Daily Papers

Large language models exhibit exceptional generalization capabilities, primarily attributed to the utilization of diversely sourced data. However, conventional practices in integrating this diverse data heavily rely on heuristic schemes, lacking theoretical guidance. This research tackles these limitations by investigating strategies based on low-cost proxies for data mixtures, with the aim of streamlining data curation to enhance training efficiency. Specifically, we propose a unified scaling law, termed BiMix, which accurately models the bivariate scaling behaviors of both data quantity and mixing proportions. We conduct systematic experiments and provide empirical evidence for the predictive power and fundamental principles of BiMix. Notably, our findings reveal that entropy-driven training-free data mixtures can achieve comparable or even better performance than more resource-intensive methods. We hope that our quantitative insights can shed light on further judicious research and development in cost-effective language modeling.

Training large language models with data collected from various domains can improve their performance on downstream tasks. However, given a fixed training budget, the sampling proportions of these different domains significantly impact the model's performance. How can we determine the domain weights across different data domains to train the best-performing model within constrained computational resources? In this paper, we provide a comprehensive overview of existing data mixture methods. First, we propose a fine-grained categorization of existing methods, extending beyond the previous offline and online classification. Offline methods are further grouped into heuristic-based, algorithm-based, and function fitting-based methods. For online methods, we categorize them into three groups: online min-max optimization, online mixing law, and other approaches by drawing connections with the optimization frameworks underlying offline methods. Second, we summarize the problem formulations, representative algorithms for each subtype of offline and online methods, and clarify the relationships and distinctions among them. Finally, we discuss the advantages and disadvantages of each method and highlight key challenges in the field of data mixture.

Determining the optimal data mixture for large language model training remains a challenging problem with an outsized impact on performance. In practice, language model developers continue to rely on heuristic exploration since no learning-based approach has emerged as a reliable solution. In this work, we propose to view the selection of training data mixtures as a black-box hyperparameter optimization problem, for which Bayesian Optimization is a well-established class of appropriate algorithms. Firstly, we cast data mixture learning as a sequential decision-making problem, in which we aim to find a suitable trade-off between the computational cost of training exploratory (proxy-) models and final mixture performance. Secondly, we systematically explore the properties of transferring mixtures learned at a small scale to larger-scale experiments, providing insights and highlighting opportunities for research at a modest scale. By proposing Multi-fidelity Bayesian Optimization as a suitable method in this common scenario, we introduce a natural framework to balance experiment cost with model fit, avoiding the risks of overfitting to smaller scales while minimizing the number of experiments at high cost. We present results for pre-training and instruction finetuning across models ranging from 1 million to 7 billion parameters, varying from simple architectures to state-of-the-art models and benchmarks spanning dozens of datasets. We demonstrate consistently strong results relative to a wide range of baselines, resulting inspeed-ups of over 500% in determining the best data mixture on our largest experiments. In addition, we broaden access to research by sharing ADMIRE IFT Runs, a dataset of 460 full training & evaluation runs worth over 13,000 GPU hours, greatly reducing the cost of conducting research in this area.

Pretraining data of large language models composes multiple domains (e.g., web texts, academic papers, codes), whose mixture proportions crucially impact the competence of outcome models. While existing endeavors rely on heuristics or qualitative strategies to tune the proportions, we discover the quantitative predictability of model performance regarding the mixture proportions in function forms, which we refer to as the data mixing laws. Fitting such functions on sample mixtures unveils model performance on unseen mixtures before actual runs, thus guiding the selection of an ideal data mixture. Furthermore, we propose nested use of the scaling laws of training steps, model sizes, and our data mixing law to enable predicting the performance of large models trained on massive data under various mixtures with only small-scale training. Moreover, experimental results verify that our method effectively optimizes the training mixture of a 1B model trained for 100B tokens in RedPajama, reaching a performance comparable to the one trained for 48% more steps on the default mixture. Extending the application of data mixing laws to continual training accurately predicts the critical mixture proportion that avoids catastrophic forgetting and outlooks the potential for dynamic data schedules

Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs) performance on challenging math, physics, and coding tasks. We explore three approaches: (1) EM-FT minimizes token-level entropy similarly to instruction finetuning, but on unlabeled outputs drawn from the model; (2) EM-RL: reinforcement learning with negative entropy as the only reward to maximize; (3) EM-INF: inference-time logit adjustment to reduce entropy without any training data or parameter updates. On Qwen-7B, EM-RL, without any labeled data, achieves comparable or better performance than strong RL baselines such as GRPO and RLOO that are trained on 60K labeled examples. Furthermore, EM-INF enables Qwen-32B to match or exceed the performance of proprietary models like GPT-4o, Claude 3 Opus, and Gemini 1.5 Pro on the challenging SciCode benchmark, while being 3x more efficient than self-consistency and sequential refinement. Our findings reveal that many pretrained LLMs possess previously underappreciated reasoning capabilities that can be effectively elicited through entropy minimization alone, without any labeled data or even any parameter updates.

While large and diverse datasets have driven recent advances in large models, identifying the optimal data mixture for pre-training and post-training remains a significant open problem. We address this challenge with FASTMIX, a novel framework that automates data mixture discovery while training only a single proxy model. Instead of relying on predefined heuristics or resource-intensive simulations, FASTMIX jointly optimizes mixture coefficients and model parameters, substantially improving efficiency and scalability over prior approaches. At the core of FASTMIX is a reformulation of mixture selection as a bilevel optimization problem. Under this reformulation, we show that optimizing mixture ratios is mathematically equivalent to assigning per-source loss weights under uniform source sampling. This embeds the mixture coefficients directly into the differentiable iterative optimization objective, enabling efficient, gradient-based optimization of both mixture and model. To solve the optimization problem, FASTMIX implements an approximate iterative optimization procedure, alternating between (i) updating model parameters on data sampled according to current mixture ratios (inner loop) and (ii) updating mixture ratios based on validation feedback (outer loop). Across pre- and post-training, FASTMIX outperforms baselines while drastically reducing search cost. Code (https://github.com/hrtan/fastmix)

We propose a method to optimize language model pre-training data mixtures through efficient approximation of the cross-entropy loss corresponding to each candidate mixture via a Mixture of Data Experts (MDE). We use this approximation as a source of additional features in a regression model, trained from observations of model loss for a small number of mixtures. Experiments with Transformer decoder-only language models in the range of 70M to 1B parameters on the SlimPajama dataset show that our method achieves significantly better performance than approaches that train regression models using only the mixture rates as input features. Combining this improved optimization method with an objective that takes into account cross-entropy on end task data leads to superior performance on few-shot downstream evaluations. We also provide theoretical insights on why aggregation of data expert predictions can provide good approximations to model losses for data mixtures.

It is often advantageous to train models on a subset of the available train examples, because the examples are of variable quality or because one would like to train with fewer examples, without sacrificing performance. We present Gradient Information Optimization (GIO), a scalable, task-agnostic approach to this data selection problem that requires only a small set of (unlabeled) examples representing a target distribution. GIO begins from a natural, information-theoretic objective that is intractable in practice. Our contribution is in showing that it can be made highly scalable through a simple relaxation of the objective and a highly efficient implementation. In experiments with machine translation, spelling correction, and image recognition, we show that GIO delivers outstanding results with very small train sets. These findings are robust to different representation models and hyperparameters for GIO itself. GIO is task- and domain-agnostic and can be applied out-of-the-box to new datasets and domains.

Pre-training datasets are typically collected from web content and lack inherent domain divisions. For instance, widely used datasets like Common Crawl do not include explicit domain labels, while manually curating labeled datasets such as The Pile is labor-intensive. Consequently, identifying an optimal pre-training data mixture remains a challenging problem, despite its significant benefits for pre-training performance. To address these challenges, we propose CLustering-based Iterative Data Mixture Bootstrapping (CLIMB), an automated framework that discovers, evaluates, and refines data mixtures in a pre-training setting. Specifically, CLIMB embeds and clusters large-scale datasets in a semantic space and then iteratively searches for optimal mixtures using a smaller proxy model and a predictor. When continuously trained on 400B tokens with this mixture, our 1B model exceeds the state-of-the-art Llama-3.2-1B by 2.0%. Moreover, we observe that optimizing for a specific domain (e.g., Social Sciences) yields a 5% improvement over random sampling. Finally, we introduce ClimbLab, a filtered 1.2-trillion-token corpus with 20 clusters as a research playground, and ClimbMix, a compact yet powerful 400-billion-token dataset designed for efficient pre-training that delivers superior performance under an equal token budget. We analyze the final data mixture, elucidating the characteristics of an optimal data mixture. Our data is available at: https://research.nvidia.com/labs/lpr/climb/

In standard autoregressive generation, an LLM predicts the next-token distribution, samples a discrete token, and then discards the distribution, passing only the sampled token as new input. To preserve this distribution's rich information, we propose Mixture of Inputs (MoI), a training-free method for autoregressive generation. After generating a token following the standard paradigm, we construct a new input that blends the generated discrete token with the previously discarded token distribution. Specifically, we employ a Bayesian estimation method that treats the token distribution as the prior, the sampled token as the observation, and replaces the conventional one-hot vector with the continuous posterior expectation as the new model input. MoI allows the model to maintain a richer internal representation throughout the generation process, resulting in improved text quality and reasoning capabilities. On mathematical reasoning, code generation, and PhD-level QA tasks, MoI consistently improves performance across multiple models including QwQ-32B, Nemotron-Super-49B, Gemma-3-27B, and DAPO-Qwen-32B, with no additional training and negligible computational overhead.

Training data compositions for Large Language Models (LLMs) can significantly affect their downstream performance. However, a thorough data ablation study exploring large sets of candidate data mixtures is typically prohibitively expensive since the full effect is seen only after training the models; this can lead practitioners to settle for sub-optimal data mixtures. We propose an efficient method for approximating data ablations which trains individual models on subsets of a training corpus and reuses them across evaluations of combinations of subsets. In continued pre-training experiments, we find that, given an arbitrary evaluation set, the perplexity score of a single model trained on a candidate set of data is strongly correlated with perplexity scores of parameter averages of models trained on distinct partitions of that data. From this finding, we posit that researchers and practitioners can conduct inexpensive simulations of data ablations by maintaining a pool of models that were each trained on partitions of a large training corpus, and assessing candidate data mixtures by evaluating parameter averages of combinations of these models. This approach allows for substantial improvements in amortized training efficiency -- scaling only linearly with respect to new data -- by enabling reuse of previous training computation, opening new avenues for improving model performance through rigorous, incremental data assessment and mixing.

As language models scale, the amount of data they require grows -- yet many target data sources, such as low-resource languages or specialized domains, are inherently limited in size. A common strategy is to mix this scarce but valuable target data with abundant generic data, which presents a fundamental trade-off: too little target data in the mixture underexposes the model to the target domain, while too much target data repeats the same examples excessively, yielding diminishing returns and eventual overfitting. We study this trade-off across more than 2,000 language-model training runs spanning multiple model and target dataset sizes, as well as several data types, including multilingual, domain-specific, and quality-filtered mixtures. Across all settings, we find that repetition is a central driver of target-domain performance, and that mixture training tolerates much higher repetition than single-source training: scarce target corpora can be reused 15-20 times, with the optimal number of repetitions depending on the target data size, compute budget, and model scale. Next, we introduce a repetition-aware mixture scaling law that accounts for the decreasing value of repeated target tokens and the regularizing role of generic data. Optimizing the scaling law provides a principled way to compute effective mixture configurations, yielding practical mixture recommendations for pretraining under data constraints.

We present MixtureVitae, an open-access pretraining corpus built to minimize legal risk while providing strong model performance. MixtureVitae follows a risk-mitigated sourcing strategy that combines public-domain and permissively licensed text (e.g., CC-BY/Apache) with carefully justified low-risk additions (e.g., government works and EU TDM-eligible sources), alongside targeted instruction, reasoning and synthetic data with documented provenance. We detail a transparent, multi-stage pipeline for license-aware filtering, safety and quality screening, and domain-aware mixing, and we release the dataset and curation recipes to support reproducible research. In controlled experiments using the open-sci-ref training protocol (fixed architectures at 130M/400M/1.3B/1.7B parameters; training budgets of 50B and 300B tokens), models trained on MixtureVitae consistently outperform other permissive datasets across a suite of standard benchmarks, and at the 1.7B/300B setting they surpass FineWeb-Edu and approach DCLM in the later stages of training. Performance is particularly strong on math/code and competitive on QA tasks. These results demonstrate that permissive-first, risk-mitigated data provides a practical and legally mitigated foundation for training capable LLMs, reducing reliance on indiscriminate web scraping without sacrificing competitiveness. Code: https://github.com/ontocord/mixturevitae

While data curation for Vision Language Models (VLMs) is increasingly active, public practice for constructing pretraining mixtures remains largely heuristic: practitioners stack datasets that pass quality filters, set cross-domain ratios by intuition, and lack a principled, attributable criterion for admitting new data, while frontier recipes remain undisclosed. We formulate data construction as a systematic mixture-optimization problem and turn it into a reproducible engineering discipline by decoupling the mixture into two orthogonal sub-problems: inter-class ratios across capabilities and intra-class ratios within a category. For inter-class allocation, we use a single-variable iterative search; for intra-class composition, we apply a multidimensional, dataset-level assessment scoring Quality and Difficulty, and formulate selection as a constrained convex optimization with a diversity objective. The DecoupleMix framework delivers two critical capabilities: guiding what data to collect next and rendering dataset validation a controlled, attributable experiment. Experiments show our approach consistently surpasses heuristic baselines. Moreover, optimal ratios discovered on small-scale proxies transfer seamlessly to larger scales without retuning. Using 80B additional multimodal continue-pretraining tokens, our VLM is competitive with strong open-source models trained with substantially larger multimodal budgets.

As large language models continue to scale, their growing computational and storage demands pose significant challenges for real-world deployment. In this work, we investigate redundancy within Transformer-based models and propose an entropy-based pruning strategy to enhance efficiency while maintaining performance. Empirical analysis reveals that the entropy of hidden representations decreases in the early blocks but progressively increases across most subsequent blocks. This trend suggests that entropy serves as a more effective measure of information richness within computation blocks. Unlike cosine similarity, which primarily captures geometric relationships, entropy directly quantifies uncertainty and information content, making it a more reliable criterion for pruning. Extensive experiments demonstrate that our entropy-based pruning approach surpasses cosine similarity-based methods in reducing model size while preserving accuracy, offering a promising direction for efficient model deployment.

The data mixture for large language model pre-training significantly impacts performance, yet how to determine an effective mixture remains unclear. We propose RegMix to automatically identify a high-performing data mixture by formulating it as a regression task. RegMix involves training a set of small models with diverse data mixtures and fitting a regression model to predict their performance given their respective mixtures. With the fitted regression model, we simulate the top-ranked mixture and use it to train a large-scale model with orders of magnitude more compute. To empirically validate RegMix, we train 512 models with 1M parameters for 1B tokens of different mixtures to fit the regression model and find the optimal mixture. Using this mixture we train a 1B parameter model for 25B tokens (i.e. 1000x larger and 25x longer) which we find performs best among 64 candidate 1B parameter models with other mixtures. Further, our method demonstrates superior performance compared to human selection and achieves results that match or surpass DoReMi, while utilizing only 10% of the compute budget. Our experiments also show that (1) Data mixtures significantly impact performance with single-task performance variations of up to 14.6%; (2) Web corpora rather than data perceived as high-quality like Wikipedia have the strongest positive correlation with downstream performance; (3) Domains interact in complex ways often contradicting common sense, thus automatic approaches like RegMix are needed; (4) Data mixture effects transcend scaling laws, and our approach captures the complexity by considering all domains together. Our code is available at https://github.com/sail-sg/regmix.

Large Language Models (LLMs) and agent-based systems often struggle with compositional generalization due to a data bottleneck in which complex skill combinations follow a long-tailed, power-law distribution, limiting both instruction-following performance and generalization in agent-centric tasks. To address this challenge, we propose STEPS, a Skill Taxonomy guided Entropy-based Post-training data Synthesis framework for generating compositionally challenging data. STEPS explicitly targets compositional generalization by uncovering latent relationships among skills and organizing them into an interpretable, hierarchical skill taxonomy using structural information theory. Building on this taxonomy, we formulate data synthesis as a constrained information maximization problem, selecting skill combinations that maximize marginal structural information within the hierarchy while preserving semantic coherence. Experiments on challenging instruction-following benchmarks show that STEPS outperforms existing data synthesis baselines, while also yielding improved compositional generalization in downstream agent-based evaluations.

The composition of training data mixtures is critical for effectively training large language models (LLMs), as it directly impacts their performance on downstream tasks. Our goal is to identify an optimal data mixture to specialize an LLM for a specific task with access to only a few examples. Traditional approaches to this problem include ad-hoc reweighting methods, importance sampling, and gradient alignment techniques. This paper focuses on gradient alignment and introduces Dynamic Gradient Alignment (DGA), a scalable online gradient alignment algorithm. DGA dynamically estimates the pre-training data mixture on which the models' gradients align as well as possible with those of the model on the specific task. DGA is the first gradient alignment approach that incurs minimal overhead compared to standard pre-training and outputs a competitive model, eliminating the need for retraining the model. Experimentally, we demonstrate significant improvements over importance sampling in two key scenarios: (i) when the pre-training set is small and importance sampling overfits due to limited data; and (ii) when there is insufficient specialized data, trapping importance sampling on narrow pockets of data. Our findings underscore the effectiveness of gradient alignment methods in optimizing training data mixtures, particularly in data-constrained environments, and offer a practical solution for enhancing LLM performance on specific tasks with limited data availability.

We propose Score-of-Mixture Training (SMT), a novel framework for training one-step generative models by minimizing a class of divergences called the alpha-skew Jensen-Shannon divergence. At its core, SMT estimates the score of mixture distributions between real and fake samples across multiple noise levels. Similar to consistency models, our approach supports both training from scratch (SMT) and distillation using a pretrained diffusion model, which we call Score-of-Mixture Distillation (SMD). It is simple to implement, requires minimal hyperparameter tuning, and ensures stable training. Experiments on CIFAR-10 and ImageNet 64x64 show that SMT/SMD are competitive with and can even outperform existing methods.

Recently, continual learning (CL) has gained significant interest because it enables deep learning models to acquire new knowledge without forgetting previously learnt information. However, most existing works require knowing the task identities and boundaries, which is not realistic in a real context. In this paper, we address a more challenging and realistic setting in CL, namely the Task-Free Continual Learning (TFCL) in which a model is trained on non-stationary data streams with no explicit task information. To address TFCL, we introduce an evolved mixture model whose network architecture is dynamically expanded to adapt to the data distribution shift. We implement this expansion mechanism by evaluating the probability distance between the knowledge stored in each mixture model component and the current memory buffer using the Hilbert Schmidt Independence Criterion (HSIC). We further introduce two simple dropout mechanisms to selectively remove stored examples in order to avoid memory overload while preserving memory diversity. Empirical results demonstrate that the proposed approach achieves excellent performance.

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot product function. In this paper, we propose a new representation learning framework for dense retrieval. Instead of learning a vector for each query and document, our framework learns a multivariate distribution and uses negative multivariate KL divergence to compute the similarity between distributions. For simplicity and efficiency reasons, we assume that the distributions are multivariate normals and then train large language models to produce mean and variance vectors for these distributions. We provide a theoretical foundation for the proposed framework and show that it can be seamlessly integrated into the existing approximate nearest neighbor algorithms to perform retrieval efficiently. We conduct an extensive suite of experiments on a wide range of datasets, and demonstrate significant improvements compared to competitive dense retrieval models.

Determining an effective data mixture is a key factor in Large Language Model (LLM) pre-training, where models must balance general competence with proficiency on hard tasks such as math and code. However, identifying an optimal mixture remains an open challenge, as existing approaches either rely on unreliable tiny-scale proxy experiments or require prohibitively expensive large-scale exploration. To address this, we propose Decouple Searching from Training Mix (DeMix), a novel framework that leverages model merging to predict optimal data ratios. Instead of training proxy models for every sampled mixture, DeMix trains component models on candidate datasets at scale and derives data mixture proxies via weighted model merging. This paradigm decouples search from training costs, enabling evaluation of unlimited sampled mixtures without extra training burden and thus facilitating better mixture discovery through more search trials. Extensive experiments demonstrate that DeMix breaks the trade-off between sufficiency, accuracy and efficiency, obtaining the optimal mixture with higher benchmark performance at lower search cost. Additionally, we release the DeMix Corpora, a comprehensive 22T-token dataset comprising high-quality pre-training data with validated mixtures to facilitate open research. Our code and DeMix Corpora is available at https://github.com/Lucius-lsr/DeMix.

Multimodal large language models (MLLMs) incur substantial inference cost due to the processing of hundreds of visual tokens per image. Although token pruning has proven effective for accelerating inference, determining when and where to prune remains largely heuristic. Existing approaches typically rely on static, empirically selected layers, which limit interpretability and transferability across models. In this work, we introduce a matrix-entropy perspective and identify an "Entropy Collapse Layer" (ECL), where the information content of visual representations exhibits a sharp and consistent drop, which provides a principled criterion for selecting the pruning stage. Building on this observation, we propose EntropyPrune, a novel matrix-entropy-guided token pruning framework that quantifies the information value of individual visual tokens and prunes redundant ones without relying on attention maps. Moreover, to enable efficient computation, we exploit the spectral equivalence of dual Gram matrices, reducing the complexity of entropy computation and yielding up to a 64x theoretical speedup. Extensive experiments on diverse multimodal benchmarks demonstrate that EntropyPrune consistently outperforms state-of-the-art pruning methods in both accuracy and efficiency. On LLaVA-1.5-7B, our method achieves a 68.2% reduction in FLOPs while preserving 96.0% of the original performance. Furthermore, EntropyPrune generalizes effectively to high-resolution and video-based models, highlighting the strong robustness and scalability in practical MLLM acceleration. The code will be publicly available at https://github.com/YahongWang1/EntropyPrune.

Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorov's axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on Neural Mixture Densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DNMMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorov's axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.

Mixture-of-Experts (MoE) models have shown remarkable capability in instruction tuning, especially when the number of tasks scales. However, previous methods simply merge all training tasks (e.g. creative writing, coding, and mathematics) and apply fixed sampling weights, without considering the importance of different tasks as the model training state changes. In this way, the most helpful data cannot be effectively distinguished, leading to suboptimal model performance. To reduce the potential redundancies of datasets, we make the first attempt and propose a novel dynamic data mixture for MoE instruction tuning. Specifically, inspired by MoE's token routing preference, we build dataset-level representations and then capture the subtle differences among datasets. Finally, we propose to dynamically adjust the sampling weight of datasets by their inter-redundancies, thus maximizing global performance under a limited training budget. The experimental results on two MoE models demonstrate the effectiveness of our approach on both downstream knowledge \& reasoning tasks and open-ended queries. Code and models are available at https://github.com/Spico197/MoE-SFT .

Effective implementations of sampling-based probabilistic inference often require manually constructed, model-specific proposals. Inspired by recent progresses in meta-learning for training learning agents that can generalize to unseen environments, we propose a meta-learning approach to building effective and generalizable MCMC proposals. We parametrize the proposal as a neural network to provide fast approximations to block Gibbs conditionals. The learned neural proposals generalize to occurrences of common structural motifs across different models, allowing for the construction of a library of learned inference primitives that can accelerate inference on unseen models with no model-specific training required. We explore several applications including open-universe Gaussian mixture models, in which our learned proposals outperform a hand-tuned sampler, and a real-world named entity recognition task, in which our sampler yields higher final F1 scores than classical single-site Gibbs sampling.

Training machine learning models on massive datasets is expensive and time-consuming. Dataset distillation addresses this by creating a small synthetic dataset that achieves the same performance as the full dataset. Recent methods use diffusion models to generate distilled data, either by promoting diversity or matching training gradients. However, existing approaches produce redundant training signals, where samples convey overlapping information. Empirically, disjoint subsets of distilled datasets capture 80-90% overlapping signals. This redundancy stems from optimizing visual diversity or average training dynamics without accounting for similarity across samples, leading to datasets where multiple samples share similar information rather than complementary knowledge. We propose learnability-driven dataset distillation, which constructs synthetic datasets incrementally through successive stages. Starting from a small set, we train a model and generate new samples guided by learnability scores that identify what the current model can learn from, creating an adaptive curriculum. We introduce Learnability-Guided Diffusion (LGD), which balances training utility for the current model with validity under a reference model to generate curriculum-aligned samples. Our approach reduces redundancy by 39.1%, promotes specialization across training stages, and achieves state-of-the-art results on ImageNet-1K (60.1%), ImageNette (87.2%), and ImageWoof (72.9%). Our code is available on our project page https://jachansantiago.github.io/learnability-guided-distillation/.

The growing computational demands of large language models (LLMs) make efficient inference and activation strategies increasingly critical. While recent approaches, such as Mixture-of-Experts (MoE), leverage selective activation but require specialized training, training-free sparse activation methods offer broader applicability and superior resource efficiency through their plug-and-play design. However, many existing methods rely solely on hidden state magnitudes to determine activation, resulting in high approximation errors and suboptimal inference accuracy. To address these limitations, we propose WINA (Weight Informed Neuron Activation), a novel, simple, and training-free sparse activation framework that jointly considers hidden state magnitudes and the column-wise ell_2-norms of weight matrices. We show that this leads to a sparsification strategy that obtains optimal approximation error bounds with theoretical guarantees tighter than existing techniques. Empirically, WINA also outperforms state-of-the-art methods (e.g., