQ) networks, whose layers can be quantized to different bitwidths, achieve better task performance for the same resource constraint compared to networks with homogeneous bitwidths. However, finding the optimal bitwidth allocation is a challenging problem as the search space grows exponentially with the number of layers in the network. In this paper, we propose QBitOpt, a novel algorithm for updating bitwidths during quantization-aware training (QAT). We formulate the bitwidth allocation problem as a constraint optimization problem. By combining fast-to-compute sensitivities with efficient solvers during QAT, QBitOpt can produce mixed-precision networks with high task performance guaranteed to satisfy strict resource constraints. This contrasts with existing mixed-precision methods that learn bitwidths using gradients and cannot provide such guarantees. We evaluate QBitOpt on ImageNet and confirm that we outperform existing fixed and mixed-precision methods under average bitwidth constraints commonly found in the literature.

Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives and are gaining more attention in machine learning applications. Imposing such quasimetric structures in model representations has been shown to improve many tasks, including reinforcement learning (RL) and causal relation learning. In this work, we present four desirable properties in such quasimetric models, and show how prior works fail at them. We propose Interval Quasimetric Embedding (IQE), which is designed to satisfy all four criteria. On three quasimetric learning experiments, IQEs show strong approximation and generalization abilities, leading to better performance and improved efficiency over prior methods. Project Page: https://www.tongzhouwang.info/interval_quasimetric_embedding Quasimetric Learning Code Package: https://www.github.com/quasimetric-learning/torch-quasimetric

Deep metric learning objectives (e.g., triplet loss) require storing and comparing high-dimensional embeddings, making the per-batch loss buffer scale as O(Scdot D), where S is the number of samples in a batch and D is the feature dimension, thus limiting training on memory-constrained hardware. We propose Shadow Loss, a proxy-free, parameter-free objective that measures similarity via scalar projections onto the anchor direction, reducing the loss-specific buffer from O(Scdot D) to O(S) while preserving the triplet structure. We analyze gradients, provide a Lipschitz continuity bound, and show that Shadow Loss penalizes trivial collapse for stable optimization. Across fine-grained retrieval (CUB-200, CARS196), large-scale product retrieval (Stanford Online Products, In-Shop Clothes), and standard/medical benchmarks (CIFAR-10/100, Tiny-ImageNet, HAM-10K, ODIR-5K), Shadow Loss consistently outperforms recent objectives (Triplet, Soft-Margin Triplet, Angular Triplet, SoftTriple, Multi-Similarity). It also converges in approx 1.5-2times fewer epochs under identical backbones and mining. Furthermore, it improves representation separability as measured by higher silhouette scores. The design is architecture-agnostic and vectorized for efficient implementation. By decoupling discriminative power from embedding dimensionality and reusing batch dot-products, Shadow Loss enables memory-linear training and faster convergence, making deep metric learning practical on both edge and large-scale systems.

The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings

Reinforcement learning with verifiable rewards has rapidly advanced reasoning in vision--language models. However, for chest X-ray report generation, the standard rewards (i.e. exact-match accuracy and step-level processes) are incompatible because the reports consist of unordered and orthogonal findings, rather than a causal reasoning chain. We address this gap with a set-based view: each report is split into sentences and embedded by a frozen sentence transformer, yielding unordered embedding sets. We propose the use of set-to-set distances between generated and reference embeddings as continuous, permutation-invariant rewards. Across two datasets and three vision--language models (Qwen3-VL-2B/4B, Gemma3-4B), post-training with set-to-set distance based rewards via GRPO consistently outperforms supervised fine-tuning and exact-match GRPO on all headline metrics (BERTScore, RadGraph F1 and CheXbert F1 by average \%6.80, \%7.82 and \%4.45 relative improvements respectively). The same set distances also enable test-time best-of-N selection: scoring candidates by their distance to training-report embeddings outperforms random selection on our trained models as well as three closed-source LLMs (Mistral-Small, Gemini-2.5 Flash-Lite, GPT-4o-mini) with on average \%16.4 relative improvement on BERTScore. Used as a streaming signal, they support a more efficient form of test-time scaling: pruning low-scoring candidates mid-generation reduces generated tokens by over 50\% while preserving the Findings quality of full best-of-N selection. Together these results establish set-distance rewards as a unified signal for both post-training and test-time scaling in chest X-ray report generation. Our code is publicly https://anonymous.4open.science/r/Set-Distance-Rewards-CXR-BFDA{available}.

The current best bounds on the matrix multiplication exponent ω are obtained through a refinement of the laser method called combination loss analysis (Duan et al., 2022; Williams et al., 2024; Alman et al., 2025). In this note, we address the optimization problem at the core of this approach and propose several improvements. First, we reformulate the optimization problem allowing us to solve it in a larger setting than was previously possible. Second, we leverage recent advances in machine learning to design a new optimization algorithm for this problem. Finally, we refine the resulting optimization algorithm with AlphaEvolve. Our combined approach yields an upper bound of ω < 2.371177, improving the previous best bound of 2.371339.

We simplify space binding by focusing on two core components, a single encoder per modality and high-quality data; enabling training state-of-the-art models on a single GPU in a few hours as opposed to multiple days. We present EBind, an Easy, data-centric, and parameter-efficient method to Bind the embedding spaces of multiple contrastive models. We demonstrate that a simple 1.8B-parameter image-text-video-audio-3D model can outperform models 4 to 17x the size. The key to achieving this is a carefully curated dataset of three complementary data sources: i) 6.7M fully-automated multimodal quintuples sourced via SOTA retrieval models, ii) 1M diverse, semi-automated triples annotated by humans as negative, partial, or positive matches, and iii) 3.4M pre-existing captioned data items. We use 13 different evaluations to demonstrate the value of each data source. Due to limitations with existing benchmarks, we further introduce the first high-quality, consensus-annotated zero-shot classification benchmark between audio and PCs. In contrast to related work, we will open-source our code, model weights, and datasets.

We measure how much one extra recurrence is worth to a looped (depth-recurrent) language model, in equivalent unique parameters. From an iso-depth sweep of 116 pretraining runs across recurrence counts r in {1, 2, 4, 8} spanning {sim}50times in training compute, we fit a joint scaling law L = E + A,(N_once + r^φ N_rec)^{-α} + B,D^{-β} and recover a new recurrence-equivalence exponent φ= 0.46. Intuitively, φ tells us whether looping a block r times is equivalent in validation loss to r unique blocks of a non-looped model (full equivalence, φ{=}1) or to a single block run repeatedly with no capacity gain (φ{=}0). Our φ= 0.46 sits in between, so each additional recurrence predictably increases validation loss at matched training compute. For example, at r{=}4 a 410M looped model performs on par with a 580M non-looped model, but incurs the training cost of a 1B non-looped one. We demonstrate the utility of φ as a measurement tool on two probes. Truncated backpropagation lowers φ to 0.38, indicating that the loop mechanism is poorly trained under truncation, even though validation loss decreases. Conversely, hyperconnections raise φ to 0.65, a genuine capacity gain. Our method applies to any looped LM and separates true loop improvements from token-budget gains.

Post-training paradigms for Large Language Models (LLMs), primarily Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), face a fundamental dilemma: SFT provides stability (low variance) but suffers from high fitting bias, while RL enables exploration (low bias) but grapples with high gradient variance. Existing unified optimization strategies often employ naive loss weighting, overlooking the statistical conflict between these distinct gradient signals. In this paper, we provide a rigorous theoretical analysis of this bias-variance trade-off and propose DYPO (Dynamic Policy Optimization), a unified framework designed to structurally mitigate this conflict. DYPO integrates three core components: (1) a Group Alignment Loss (GAL) that leverages intrinsic group dynamics to significantly reduce RL gradient variance; (2) a Multi-Teacher Distillation mechanism that corrects SFT fitting bias via diverse reasoning paths; and (3) a Dynamic Exploitation-Exploration Gating mechanism that adaptively arbitrates between stable SFT and exploratory RL based on reward feedback. Theoretical analysis confirms that DYPO linearly reduces fitting bias and minimizes overall variance. Extensive experiments demonstrate that DYPO significantly outperforms traditional sequential pipelines, achieving an average improvement of 4.8\% on complex reasoning benchmarks and 13.3\% on out-of-distribution tasks. Our code is publicly available at https://github.com/Tocci-Zhu/DYPO.

Timestep sampling p(t) is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from 3.85 (Uniform) to 3.22 while reaching peak performance at 100k rather than 150k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

Most competitive 4-bit LLM research pipelines now open the same way: apply a linear, function-preserving transform (rotation, scaling, permutation, non-orthogonal affine) so the outlier mass sits more favorably against the group scales, and only then round. Yet we are aware of no survey dedicated to this transform stage, and its literature is quietly re-deriving an older theory. We identify and formalize the principle that organizes it, the Great Inversion: allocation-flexible coding rewards energy concentration, whereas the grouped shared-scale quantization a deployed matrix instruction performs rewards within-group flattening. Classical transform coding (1963: decorrelate, allocate bits, quantize) spends different bits per coordinate at a fixed total rate; for a Gaussian source at high rate the Karhunen-Loeve transform's concentration minimizes distortion. A deployed operand tile instead carries one absolute-maximum scale per group and equal bits everywhere, with no allocation; on a uniform grid that objective rewards flattening, approached by Hadamard incoherence. We prove that opposition under within-group majorization: the prescriptions point in opposite directions, each backed by a proof against its own objective, and for a generic spectrum no optimality guarantee transfers. A second axis is the number format: the non-uniform FP4 grid makes flattening buy less, MXFP4's power-of-two block scale still rewards a rotation confined to that block, and NVFP4's mantissa-carrying scale largely removes that pull, so the target pole depends jointly on allocation regime and format. We survey 200 works to a June 2026 cutoff; classify 43 transform methods by structure, data-awareness, searched-versus-constructed, and runtime cost; record, where reported, how they compose with GPTQ rounding; distill a first-choice guide by deployment regime; and close with the open problems it exposes.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6%, and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7%. This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which includes the aforementioned example. Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples (many of which yield approximately 30% or greater improvement on MATH500 when employed as a single training example). In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-domain generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by adding entropy loss with an appropriate coefficient) in 1-shot RLVR training. As a bonus, we observe that applying entropy loss alone, without any outcome reward, significantly enhances Qwen2.5-Math-1.5B's performance on MATH500 by 27.4%. These findings can inspire future work on RLVR data efficiency and encourage a re-examination of both recent progress and the underlying mechanisms in RLVR. Our code, model, and data are open source at https://github.com/ypwang61/One-Shot-RLVR

We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw i.i.d. samples. We define a loss to be black-box proper if the generative distribution that minimizes expected loss is equal to the target distribution. Using techniques from statistical estimation theory, we give a general construction and characterization of black-box proper losses: they must take a polynomial form, and the number of draws from the model and target distribution must exceed the degree of the polynomial. The characterization rules out a loss whose expectation is the cross-entropy between the target distribution and the model. By extending the construction to arbitrary sampling schemes such as Poisson sampling, however, we show that one can construct such a loss.

We compare two strategies for compressing the KV cache in transformer inference: rank reduction (discard dimensions) and quantization (keep all dimensions, reduce precision). At matched storage budgets across five models (124M-14B, MHA and GQA), we find that quantization consistently outperforms rank reduction by 4-364 PPL depending on model and compression level. The gap persists even when rank reduction is combined with quantization in hybrid baselines, and it grows with GQA aggressiveness. On LAMBADA, INT4 matches FP16 accuracy (+0.23 PPL on Mistral 7B, +0.58 on GPT-2) while rank-32 at identical storage collapses to 0.4%. We trace this gap to a structural asymmetry: under softmax attention routing, removing a dimension can flip which token is attended (a discrete failure), while quantization noise is bounded and typically preserves score ordering. We formalize this via a perturbation result showing projection damage exceeds quantization damage by 3 x 2^(2b) per direction under the softmax Fisher metric. A basis ablation confirms the finding is basis-independent (spread <0.4 PPL), establishing that the advantage comes from preserving dimensions, not from a better coordinate system. Joint K+V INT4 quantization achieves 75% total KV reduction at only +0.18 PPL on Mistral 7B.

Post-training quantization (PTQ) reduces the memory footprint of LLMs by quantizing their weights to low-precision. In this work, we introduce QuIP#, a weight-only PTQ method that achieves state-of-the-art results in extreme compression regimes (le 4 bits per weight) using three novel techniques. First, QuIP# improves the incoherence processing from QuIP by using the randomized Hadamard transform, which is faster and has better theoretical properties. Second, QuIP# uses vector quantization techniques to take advantage of the ball-shaped sub-Gaussian distribution that incoherent weights possess: specifically, we introduce a set of hardware-efficient codebooks based on the highly symmetric E_8 lattice, which achieves the optimal 8-dimension unit ball packing. Third, QuIP# uses fine-tuning to improve fidelity to the original model. Our experiments show that QuIP# outperforms existing PTQ methods, enables new behaviors in PTQ scaling, and supports fast inference.

We propose a simple pairwise sigmoid loss for image-text pre-training. Unlike standard contrastive learning with softmax normalization, the sigmoid loss operates solely on image-text pairs and does not require a global view of the pairwise similarities for normalization. The sigmoid loss simultaneously allows further scaling up the batch size, while also performing better at smaller batch sizes. With only four TPUv4 chips, we can train a Base CLIP model at 4k batch size and a Large LiT model at 20k batch size, the latter achieves 84.5% ImageNet zero-shot accuracy in two days. This disentanglement of the batch size from the loss further allows us to study the impact of examples vs pairs and negative to positive ratio. Finally, we push the batch size to the extreme, up to one million, and find that the benefits of growing batch size quickly diminish, with a more reasonable batch size of 32k being sufficient. We hope our research motivates further explorations in improving the quality and efficiency of language-image pre-training.

In this work, we revisit Transformer optimization through the lens of second-order geometry and establish a direct connection between architectural design, activation scale, the Hessian matrix, and the maximum tolerable learning rate. We introduce a simple normalization strategy, termed SimpleNorm, which stabilizes intermediate activation scales by construction. Then, by analyzing the Hessian of the loss with respect to network activations, we theoretically show that SimpleNorm significantly reduces the spectral norm of the Hessian, thereby permitting larger stable learning rates. We validate our theoretical findings through extensive experiments on large GPT models at parameter scales 1B, 1.4B, 7B and 8B. Empirically, SimpleGPT, our SimpleNorm-based network, tolerates learning rates 3times-10times larger than standard convention, consistently demonstrates strong optimization stability, and achieves substantially better performance than well-established baselines. Specifically, when training 7B-scale models for 60K steps, SimpleGPT achieves a training loss that is 0.08 lower than that of LLaMA2 with QKNorm, reducing the loss from 2.290 to 2.208. Our source code will be released at https://github.com/Ocram7/SimpleGPT.

Weight quantization has become a standard tool for efficient LLM deployment, especially for local inference, where models are now routinely served at 2-3 bits per parameter. The state of the art is currently split into two sets of methods: simple scalar quantization techniques, such as GPTQ or AWQ, which are widely deployed but plateau in accuracy at 3-4 bits per parameter (bpp), and "second-generation" vector- or trellis-quantized methods, such as QTIP, GPTVQ and AQLM, which push the accuracy frontier at low bit-widths but are notoriously hard to implement and to scale, and have gained relatively less traction. In this paper, we ask whether this gap is fundamental, or whether a carefully optimized scalar quantizer can recover most of it. We answer in the affirmative, by introducing GSQ (Gumbel-Softmax Quantization), a post-training scalar quantization method which jointly learns the per-coordinate grid assignments and the per-group scales using a Gumbel-Softmax relaxation of the discrete grid. GSQ matches the cardinality of the relaxation to the small number of levels available in the target bit-width regime (e.g., 3-8 levels for ternary and 3 bpp, respectively), making the relaxation tight and the optimization tractable. Practically, on the standard Llama-3.1-8B/70B-Instruct models, GSQ closes most of the gap between scalar quantization and the QTIP frontier at 2 and 3 bits, while using a symmetric scalar grid with group-wise quantization, and thus fully compatible with existing scalar inference kernels. We further show that GSQ scales to trillion-scale Mixture-of-Experts models such as Kimi-K2.5, where vector-quantized methods are difficult to apply.

In multi-task learning (MTL), gradient balancing has recently attracted more research interest than loss balancing since it often leads to better performance. However, loss balancing is much more efficient than gradient balancing, and thus it is still worth further exploration in MTL. Note that prior studies typically ignore that there exist varying improvable gaps across multiple tasks, where the improvable gap per task is defined as the distance between the current training progress and desired final training progress. Therefore, after loss balancing, the performance imbalance still arises in many cases. In this paper, following the loss balancing framework, we propose two novel improvable gap balancing (IGB) algorithms for MTL: one takes a simple heuristic, and the other (for the first time) deploys deep reinforcement learning for MTL. Particularly, instead of directly balancing the losses in MTL, both algorithms choose to dynamically assign task weights for improvable gap balancing. Moreover, we combine IGB and gradient balancing to show the complementarity between the two types of algorithms. Extensive experiments on two benchmark datasets demonstrate that our IGB algorithms lead to the best results in MTL via loss balancing and achieve further improvements when combined with gradient balancing. Code is available at https://github.com/YanqiDai/IGB4MTL.

Post-training quantization is widely used for compressing large neural networks, but aggressive low-bit quantization can significantly degrade model quality. A common remedy is to augment the quantized weights with a low-rank correction, leading to approximations of the form Wapprox Q+LR. In this paper, we study this low-precision plus low-rank representation through the layer-wise reconstruction objective |XW-X(Q+LR)|_F^2, where X is a calibration matrix. We establish, to our knowledge, the first information-theoretic lower bounds for this problem under finite-alphabet and bounded low-rank compensation constraints. We then propose GPTQ-intrinsic LoRA, a training-free algorithm that incorporates the low-rank correction directly into a GPTQ-style quantization pass by appropriately augmenting the calibration Hessian. For the choice L=V_r, where V_r contains the top right singular vectors of X, we prove layer-wise reconstruction error bounds in which the usual GPTQ dependence on |X|_F^2 is replaced by the rank-r residual |X-X_r|_F^2, up to regularization terms. Under natural structural assumptions, these bounds match the information-theoretic lower bounds in their dominant scaling, up to constants and mild factors. We also introduce Bid-Up, a fixed-grid quantization refinement step that can be alternated with optimal low-rank compensation with guaranteed non-increasing layer-wise reconstruction error. Experiments on Qwen3 language models and DeiT vision transformers show that GPTQ-intrinsic LoRA improves over GPTQ and GPTQ followed by low-rank compensation, with additional gains from refinement loops.

There has been significant interest in "extreme" compression of large language models (LLMs), i.e., to 1-2 bits per parameter, which allows such models to be executed efficiently on resource-constrained devices. Existing work focused on improved one-shot quantization techniques and weight representations; yet, purely post-training approaches are reaching diminishing returns in terms of the accuracy-vs-bit-width trade-off. State-of-the-art quantization methods such as QuIP# and AQLM include fine-tuning (part of) the compressed parameters over a limited amount of calibration data; however, such fine-tuning techniques over compressed weights often make exclusive use of straight-through estimators (STE), whose performance is not well-understood in this setting. In this work, we question the use of STE for extreme LLM compression, showing that it can be sub-optimal, and perform a systematic study of quantization-aware fine-tuning strategies for LLMs. We propose PV-Tuning - a representation-agnostic framework that generalizes and improves upon existing fine-tuning strategies, and provides convergence guarantees in restricted cases. On the practical side, when used for 1-2 bit vector quantization, PV-Tuning outperforms prior techniques for highly-performant models such as Llama and Mistral. Using PV-Tuning, we achieve the first Pareto-optimal quantization for Llama 2 family models at 2 bits per parameter.

We analyse three KV cache quantization schemes under a fair bit budget: KV (scalar MSE baseline), KQV (WHT + MSE on K; WHT + MSE + QJL on V), and QKQV (WHT + MSE + QJL on both). Starting from the Beta distribution on the hypersphere, we trace how QJL on K inflates inner product variance by π/2, which softmax amplifies nonlinearly via Jensen's inequality, and we present statistical inference and information metrics to highlight practical differences. Three empirical findings emerge. (1)~At n=4 (the practically dominant budget), KQV wins on every measure -- KL divergence, geometric K error, and 6D distance -- across all distributions and ranks tested. (2)~The K--V asymmetry is unconditional: QKQV is consistently worse than KQV in KL divergence at every budget and distribution. (3)~A budget-dependent crossover exists: QKQV achieves better geometric K reconstruction at n in {2,3,5}, KQV at n in {4,6}, invariant to rank and tail weight -- an open rate-distortion problem. KL(p_{ref} | p_{quant}), K-only by construction, bridges K direction error to routing corruption and output collapse. We present a sufficient condition when the Jensen mechanism amplifies superlinearly through the softmax. At n in {2,3,5}, QKQV wins geometrically because this assumption does not bind. At n=4, elevated K error and KL divergence for QKQV strongly suggest the Jensen mechanism is the operative cause of the crossover, providing a new perspective and explanation.

Cross-entropy loss has long been the standard choice for training deep neural networks, yet it suffers from interpretability limitations, unbounded weight growth, and inefficiencies that can contribute to costly training dynamics. The harmonic loss is a distance-based alternative grounded in Euclidean geometry that improves interpretability and mitigates phenomena such as grokking, or delayed generalization on the test set. However, the study of harmonic loss remains narrow: only Euclidean distance is explored, and no systematic evaluation of computational efficiency or sustainability was conducted. We extend harmonic loss by systematically investigating a broad spectrum of distance metrics as replacements for the Euclidean distance. We comprehensively evaluate distance-tailored harmonic losses on both vision backbones and large language models. Our analysis is framed around a three-way evaluation of model performance, interpretability, and sustainability. On vision tasks, cosine distances provide the most favorable trade-off, consistently improving accuracy while lowering carbon emissions, whereas Bray-Curtis and Mahalanobis further enhance interpretability at varying efficiency costs. On language models, cosine-based harmonic losses improve gradient and learning stability, strengthen representation structure, and reduce emissions relative to cross-entropy and Euclidean heads. Our code is available at: https://anonymous.4open.science/r/rethinking-harmonic-loss-5BAB/.

In contrastive learning, two views of an original image, generated by different augmentations, are considered a positive pair, and their similarity is required to be high. Similarly, two views of distinct images form a negative pair, with encouraged low similarity. Typically, a single similarity measure, provided by a lone projection head, evaluates positive and negative sample pairs. However, due to diverse augmentation strategies and varying intra-sample similarity, views from the same image may not always be similar. Additionally, owing to inter-sample similarity, views from different images may be more akin than those from the same image. Consequently, enforcing high similarity for positive pairs and low similarity for negative pairs may be unattainable, and in some cases, such enforcement could detrimentally impact performance. To address this challenge, we propose using multiple projection heads, each producing a distinct set of features. Our pre-training loss function emerges from a solution to the maximum likelihood estimation over head-wise posterior distributions of positive samples given observations. This loss incorporates the similarity measure over positive and negative pairs, each re-weighted by an individual adaptive temperature, regulated to prevent ill solutions. Our approach, Adaptive Multi-Head Contrastive Learning (AMCL), can be applied to and experimentally enhances several popular contrastive learning methods such as SimCLR, MoCo, and Barlow Twins. The improvement remains consistent across various backbones and linear probing epochs, and becomes more significant when employing multiple augmentation methods.

We provide evidence of quantum kernel advantage under noiseless simulation in binary insurance classification on MIMIC-CXR chest radiographs using quantum support vector machines (QSVM) with frozen embeddings from three medical foundation models (MedSigLIP-448, RAD-DINO, ViT-patch32). We propose a two-tier fair comparison framework in which both classifiers receive identical PCA-q features. At Tier 1 (untuned QSVM vs. untuned linear SVM, C = 1 both sides), QSVM wins minority-class F1 in all 18 tested configurations (17 at p < 0.001, 1 at p < 0.01). The classical linear kernel collapses to majority-class prediction on 90-100% of seeds at every qubit count, while QSVM maintains non-trivial recall. At q = 11 (MedSigLIP-448 plateau center), QSVM achieves mean F1 = 0.343 vs. classical F1 = 0.050 (F1 gain = +0.293, p < 0.001) without hyperparameter tuning. Under Tier 2 (untuned QSVM vs. C-tuned RBF SVM), QSVM wins all seven tested configurations (mean gain +0.068, max +0.112). Eigenspectrum analysis reveals quantum kernel effective rank reaches 69.80 at q = 11, far exceeding linear kernel rank, while classical collapse remains C-invariant. A full qubit sweep reveals architecture-dependent concentration onset across models. Code: https://github.com/sebasmos/qml-medimage

Supervised low-level vision models rely on pixel-wise losses against paired references, yet paired training sets exhibit per-pair photometric inconsistency, say, different image pairs demand different global brightness, color, or white-balance mappings. This inconsistency enters through task-intrinsic photometric transfer (e.g., low-light enhancement) or unintended acquisition shifts (e.g., de-raining), and in either case causes an optimization pathology. Standard reconstruction losses allocate disproportionate gradient budget to conflicting per-pair photometric targets, crowding out content restoration. In this paper, we investigate this issue and prove that, under least-squares decomposition, the photometric and structural components of the prediction-target residual are orthogonal, and that the spatially dense photometric component dominates the gradient energy. Motivated by this analysis, we propose Photometric Alignment Loss (PAL). This flexible supervision objective discounts nuisance photometric discrepancy via closed-form affine color alignment while preserving restoration-relevant supervision, requiring only covariance statistics and tiny matrix inversion with negligible overhead. Across 6 tasks, 16 datasets, and 16 architectures, PAL consistently improves metrics and generalization. The implementation is in the appendix.

Quality and diversity are two critical metrics for the training data of large language models (LLMs), positively impacting performance. Existing studies often optimize these metrics separately, typically by first applying quality filtering and then adjusting data proportions. However, these approaches overlook the inherent trade-off between quality and diversity, necessitating their joint consideration. Given a fixed training quota, it is essential to evaluate both the quality of each data point and its complementary effect on the overall dataset. In this paper, we introduce a unified data selection framework called QuaDMix, which automatically optimizes the data distribution for LLM pretraining while balancing both quality and diversity. Specifically, we first propose multiple criteria to measure data quality and employ domain classification to distinguish data points, thereby measuring overall diversity. QuaDMix then employs a unified parameterized data sampling function that determines the sampling probability of each data point based on these quality and diversity related labels. To accelerate the search for the optimal parameters involved in the QuaDMix framework, we conduct simulated experiments on smaller models and use LightGBM for parameters searching, inspired by the RegMix method. Our experiments across diverse models and datasets demonstrate that QuaDMix achieves an average performance improvement of 7.2% across multiple benchmarks. These results outperform the independent strategies for quality and diversity, highlighting the necessity and ability to balance data quality and diversity.

We introduce for continual learning Autodiff Quadratic Consolidation (AQC), which approximates the previous loss function with a quadratic function, and Neural Consolidation (NC), which approximates the previous loss function with a neural network. Although they are not scalable to large neural networks, they can be used with a fixed pre-trained feature extractor. We empirically study these methods in class-incremental learning, for which regularization-based methods produce unsatisfactory results, unless combined with replay. We find that for small datasets, quadratic approximation of the previous loss function leads to poor results, even with full Hessian computation, and NC could significantly improve the predictive performance, while for large datasets, when used with a fixed pre-trained feature extractor, AQC provides superior predictive performance. We also find that using tanh-output features can improve the predictive performance of AQC. In particular, in class-incremental Split MNIST, when a Convolutional Neural Network (CNN) with tanh-output features is pre-trained on EMNIST Letters and used as a fixed pre-trained feature extractor, AQC can achieve predictive performance comparable to joint training.

The performance of machine learning models is determined by the quality of their learned features. They should be invariant under irrelevant data variation but sensitive to task-relevant details. To visualize whether this is the case, we propose a method to analyze feature extractors by sampling from their fibers -- equivalence classes defined by their invariances -- given an arbitrary representative. Unlike existing work where a dedicated generative model is trained for each feature detector, our algorithm is training-free and exploits a pretrained diffusion or flow-matching model as a prior. The fiber loss -- which penalizes mismatch in features -- guides the denoising process toward the desired equivalence class, via non-linear diffusion trajectory matching. This replaces days of training for invariance learning with a single guided generation procedure at comparable fidelity. Experiments on popular datasets (ImageNet, CheXpert) and model types (ResNet, DINO, BiomedClip) demonstrate that our framework can reveal invariances ranging from very desirable to concerning behaviour. For instance, we show how Qwen-2B places patients with situs inversus (heart on the right side) in the same fiber as typical anatomy.

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects.

Post-training model quantization is a widely adopted technique for reducing the memory and computational costs of large language models (LLMs). However, most existing methods rely on uniform or heuristic bitwidth assignments, failing to account for the nonuniform sensitivity of weights to quantization noise. In this paper, we propose a novel framework for allocating quantization bitwidths based on sensitivity metrics derived from a Hessian proxy. We make key assumptions, which allow the layer/component-wise loss function to be expressed as an explicit function of the bitwidths. This enables a neat formulation of the bit allocation problem as a convex optimization task, whose closed-form solution adapts precision across weights to minimize the layer-wise quantization loss. Inspecting the solution provides several insights (such as the equal-loss structure), which are then exploited to design the proposed BAQ (Bit Allocation Quantization) algorithm. The proposed algorithm achieves a good trade-off between loss minimization and complexity and allows BAQ to be integrated into standard quantization pipelines with minimal overhead. Experimental results show that BAQ consistently outperforms GPTQ, achieving up to 56times lower perplexity at the same bitwidth on large language models ranging from 125M to 30B parameters. Leveraging our analytical results derived from solving the optimal bit allocation problem, we also provide a theoretical explanation for the observed gains. All codes of this paper are available at https://github.com/CSU-ModelCompression/BAQ.

Serving Large Language Models (LLMs) is costly. However, post-training weight quantization can address this problem by both compressing their sizes for limited memory and saving bandwidth for acceleration. As not all weight dimensions are equally important, those methods typically rely on a sensitivity metric, which indicates the element-wise influence of weights on loss function and is used to preprocess original weights for better quantization. In this work, we conduct an empirical study on the accuracy of the sensitivity metric, and find that existing gradient and Hessian based metrics are very inaccurate: they underestimate quantization's impact on the loss function by orders of magnitude, mainly due to the small convergence radius of local 2nd order approximation, \ie, gradient and Hessian term in Taylor's formula. To tackle this problem, we propose Post-quantization Integral (PQI), an accurate metric to estimate posterior sensitivity in a fine-grained manner. To leverage this accurate metric, we further propose ReQuant, a simple yet powerful framework that mainly consists of two Dense-and-Sparse detach components: self-adaptive outlier selection and step-wise significant weights detach. Results show that ReQuant boosts state-of-the-art post-training quantization methods, with a pronounced improvement of 2.66 perplexity gain on Llama 3.2 1B with QTIP.

Weight-only post-training quantization (PTQ) can alleviate the computational burden of serving large language models (LLMs) at scale. However, existing PTQ methods often fail to generalize across models and suffer severe accuracy loss below 2 bits. Many leverage unstructured sparsity to mitigate this loss, but at the cost of regularity and GPU-friendly execution. We present QTEA, a sub-2-bit PTQ framework that quantizes weights into ternary values and uses salient weights as residual error compensators. To maintain hardware efficiency, residuals are assigned to selected columns with semi-structured \(1{:}4\) sparsity within the salient columns. We further add column-wise rescale refinement to GPTQ-style column-by-column quantization, alternately updating per-column scales and ternary assignments to reduce reconstruction error. We also identify order-dependent error propagation in GPTQ and introduce error decay to attenuate late-stage error accumulation. On Qwen3-14B, QTEA compresses all weights to an effective 1.7 bits per weight while improving average accuracy over the strongest ternary PTQ baseline by 16.7\%. It also achieves 1.40\(\times\) and 2.61\(\times\) lower perplexity on WikiText and C4 respectively. This trend holds on Llama3-8B, where QTEA obtains a 6.6\% accuracy gain and 1.34\(\times\)/1.95\(\times\) lower perplexity on the same datasets. Finally, we develop a lookup-table based kernel that achieves 7.2\(\times\) faster per-token generation over an FP16 baseline. Code is available at https://github.com/Intelligent-Microsystems-Lab/QTEA.

Image-to-image translation is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image using a training set of aligned image pairs. However, for many tasks, paired training data will not be available. We present an approach for learning to translate an image from a source domain X to a target domain Y in the absence of paired examples. Our goal is to learn a mapping G: X rightarrow Y such that the distribution of images from G(X) is indistinguishable from the distribution Y using an adversarial loss. Because this mapping is highly under-constrained, we couple it with an inverse mapping F: Y rightarrow X and introduce a cycle consistency loss to push F(G(X)) approx X (and vice versa). Qualitative results are presented on several tasks where paired training data does not exist, including collection style transfer, object transfiguration, season transfer, photo enhancement, etc. Quantitative comparisons against several prior methods demonstrate the superiority of our approach.

Straight-through estimator (STE), which enables the gradient flow over the non-differentiable function via approximation, has been favored in studies related to quantization-aware training (QAT). However, STE incurs unstable convergence during QAT, resulting in notable quality degradation in low precision. Recently, pseudoquantization training has been proposed as an alternative approach to updating the learnable parameters using the pseudo-quantization noise instead of STE. In this study, we propose a novel noise proxy-based integrated pseudoquantization (NIPQ) that enables unified support of pseudoquantization for both activation and weight by integrating the idea of truncation on the pseudo-quantization framework. NIPQ updates all of the quantization parameters (e.g., bit-width and truncation boundary) as well as the network parameters via gradient descent without STE instability. According to our extensive experiments, NIPQ outperforms existing quantization algorithms in various vision and language applications by a large margin.

Collaborative filtering (CF) is a widely studied research topic in recommender systems. The learning of a CF model generally depends on three major components, namely interaction encoder, loss function, and negative sampling. While many existing studies focus on the design of more powerful interaction encoders, the impacts of loss functions and negative sampling ratios have not yet been well explored. In this work, we show that the choice of loss function as well as negative sampling ratio is equivalently important. More specifically, we propose the cosine contrastive loss (CCL) and further incorporate it to a simple unified CF model, dubbed SimpleX. Extensive experiments have been conducted on 11 benchmark datasets and compared with 29 existing CF models in total. Surprisingly, the results show that, under our CCL loss and a large negative sampling ratio, SimpleX can surpass most sophisticated state-of-the-art models by a large margin (e.g., max 48.5% improvement in NDCG@20 over LightGCN). We believe that SimpleX could not only serve as a simple strong baseline to foster future research on CF, but also shed light on the potential research direction towards improving loss function and negative sampling. Our source code will be available at https://reczoo.github.io/SimpleX.

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine learning practice. The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns. However, in the modern practice, very rich models such as neural networks are trained to exactly fit (i.e., interpolate) the data. Classically, such models would be considered over-fit, and yet they often obtain high accuracy on test data. This apparent contradiction has raised questions about the mathematical foundations of machine learning and their relevance to practitioners. In this paper, we reconcile the classical understanding and the modern practice within a unified performance curve. This "double descent" curve subsumes the textbook U-shaped bias-variance trade-off curve by showing how increasing model capacity beyond the point of interpolation results in improved performance. We provide evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets, and we posit a mechanism for its emergence. This connection between the performance and the structure of machine learning models delineates the limits of classical analyses, and has implications for both the theory and practice of machine learning.

In a typical multi-label setting, a picture contains on average few positive labels, and many negative ones. This positive-negative imbalance dominates the optimization process, and can lead to under-emphasizing gradients from positive labels during training, resulting in poor accuracy. In this paper, we introduce a novel asymmetric loss ("ASL"), which operates differently on positive and negative samples. The loss enables to dynamically down-weights and hard-thresholds easy negative samples, while also discarding possibly mislabeled samples. We demonstrate how ASL can balance the probabilities of different samples, and how this balancing is translated to better mAP scores. With ASL, we reach state-of-the-art results on multiple popular multi-label datasets: MS-COCO, Pascal-VOC, NUS-WIDE and Open Images. We also demonstrate ASL applicability for other tasks, such as single-label classification and object detection. ASL is effective, easy to implement, and does not increase the training time or complexity. Implementation is available at: https://github.com/Alibaba-MIIL/ASL.

Current model quantization methods have shown their promising capability in reducing storage space and computation complexity. However, due to the diversity of quantization forms supported by different hardware, one limitation of existing solutions is that usually require repeated optimization for different scenarios. How to construct a model with flexible quantization forms has been less studied. In this paper, we explore a one-shot network quantization regime, named Elastic Quantization Neural Networks (EQ-Net), which aims to train a robust weight-sharing quantization supernet. First of all, we propose an elastic quantization space (including elastic bit-width, granularity, and symmetry) to adapt to various mainstream quantitative forms. Secondly, we propose the Weight Distribution Regularization Loss (WDR-Loss) and Group Progressive Guidance Loss (GPG-Loss) to bridge the inconsistency of the distribution for weights and output logits in the elastic quantization space gap. Lastly, we incorporate genetic algorithms and the proposed Conditional Quantization-Aware Accuracy Predictor (CQAP) as an estimator to quickly search mixed-precision quantized neural networks in supernet. Extensive experiments demonstrate that our EQ-Net is close to or even better than its static counterparts as well as state-of-the-art robust bit-width methods. Code can be available at https://github.com/xuke225/EQ-Net.git{https://github.com/xuke225/EQ-Net}.

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and model expressiveness. While existing ultra-low-bit PTQ methods rely on binary approximations or complex compensation mechanisms, they suffer from either limited representational capacity or computational overhead that undermines their efficiency gains. We introduce PTQ to Trit-Planes (PTQTP), the first ternary-weight PTQ framework that decomposes weight matrices into structured ternary {-1, 0, 1} trit-planes using 2x1.58-bit representation. PTQTP achieves multiplication-free inference, identical to 1-bit quantization, while maintaining superior expressiveness through its novel structured decomposition. Our approach provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment across diverse modern LLMs without architectural modifications; and (3) uniform ternary operations that eliminate the need for mixed-precision or compensation schemes. Comprehensive experiments across LLaMA3.x and Qwen3 model families (0.6B-70B parameters) demonstrate that PTQTP significantly outperforms existing low-bit PTQ methods, achieving 82.4% mathematical reasoning retention versus 0% for competing approaches. PTQTP approaches and sometimes surpasses 1.58-bit quantization-aware training performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods. These results establish PTQTP as a practical solution for efficient LLM deployment in resource-constrained environments.

The growing number of parameters and computational demands of large language models (LLMs) present significant challenges for their efficient deployment. Recently, there is an increasing interest in quantizing weights to extremely low precision while offsetting the resulting error with low-rank, high-precision error reconstruction terms. The combination of quantization and low-rank approximation is now popular in both adapter-based, parameter-efficient fine-tuning methods such as LoftQ and low-precision inference techniques including ZeroQuant-V2. Usually, the low-rank terms are calculated via the singular value decomposition (SVD) of the weight quantization error, minimizing the Frobenius and spectral norms of the weight approximation error. Recent methods like LQ-LoRA and LQER introduced hand-crafted heuristics to minimize errors in layer outputs (activations) rather than weights, resulting improved quantization results. However, these heuristic methods lack an analytical solution to guide the design of quantization error reconstruction terms. In this paper, we revisit this problem and formulate an analytical framework, named Quantization Error Reconstruction Analysis (QERA), and offer a closed-form solution to the problem. We show QERA benefits both existing low-precision fine-tuning and inference methods -- QERA achieves a fine-tuned accuracy gain of Δ_{acc} = 6.05% of 2-bit RoBERTa-base on GLUE compared to LoftQ; and obtains Δ_{acc} = 2.97% higher post-training quantization accuracy of 4-bit Llama-3.1-70B on average than ZeroQuant-V2 and Δ_{ppl} = - 0.28 lower perplexity on WikiText2 than LQER.

Multimodal agents repeatedly re-examine the same video frames, UI screenshots, and rendered artifacts as their context window slides and reasoning iterates, yet every look-back re-encodes from scratch, because prefix caches serve reuse only at a fixed leading position. We show this recompute is avoidable, and identify exactly what naive KV reuse loses: the cross-chunk conditioning a chunk absorbs from its neighbours. This loss is asymmetric. The direct readout of a cached chunk is recovered exactly and for free by the standard state-merge. What remains is a diffuse, low-rank residue concentrated in deep layers, invisible to single-hop retrieval but precisely what multi-hop reasoning binds on. Blind reuse therefore leaves single-hop recall intact while halving multi-hop accuracy; this is the failure mode prior position-independent caches, designed for single-context or single-image reuse, do not address. We repair it with a small, training-free low-rank conditioning patch stored alongside each position-free chunk. Reuse reduces to one operator across MLA, GQA, and MHA: exact RoPE re-rotation to any target position, plus the patch that restores cross-chunk binding. This makes three window operations cheap: reorder (one patch serves every ordering of a cached set), sliding-window survival (surviving chunks relocate via rotation only, zero re-encode), and recall (an evicted chunk is rehydrated by its patch, never re-encoded). A rank-m patch recovers full task accuracy on cross-chunk-binding benchmarks, MM-NIAH across two attention families and two-page doc-QA, at a fraction of the KV footprint, and reconstructs re-prefill KV to within bf16 rounding in a production SGLang kernel across six backbones. The conditioning signal is strongest in redundant vision and video streams, making our solution most impactful where multimodal agents spend their recompute budget.

In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model quality. Motivated by prior work connecting the geometry of the loss landscape and generalization, we introduce a novel, effective procedure for instead simultaneously minimizing loss value and loss sharpness. In particular, our procedure, Sharpness-Aware Minimization (SAM), seeks parameters that lie in neighborhoods having uniformly low loss; this formulation results in a min-max optimization problem on which gradient descent can be performed efficiently. We present empirical results showing that SAM improves model generalization across a variety of benchmark datasets (e.g., CIFAR-10, CIFAR-100, ImageNet, finetuning tasks) and models, yielding novel state-of-the-art performance for several. Additionally, we find that SAM natively provides robustness to label noise on par with that provided by state-of-the-art procedures that specifically target learning with noisy labels. We open source our code at https://github.com/google-research/sam.

Post-training alignment of video generation models with human preferences is a critical goal. Developing effective Reward Models (RMs) for this process faces significant methodological hurdles. Current data collection paradigms, reliant on in-prompt pairwise annotations, suffer from labeling noise. Concurrently, the architectural design of VLM-based RMs, particularly their output mechanisms, remains underexplored. Furthermore, RM is susceptible to reward hacking in post-training. To mitigate these limitations, we propose SoliReward, a systematic framework for video RM training. Our framework first sources high-quality, cost-efficient data via single-item binary annotations, then constructs preference pairs using a cross-prompt pairing strategy. Architecturally, we employ a Hierarchical Progressive Query Attention mechanism to enhance feature aggregation. Finally, we introduce a modified BT loss that explicitly accommodates win-tie scenarios. This approach regularizes the RM's score distribution for positive samples, providing more nuanced preference signals to alleviate over-focus on a small number of top-scoring samples. Our approach is validated on benchmarks evaluating physical plausibility, subject deformity, and semantic alignment, demonstrating improvements in direct RM evaluation metrics and in the efficacy of post-training on video generation models. Code and benchmark will be publicly available.

Weight-Decomposed Low-Rank Adaptation (DoRA) extends LoRA by decoupling weight magnitude from direction, but its forward pass requires the row-wise norm of W + sBA, a computation that every major framework we surveyed implements by materializing the dense [d_out, d_in] product BA. At d_in = 8192 and rank r = 384, a single module's norm requires about 512 MB of transient working memory in bf16, making high-rank DoRA costly and often infeasible on common single-GPU setups once hundreds of adapted modules and checkpointing are involved. We present two systems contributions. A factored norm decomposes the squared norm into base, cross, and Gram terms computable through O(d_out r + r^2) intermediates, eliminating the dense product. Fused Triton kernels collapse the four-kernel DoRA composition into a single pass, reducing memory traffic by about 4x and using a numerically stable form that avoids catastrophic cancellation in the near-unity rescaling regime where magnitude scales concentrate in practice. Across six 8-32B vision-language models (VLMs) on three NVIDIA GPUs (RTX 6000 PRO, H200, B200) at r = 384 in bf16, the fused implementation is 1.5-2.0x faster than Hugging Face PEFT's DoRA implementation for inference and 1.5-1.9x faster for gradient computation (optimizer step excluded), with up to 7 GB lower peak VRAM. Microbenchmarks on six GPUs spanning four architecture generations (L40S, A100, RTX 6000 PRO, H200, B200, B300) confirm 1.5-2.7x compose-kernel speedup. Final-logit cosine similarity exceeds 0.9999 across all model/GPU pairs, and multi-seed training curves match within 7.1 x 10^-4 mean per-step loss delta over 2000 steps.

We present HyperQuant (Hadamard, optimallY Packing, Entropy Rice-coding), a unified post-training quantization pipeline for the weights and the KV cache of large language and diffusion transformers. Across a suite of self-contained experiments (Table 1), HyperQuant outperforms the recent HIGGS scheme at every operating point from 3 to 5 bits per scalar (bps) on weights, and beats both TurboQuant and OCTOPUS on KV quantization down to 1.7 bps. Beyond the LLM setting, HyperQuant quantizes the 19B-parameter LTX-2 DiT video model with no observable per-frame artifacts. End-to-end on an H100 at 4 bps, HyperQuant compresses the linear weights ~3.9x and the KV cache ~3.79x at near-lossless quality. HyperQuant combines four known ideas into a single construction: (i) a per-tile Randomized Hadamard Transform that makes the per-coordinate distribution of weights and activations approximately Gaussian; (ii) quantization to a low-dimensional optimal lattice (E8, D4, A2, or Z); (iii) lossless bit-stripping and near-entropy-optimal variable-length Rice coding of the lattice indices; and (iv) bias-correction methods for the KV cache that keep the reconstruction unbiased under inner products, preserving attention semantics. We further integrate the pipeline with 8-bit and 4-bit Tensor-Core MMA paths (fp8-e4m3, int8, nvfp4, mxfp4), and find that int8 beats fp8 on the post-RHT lattice output. Project page: https://moonmath.ai/hyperquant/

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law assumes every training token is unique. This limits its ability to guide pretraining decisions in data-constrained regimes. We model the excess loss under repetition with a simple additive overfitting penalty and find that it accurately describes model behavior. Our scaling law yields qualitatively new compute-optimal allocation advice. Beyond a point, further repetition is counterproductive and compute is better spent on model capacity. We show that following our law's recommended configuration improves performance in data-constrained regimes. Finally, because our one-parameter form isolates overfitting in a single coefficient, it enables direct comparison across training configurations. As a case study, we show that strong weight decay (λ=1.0) reduces this coefficient by approximately 70%, providing a scaling-law explanation for recent findings that optimal weight decay in data-constrained regimes is an order of magnitude larger than standard practice.

Gradient descent on a factored model W = UV^top is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not. We trace the difference to the gauge symmetry of the loss, its invariance under (U, V) mapsto (UQ, VQ). Gradient flow's low-rank mechanism is available to an optimizer only if that optimizer is gauge-equivariant, a condition necessary for the transfer but not sufficient for low-rank recovery. Gradient descent, momentum, "shared-scalar" Adam, Muon, and Shampoo satisfy it. Adam, RMSProp, and the other coordinate-wise methods do not. A structure theorem characterizes the memoryless equivariant rules as exactly the Gram-determined left preconditioners, and a transfer theorem carries gradient flow's pathwise properties to common-scalar flows. We then sort nine update rules on underdetermined matrix sensing by recovery error against the planted ground truth. A one-parameter family from coordinate-wise to shared-scalar preconditioning restores the bias monotonically, isolating anisotropy as the cause. A "spectral schedule" reconciles two opposing reports about Muon: equal-rate updates recover exactly low-rank targets but lose their edge as the spectral tail grows. In transformers, Adam separates two gauge-equivalent initializations at the first step, where the equivariant optimizers stay at float precision, and ends with the per-head invariants W_Q^top W_K 56% apart in relative Frobenius distance, a gap no per-head rotation can close. On two hyperspectral datasets at matched training loss, gradient descent cuts held-out error by 43-44% at the lowest sampling density, and at lower effective rank. Basis choice is therefore not a tuning detail but a decision about which interpolant the optimizer selects.

In deep metric learning, the Triplet Loss has emerged as a popular method to learn many computer vision and natural language processing tasks such as facial recognition, object detection, and visual-semantic embeddings. One issue that plagues the Triplet Loss is network collapse, an undesirable phenomenon where the network projects the embeddings of all data onto a single point. Researchers predominately solve this problem by using triplet mining strategies. While hard negative mining is the most effective of these strategies, existing formulations lack strong theoretical justification for their empirical success. In this paper, we utilize the mathematical theory of isometric approximation to show an equivalence between the Triplet Loss sampled by hard negative mining and an optimization problem that minimizes a Hausdorff-like distance between the neural network and its ideal counterpart function. This provides the theoretical justifications for hard negative mining's empirical efficacy. In addition, our novel application of the isometric approximation theorem provides the groundwork for future forms of hard negative mining that avoid network collapse. Our theory can also be extended to analyze other Euclidean space-based metric learning methods like Ladder Loss or Contrastive Learning.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Loss reweighting has shown significant benefits for machine unlearning with large language models (LLMs). However, their exact functionalities are left unclear and the optimal strategy remains an open question, thus impeding the understanding and improvement of existing methodologies. In this paper, we identify two distinct goals of loss reweighting, namely, Saturation and Importance -- the former indicates that those insufficiently optimized data should be emphasized, while the latter stresses some critical data that are most influential for loss minimization. To study their usefulness, we design specific reweighting strategies for each goal and evaluate their respective effects on unlearning. We conduct extensive empirical analyses on well-established benchmarks, and summarize some important observations as follows: (i) Saturation enhances efficacy more than importance-based reweighting, and their combination can yield additional improvements. (ii) Saturation typically allocates lower weights to data with lower likelihoods, whereas importance-based reweighting does the opposite. (iii) The efficacy of unlearning is also largely influenced by the smoothness and granularity of the weight distributions. Based on these findings, we propose SatImp, a simple reweighting method that combines the advantages of both saturation and importance. Empirical results on extensive datasets validate the efficacy of our method, potentially bridging existing research gaps and indicating directions for future research. Our code is available at https://github.com/tmlr-group/SatImp.

The Federated Learning setting has a central server coordinating the training of a model on a network of devices. One of the challenges is variable training performance when the dataset has a class imbalance. In this paper, we address this by introducing a new loss function called Fed-Focal Loss. We propose to address the class imbalance by reshaping cross-entropy loss such that it down-weights the loss assigned to well-classified examples along the lines of focal loss. Additionally, by leveraging a tunable sampling framework, we take into account selective client model contributions on the central server to further focus the detector during training and hence improve its robustness. Using a detailed experimental analysis with the VIRTUAL (Variational Federated Multi-Task Learning) approach, we demonstrate consistently superior performance in both the balanced and unbalanced scenarios for MNIST, FEMNIST, VSN and HAR benchmarks. We obtain a more than 9% (absolute percentage) improvement in the unbalanced MNIST benchmark. We further show that our technique can be adopted across multiple Federated Learning algorithms to get improvements.

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

Dataset distillation has emerged as a powerful approach for reducing data requirements in deep learning. Among various methods, distribution matching-based approaches stand out for their balance of computational efficiency and strong performance. However, existing distance metrics used in distribution matching often fail to accurately capture distributional differences, leading to unreliable measures of discrepancy. In this paper, we reformulate dataset distillation as a minmax optimization problem and introduce Neural Characteristic Function Discrepancy (NCFD), a comprehensive and theoretically grounded metric for measuring distributional differences. NCFD leverages the Characteristic Function (CF) to encapsulate full distributional information, employing a neural network to optimize the sampling strategy for the CF's frequency arguments, thereby maximizing the discrepancy to enhance distance estimation. Simultaneously, we minimize the difference between real and synthetic data under this optimized NCFD measure. Our approach, termed Neural Characteristic Function Matching (), inherently aligns the phase and amplitude of neural features in the complex plane for both real and synthetic data, achieving a balance between realism and diversity in synthetic samples. Experiments demonstrate that our method achieves significant performance gains over state-of-the-art methods on both low- and high-resolution datasets. Notably, we achieve a 20.5\% accuracy boost on ImageSquawk. Our method also reduces GPU memory usage by over 300times and achieves 20times faster processing speeds compared to state-of-the-art methods. To the best of our knowledge, this is the first work to achieve lossless compression of CIFAR-100 on a single NVIDIA 2080 Ti GPU using only 2.3 GB of memory.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

In this paper, we present SCOREQ, a novel approach for speech quality prediction. SCOREQ is a triplet loss function for contrastive regression that addresses the domain generalisation shortcoming exhibited by state of the art no-reference speech quality metrics. In the paper we: (i) illustrate the problem of L2 loss training failing at capturing the continuous nature of the mean opinion score (MOS) labels; (ii) demonstrate the lack of generalisation through a benchmarking evaluation across several speech domains; (iii) outline our approach and explore the impact of the architectural design decisions through incremental evaluation; (iv) evaluate the final model against state of the art models for a wide variety of data and domains. The results show that the lack of generalisation observed in state of the art speech quality metrics is addressed by SCOREQ. We conclude that using a triplet loss function for contrastive regression improves generalisation for speech quality prediction models but also has potential utility across a wide range of applications using regression-based predictive models.

Model quantization has become essential for efficient large language model deployment, yet existing approaches present clear trade-offs: methods such as GPTQ and AWQ achieve practical compression but are lossy, while lossless techniques preserve fidelity but lack inference acceleration. This paper explores the middle ground of statistically-lossless compression, examining three complementary aspects of what losslessness means for quantized LLMs. First, task-lossless compression preserves zero-shot benchmark accuracy within natural sampling variance and is achievable at aggressive bitwidths. Second, we formalize the stricter notion of distribution-lossless compression, requiring the quantized model's next-token distribution to be practically indistinguishable from the original, and propose the Expected Acceptance Rate (EAR), the maximum token-agreement probability under optimal coupling, as a directly interpretable fidelity metric. For example, EAR >= 0.99 means 99% agreement. Third, we prove a gamma-squared variance law showing that symmetric quantization inflates noise variance by gamma^2 relative to asymmetric quantization, making asymmetric quantization a prerequisite for distribution-lossless fidelity but not for task-level preservation. Through SLQ, a layer-wise non-uniform method with asymmetric quantization and wide bitwidth search, we obtain task-lossless compression at well below 4 bits per parameter, as low as 3.3 bits depending on the model, distribution-lossless compression at 5-6 bits per parameter on average, and inference speedups of 1.7-3.7x compared to FP16 using optimized kernels. Source code is available at [https://github.com/IST-DASLab/SLQ](https://github.com/IST-DASLab/SLQ).

Post-training quantization (PTQ) has stood out as a cost-effective and promising model compression paradigm in recent years, as it avoids computationally intensive model retraining. Nevertheless, current PTQ methods for Vision Transformers (ViTs) still suffer from significant accuracy degradation, especially under low-bit quantization. To address these shortcomings, we analyze the prevailing Hessian-guided quantization loss, and uncover certain limitations of conventional Hessian approximations. By following the block-wise reconstruction framework, we propose a novel PTQ method for ViTs, dubbed FIMA-Q. Specifically, we firstly establish the connection between KL divergence and FIM, which enables fast computation of the quantization loss during reconstruction. We further propose an efficient FIM approximation method, namely DPLR-FIM, by employing the diagonal plus low-rank principle, and formulate the ultimate quantization loss. Our extensive experiments, conducted across various vision tasks with representative ViT-based architectures on public datasets, demonstrate that our method substantially promotes the accuracy compared to the state-of-the-art approaches, especially in the case of low-bit quantization. The source code is available at https://github.com/ShiheWang/FIMA-Q.

When finetuning large language models for specialized tasks such as mathematical reasoning, models exhibit catastrophic forgetting, losing previously learned capabilities. We investigate this by finetuning Flan-T5-Base (250M parameters) on the DeepMind Mathematics dataset and measuring forgetting on MultiNLI. Math-only training improves mathematical accuracy from 3.1\% to 12.0\% but causes NLI accuracy to collapse from 81.0\% to 16.5\%--a 64.5 percentage point drop occurring within the first 1,000 training steps. We propose mixed training strategies that interleave mathematical and NLI examples during training. Our results demonstrate that mixed training completely eliminates catastrophic forgetting while maintaining equivalent mathematical performance: the balanced 1:1 ratio achieves 12.0\% math accuracy (matching math-only) while preserving 86.2\% NLI accuracy. We systematically explore mixing ratios from 1:1 to 15:1, finding that even minimal NLI exposure (6.2\%) provides effective regularization. These findings demonstrate that specialization need not require forgetting general capabilities, with implications for scaling to larger models where mixed training may confer additional benefits beyond forgetting prevention.

Training large language models (LLMs) efficiently while preserving model quality poses significant challenges, particularly with subbyte precision supported by state-of-the-art GPUs. Current mixed-precision training approaches either apply uniform precision to all GEMM operations or rely on heuristic-based methods that fail to generalize during training, leading to suboptimal convergence and instability. To address these challenges, this paper introduces SNIP, a fine-grained adaptive mixed-precision training framework for LLM pretraining that supports subbyte precision. SNIP periodically collects statistics on activations, gradients, and optimizer states to assess the precision loss impact on model quality. We define two key metrics: loss divergence in the forward pass, caused by quantization-induced increases in training loss, and weight divergence in the backward pass, which measures error propagation through gradients affecting model updates. These metrics guide an Integer Linear Programming (ILP) problem that systematically optimizes layerwise precision to minimize overall quality loss while meeting efficiency targets. Experiments on 1B, 3B, 7B and 70B Llama-like models demonstrate that SNIP consistently outperforms existing baselines, reducing FLOPs by up to 80% while preserving model quality across different model sizes and training phases with minimal computational overhead.

Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly with respect to the input, this is however lost in single-step AT. To address CO in single-step AT, several methods have been proposed to enforce local linearity of the loss via regularization. However, these regularization terms considerably slow down training due to Double Backpropagation. Instead, in this work, we introduce a regularization term, called ELLE, to mitigate CO effectively and efficiently in classical AT evaluations, as well as some more difficult regimes, e.g., large adversarial perturbations and long training schedules. Our regularization term can be theoretically linked to curvature of the loss function and is computationally cheaper than previous methods by avoiding Double Backpropagation. Our thorough experimental validation demonstrates that our work does not suffer from CO, even in challenging settings where previous works suffer from it. We also notice that adapting our regularization parameter during training (ELLE-A) greatly improves the performance, specially in large epsilon setups. Our implementation is available in https://github.com/LIONS-EPFL/ELLE .

Learning compatible representations aims to learn feature representations that can be used interchangeably over time whenever a model undergoes updates. In this paper, we demonstrate that stationary representations learned by d-Simplex fixed classifiers imply compatibility as in its formal definition. This result establishes a foundation for future works and can be directly exploited in practical learning scenarios. We address the challenge of learning compatibility using d-Simplex fixed classifiers when the model is sequentially fine-tuned. Learning according to a d-Simplex fixed classifier with the cross-entropy loss aligns feature distributions at the first-order statistics. Consequently, it may not fully capture higher-order dependencies in the representation between model updates. To address this issue, we demonstrate that training the model using a d-Simplex fixed classifier through a convex combination of the cross-entropy loss and a contrastive loss not only captures higher-order dependencies, but is also equivalent to learning with the cross-entropy under the compatibility constraints. We confirm our findings with extensive experiments also considering a new scenario where a pre-trained model is sequentially fine-tuned and occasionally replaced with an improved model. We show that stationary representations enable uninterrupted retrieval services (without reprocessing gallery images) while improving performance during model updates and replacements, achieving state-of-the-art. Code at https://github.com/miccunifi/iamcl2r.

Reinforcement learning (RL) for large language models (LLMs) is dominated by the cost of rollout generation, which has motivated the use of low-precision rollouts (e.g., FP8) paired with a BF16 trainer to improve throughput and reduce memory pressure. This introduces a rollout-training mismatch that biases the policy gradient and can cause training to collapse outright on reasoning benchmarks. We show that the mismatch is non-stationary and acts as a double-edged sword: early in training it provides a stochastic exploration bonus, exposing the gradient to trajectories the trainer would otherwise under-sample, but the same perturbation transitions into a destabilizing source of bias as the policy concentrates. To solve this, we propose Adaptive Importance Sampling (AIS), a correction framework that adjusts the strength of its intervention on a per-batch basis. AIS combines three real-time diagnostics, namely weight reliability, divergence severity, and variance amplification, into a single mixing coefficient that interpolates between the uncorrected and fully importance-weighted gradients, suppressing the destabilizing component of the mismatch while preserving its exploratory benefit. We integrate AIS into GRPO and evaluate it on the diffusion-based LLaDA-8B-Instruct and the autoregressive Qwen3-8B and Qwen3.5-9B across mathematical reasoning and planning benchmarks. AIS matches the BF16 baseline on most tasks while retaining the 1.5 to 2.76x rollout speedup of FP8.

We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship -- an anchor point x is similar to a set of positive points Y, and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15% points, while converging three times as fast as other triplet-based losses.

Network calibration aims to accurately estimate the level of confidences, which is particularly important for employing deep neural networks in real-world systems. Recent approaches leverage mixup to calibrate the network's predictions during training. However, they do not consider the problem that mixtures of labels in mixup may not accurately represent the actual distribution of augmented samples. In this paper, we present RankMixup, a novel mixup-based framework alleviating the problem of the mixture of labels for network calibration. To this end, we propose to use an ordinal ranking relationship between raw and mixup-augmented samples as an alternative supervisory signal to the label mixtures for network calibration. We hypothesize that the network should estimate a higher level of confidence for the raw samples than the augmented ones (Fig.1). To implement this idea, we introduce a mixup-based ranking loss (MRL) that encourages lower confidences for augmented samples compared to raw ones, maintaining the ranking relationship. We also propose to leverage the ranking relationship among multiple mixup-augmented samples to further improve the calibration capability. Augmented samples with larger mixing coefficients are expected to have higher confidences and vice versa (Fig.1). That is, the order of confidences should be aligned with that of mixing coefficients. To this end, we introduce a novel loss, M-NDCG, in order to reduce the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks for network calibration demonstrate the effectiveness of RankMixup.

Pretraining of large language models is not only expensive but also prone to certain training instabilities. A specific instability that often occurs at the end of training is output logit divergence. The most widely used mitigation strategies, z-loss and logit soft-capping, merely address the symptoms rather than the underlying cause of the problem. In this paper, we analyze the instability from the perspective of the output embeddings' geometry and identify anisotropic embeddings as its source. Based on this, we propose output embedding centering (OEC) as a new mitigation strategy, and demonstrate that it suppresses output logit divergence. OEC can be implemented in two different ways: as a deterministic operation called μ-centering, or a regularization method called μ-loss. Our experiments show that both variants outperform z-loss in terms of training stability, while being on par with logit soft-capping. This holds true both in the presence and the absence of weight tying. As a secondary result, we find that μ-loss is significantly less sensitive to regularization hyperparameter tuning than z-loss.

KV-cache eviction caps the memory cost of long reasoning traces but is inherently lossy because the model decodes from a partial view of its history. Under aggressive budgets, this not only lowers accuracy but can also cause runaway degeneration, where the model produces incoherent or repetitive tokens until reaching the length limit. We characterize much of this loss as an information gapf caused by missing context, rather than a capability gap caused by limited model capacity. An evicted 7B model and a full-context 1.5B model make complementary errors, and an oracle choice between their answers recovers 79% of the accuracy gap to the full-KV 7B model. Based on this observation, we propose KV-Rescue, a training-free inference framework that bridges the information gap introduced by KV eviction using a lightweight full-context helper. KV-Rescue interleaves reasoning steps from the two models into a shared trajectory. An online detector uses entropy and compressibility to terminate the generation of incoherent or repetitive base-model candidates early. Across five math benchmarks with Qwen2.5-Math 7B and 72B, KV-Rescue recovers an average of 87% of the accuracy lost to eviction at eviction budget B=64. A decode-cost analysis further shows that preventing runaway degeneration cuts base-model token generation by 43% on average.

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language models on deterministic outcome reasoning tasks. Prior work shows RLVR works with few prompts, but prompt selection is often based only on training-accuracy variance, leading to unstable optimization directions and weaker transfer. We revisit prompt selection from a mechanism-level view and argue that an effective minibatch should provide both (i) a reliable positive anchor and (ii) explicit negative learning signals from rare failures. Based on this principle, we propose positive--negative pairing: at each update, we sample a hard-but-solvable q^{+} and an easy-but-brittle prompt q^{-}(high success rate but not perfect), characterized by low and high empirical success rates under multiple rollouts. We further introduce Weighted GRPO, which reweights binary outcomes at the pair level and uses group-normalized advantages to amplify rare successes on q^{+} into sharp positive guidance while turning rare failures on q^{-} into strong negative penalties. This bidirectional signal provides informative learning feedback for both successes and failures, improving sample efficiency without suppressing exploration. On Qwen2.5-Math-7B, a single paired minibatch per update consistently outperforms a GRPO baseline that selects two prompts via commonly used variance-based selection heuristics: AIME~2025 Pass@8 improves from 16.8 to 22.2, and AMC23 Pass@64 from 94.0 to 97.0, while remaining competitive with large-scale RLVR trained from a pool of 1209 training prompts. Similar gains are observed on Qwen2.5-Math-7B-Instruct.

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

In this paper we introduce the SCoRe (Submodular Combinatorial Representation Learning) framework, a novel approach in representation learning that addresses inter-class bias and intra-class variance. SCoRe provides a new combinatorial viewpoint to representation learning, by introducing a family of loss functions based on set-based submodular information measures. We develop two novel combinatorial formulations for loss functions, using the Total Information and Total Correlation, that naturally minimize intra-class variance and inter-class bias. Several commonly used metric/contrastive learning loss functions like supervised contrastive loss, orthogonal projection loss, and N-pairs loss, are all instances of SCoRe, thereby underlining the versatility and applicability of SCoRe in a broad spectrum of learning scenarios. Novel objectives in SCoRe naturally model class-imbalance with up to 7.6\% improvement in classification on CIFAR-10-LT, CIFAR-100-LT, MedMNIST, 2.1% on ImageNet-LT, and 19.4% in object detection on IDD and LVIS (v1.0), demonstrating its effectiveness over existing approaches.

Low-rank adaptation (LoRA) has become the dominant method for parameter-efficient LLM fine-tuning, with LoRA-based quantization error compensation (LQEC) emerging as a powerful tool for recovering accuracy in compressed LLMs. However, LQEC has underperformed in sub-4-bit scenarios, with no prior investigation into understanding this limitation. We propose RILQ (Rank-Insensitive LoRA-based Quantization Error Compensation) to understand fundamental limitation and boost 2-bit LLM accuracy. Based on rank analysis revealing model-wise activation discrepancy loss's rank-insensitive nature, RILQ employs this loss to adjust adapters cooperatively across layers, enabling robust error compensation with low-rank adapters. Evaluations on LLaMA-2 and LLaMA-3 demonstrate RILQ's consistent improvements in 2-bit quantized inference across various state-of-the-art quantizers and enhanced accuracy in task-specific fine-tuning. RILQ maintains computational efficiency comparable to existing LoRA methods, enabling adapter-merged weight-quantized LLM inference with significantly enhanced accuracy, making it a promising approach for boosting 2-bit LLM performance.

Quantization has become a crucial step for the efficient deployment of deep neural networks, where floating point operations are converted to simpler fixed point operations. In its most naive form, it simply consists in a combination of scaling and rounding transformations, leading to either a limited compression rate or a significant accuracy drop. Recently, Gradient-based post-training quantization (GPTQ) methods appears to be constitute a suitable trade-off between such simple methods and more powerful, yet expensive Quantization-Aware Training (QAT) approaches, particularly when attempting to quantize LLMs, where scalability of the quantization process is of paramount importance. GPTQ essentially consists in learning the rounding operation using a small calibration set. In this work, we challenge common choices in GPTQ methods. In particular, we show that the process is, to a certain extent, robust to a number of variables (weight selection, feature augmentation, choice of calibration set). More importantly, we derive a number of best practices for designing more efficient and scalable GPTQ methods, regarding the problem formulation (loss, degrees of freedom, use of non-uniform quantization schemes) or optimization process (choice of variable and optimizer). Lastly, we propose a novel importance-based mixed-precision technique. Those guidelines lead to significant performance improvements on all the tested state-of-the-art GPTQ methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving the way for the design of scalable, yet effective quantization methods.

Large Language Models (LLMs) excel in diverse applications but suffer inefficiency due to massive scale. While quantization reduces computational costs, existing methods degrade accuracy in medium-sized LLMs (e.g., Llama-3-8B) due to activation outliers. To address this, we propose QUAD (Quantization with Activation Decomposition), a framework leveraging Singular Value Decomposition (SVD) to suppress activation outliers for effective 4-bit quantization. QUAD estimates activation singular vectors offline using calibration data to construct an orthogonal transformation matrix P, shifting outliers to additional dimensions in full precision while quantizing rest components to 4-bit. Additionally, QUAD enables parameter-efficient fine-tuning via adaptable full-precision outlier weights, narrowing the accuracy gap between quantized and full-precision models. Experiments demonstrate that QUAD achieves 94% ~ 96% accuracy under W4A4 quantization and 98% accuracy with W4A4/A8 and parameter-efficient fine-tuning for Llama-3 and Qwen-2.5 models. Our code is available at https://github.com/hyx1999/Quad{repository}.

Post-training quantization (PTQ) offers an efficient approach to compressing large language models (LLMs), significantly reducing memory access and computational costs. Existing compensation-based weight calibration methods often rely on a second-order Taylor expansion to model quantization error, under the assumption that the first-order term is negligible in well-trained full-precision models. However, we reveal that the progressive compensation process introduces accumulated first-order deviations between latent weights and their full-precision counterparts, making this assumption fundamentally flawed. To address this, we propose FOEM, a novel PTQ method that explicitly incorporates first-order gradient terms to improve quantization error compensation. FOEM approximates gradients by performing a first-order Taylor expansion around the pre-quantization weights. This yields an approximation based on the difference between latent and full-precision weights as well as the Hessian matrix. When substituted into the theoretical solution, the formulation eliminates the need to explicitly compute the Hessian, thereby avoiding the high computational cost and limited generalization of backpropagation-based gradient methods. This design introduces only minimal additional computational overhead. Extensive experiments across a wide range of models and benchmarks demonstrate that FOEM consistently outperforms the classical GPTQ method. In 3-bit weight-only quantization, FOEM reduces the perplexity of Llama3-8B by 17.3% and increases the 5-shot MMLU accuracy from 53.8% achieved by GPTAQ to 56.1%. Moreover, FOEM can be seamlessly combined with advanced techniques such as SpinQuant, delivering additional gains under the challenging W4A4KV4 setting and further narrowing the performance gap with full-precision baselines, surpassing existing state-of-the-art methods.

As models and data scale, independently trained networks often induce analogous notions of similarity. But, matching similarities is weaker than establishing an explicit correspondence between the representation spaces, especially for multimodal models, where consistency must hold not only within each modality, but also for the learned image-text coupling. We therefore ask: given two independently trained multimodal contrastive models (with encoders (f, g) and (f,g)) -- trained on different distributions and with different architectures -- does a systematic geometric relationship exist between their embedding spaces? If so, what form does it take, and does it hold uniformly across modalities? In this work, we show that across model families such as CLIP, SigLIP, and FLAVA, this geometric relationship is well approximated by an orthogonal map (up to a global mean shift), i.e., there exists an orthogonal map Q where Q^top Q = I such that f(x)approx Q f(x) for paired images x. Strikingly, the same Q simultaneously aligns the text encoders i.e., g(y)approx Q g(y) for texts y. Theoretically, we prove that if the multimodal kernel agrees across models on a small anchor set i.e. langle f(x), g(y)rangle approx langle f(x), g(y)rangle, then the two models must be related by a single orthogonal map Q and the same Q maps images and text across models. More broadly, this finding enables backward-compatible model upgrades, avoiding costly re-embedding, and has implications for the privacy of learned representations. Our project page: https://canonical-multimodal.github.io/

The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we also propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model. We achieve improved performance compared to the recent state-of-the-art Snapshot Ensembles, on CIFAR-10, CIFAR-100, and ImageNet.

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.

Neural network training is a memory- and compute-intensive task. Quantization, which enables low-bitwidth formats in training, can significantly mitigate the workload. To reduce quantization error, recent methods have developed new data formats and additional pre-processing operations on quantizers. However, it remains quite challenging to achieve high accuracy and efficiency simultaneously. In this paper, we explore sub-8-bit integer training from its essence of gradient descent optimization. Our integer training framework includes two components: ShiftQuant to realize accurate gradient estimation, and L1 normalization to smoothen the loss landscape. ShiftQuant attains performance that approaches the theoretical upper bound of group quantization. Furthermore, it liberates group quantization from inefficient memory rearrangement. The L1 normalization facilitates the implementation of fully quantized normalization layers with impressive convergence accuracy. Our method frees sub-8-bit integer training from pre-processing and supports general devices. This framework achieves negligible accuracy loss across various neural networks and tasks (0.92% on 4-bit ResNets, 0.61% on 6-bit Transformers). The prototypical implementation of ShiftQuant achieves more than 1.85times/15.3% performance improvement on CPU/GPU compared to its FP16 counterparts, and 33.9% resource consumption reduction on FPGA than the FP16 counterparts. The proposed fully-quantized L1 normalization layers achieve more than 35.54% improvement in throughout on CPU compared to traditional L2 normalization layers. Moreover, theoretical analysis verifies the advancement of our method.

Muon is an increasingly widely used optimizer that replaces a gradient G=USV^top with its polar factor UV^top, thereby flattening the singular spectrum. However, full flattening discards singular-value information that may matter for adaptation. We introduce Muon^p, a Muon-style optimizer that instead uses fractional spectral-power updates US^pV^top for rational pin(0,1), interpolating between Muon and gradient descent. To make it practical, we prove that fractional spectral powers cannot be computed by any fixed univariate polynomial iteration, and furthermore derive low-degree odd bivariate recurrences that approximate US^pV^top using only matrix multiplications, preserving Muon's matrix-multiplication-only structure and compute complexity. We show that Muon^p maximizes the linear improvement in loss under the Schatten q-norm for q=1+1{p}. Empirically, Muon^p is especially effective for finetuning: on billion-scale models, Muon^p improves validation perplexity and downstream task performance. We further analyze when Muon^p is less suitable, through the lens of spectral geometry. Our results reveal important insights on when preserving the singular spectrum can bring significant gains, and introduce a principled way to achieve them.

While vision transformers (ViTs) have shown great potential in computer vision tasks, their intense computation and memory requirements pose challenges for practical applications. Existing post-training quantization methods leverage value redistribution or specialized quantizers to address the non-normal distribution in ViTs. However, without considering the asymmetry in activations and relying on hand-crafted settings, these methods often struggle to maintain performance under low-bit quantization. To overcome these challenges, we introduce SmoothQuant with bias term (SQ-b) to alleviate the asymmetry issue and reduce the clamping loss. We also introduce optimal scaling factor ratio search (OPT-m) to determine quantization parameters by a data-dependent mechanism automatically. To further enhance the compressibility, we incorporate the above-mentioned techniques and propose a mixed-precision post-training quantization framework for vision transformers (MPTQ-ViT). We develop greedy mixed-precision quantization (Greedy MP) to allocate layer-wise bit-width considering both model performance and compressibility. Our experiments on ViT, DeiT, and Swin demonstrate significant accuracy improvements compared with SOTA on the ImageNet dataset. Specifically, our proposed methods achieve accuracy improvements ranging from 0.90% to 23.35% on 4-bit ViTs with single-precision and from 3.82% to 78.14% on 5-bit fully quantized ViTs with mixed-precision.

We address the problem of regressing 3D human pose and shape from a single image, with a focus on 3D accuracy. The current best methods leverage large datasets of 3D pseudo-ground-truth (p-GT) and 2D keypoints, leading to robust performance. With such methods, we observe a paradoxical decline in 3D pose accuracy with increasing 2D accuracy. This is caused by biases in the p-GT and the use of an approximate camera projection model. We quantify the error induced by current camera models and show that fitting 2D keypoints and p-GT accurately causes incorrect 3D poses. Our analysis defines the invalid distances within which minimizing 2D and p-GT losses is detrimental. We use this to formulate a new loss Threshold-Adaptive Loss Scaling (TALS) that penalizes gross 2D and p-GT losses but not smaller ones. With such a loss, there are many 3D poses that could equally explain the 2D evidence. To reduce this ambiguity we need a prior over valid human poses but such priors can introduce unwanted bias. To address this, we exploit a tokenized representation of human pose and reformulate the problem as token prediction. This restricts the estimated poses to the space of valid poses, effectively providing a uniform prior. Extensive experiments on the EMDB and 3DPW datasets show that our reformulated keypoint loss and tokenization allows us to train on in-the-wild data while improving 3D accuracy over the state-of-the-art. Our models and code are available for research at https://tokenhmr.is.tue.mpg.de.

We describe the architecture and ablations of Qwen3.8-Flash-Next, a sparse mixture-of-experts model with 125B parameters, 6B activated per token, and additional 51B parameters of n-gram embedding tables held off the accelerator. On fourteen pre-training benchmarks the model leads the 397B-A17B predecessor on eight and trails it on the rest by at most 2.6 points, at 1/3 the activated parameters, 1/3 the training tokens, and roughly 1/9 the training FLOPs. Token mixing uses a layer-wise hybrid of Gated DeltaNet (GDN) and global attention, with one full-attention layer in every four; at continued-pretraining time those full-attention layers are replaced by Qwen Sparse Attention (QSA), which scores context at micro-block granularity with a compressed lightweight indexer. The residual stream is widened to four branches and read through an elementwise gate, a design we call the Gated Residual (GR). Capacity is added outside the backbone by a single n-gram embedding layer whose tables are prefetched from host memory. We evaluate every candidate change along three axes: loss together with downstream benchmarks; the cost of the change in training, prefill and decode; and its effect on the optimal hyperparameters and training stability. Loss and downstream accuracy do not always move together: enlarging the n-gram vocabulary lowers loss monotonically while downstream accuracy saturates. The architecture and the Muon optimizer together shift the optimal learning rate and batch size upwards, render batch-size warmup unnecessary, and substantially improve stability under stress tests. Loss, benchmarks, efficiency and stability form one design problem. Solved jointly, they yield a recipe that is simultaneously more efficient, more capable and more stable.

Recent advances in distilling expensive diffusion models into efficient few-step generators show significant promise. However, these methods typically demand substantial computational resources and extended training periods, limiting accessibility for resource-constrained researchers, and existing supplementary loss functions have notable limitations. Regression loss requires pre-generating large datasets before training and limits the student model to the teacher's performance, while GAN-based losses suffer from training instability and require careful tuning. In this paper, we propose Embedding Loss (EL), a novel supplementary loss function that complements existing diffusion distillation methods to enhance generation quality and accelerate training with smaller batch sizes. Leveraging feature embeddings from a diverse set of randomly initialized networks, EL effectively aligns the feature distributions between the distilled few-step generator and the original data. By computing Maximum Mean Discrepancy (MMD) in the embedded feature space, EL ensures robust distribution matching, thereby preserving sample fidelity and diversity during distillation. Within distribution matching distillation frameworks, EL demonstrates strong empirical performance for one-step generators. On the CIFAR-10 dataset, our approach achieves state-of-the-art FID values of 1.475 for unconditional generation and 1.380 for conditional generation. Beyond CIFAR-10, we further validate EL across multiple benchmarks and distillation methods, including ImageNet, AFHQ-v2, and FFHQ datasets, using DMD, DI, and CM distillation frameworks, demonstrating consistent improvements over existing one-step distillation methods. Our method also reduces training iterations by up to 80%, offering a more practical and scalable solution for deploying diffusion-based generative models in resource-constrained environments.

Scaling test-time compute has emerged as a powerful mechanism for enhancing Large Language Model (LLM) performance. However, standard post-training paradigms, Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), optimize the likelihood of individual samples under a base policy, creating a misalignment with test time procedures that rely on aggregated or filtered outputs. In this work, we propose Compute Aligned Training, which aligns training objectives with test-time strategies. By conceptualizing inference strategies as operators on the base policy, we derive new loss functions that maximize performance when said strategies are applied. We instantiate such loss functions for SFT and RL across common test time strategies. Finally, we provide empirical evidence that this training method substantially improves test time scaling over standard training.

Chinchilla Approach 2 is among the most widely used methods for fitting neural scaling laws. Its parabolic approximation introduces systematic biases in compute-optimal allocation estimates, even on noise-free synthetic data. Applied to published Llama 3 IsoFLOP data at open frontier compute scales, these biases imply a parameter underallocation corresponding to 6.5% of the 3.8times10^{25} FLOP training budget and \1.4M (90% CI: 412K-\2.9M) in unnecessary compute at 50% H100 MFU. Simulated multimodal model misallocations show even greater opportunity costs due to higher loss surface asymmetry. Three sources of this error are examined: IsoFLOP sampling grid width (Taylor approximation accuracy), uncentered IsoFLOP sampling, and loss surface asymmetry (α\neq β$). Chinchilla Approach 3 largely eliminates these biases but is often regarded as less data-efficient, numerically unstable, prone to local minima, and harder to implement. Each concern is shown to be unfounded or addressable, especially when the partially linear structure of the objective is exploited via Variable Projection, enabling unbiased inference on all five loss surface parameters through a two-dimensional optimization that is well-conditioned, analytically differentiable, and amenable to dense, or even exhaustive, grid search. It may serve as a more convenient replacement for Approach 2 or a more scalable alternative for adaptations of Approach 3 to richer scaling law formulations.

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.

This technical note revisits the relationship between RaBitQ and TurboQuant under a unified comparison framework. We compare the two methods in terms of methodology, theoretical guarantees, and empirical performance, using a reproducible, transparent, and symmetric setup. Our results show that, despite the claimed advantage of TurboQuant, TurboQuant performs worse than RaBitQ in most tested settings of inner-product estimation, nearest-neighbor search and KV cache quantization. We further find that several reported runtime and recall results in the TurboQuant paper could not be reproduced from the released implementation under the stated configuration. Overall, this note clarifies the shared structure and genuine differences between the two lines of work, while documenting reproducibility issues in the experimental results reported by the TurboQuant paper.

Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidence shows that the proposed method outperforms the previous methods on both Cifar-10 and Cifar-100 benchmarks noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated.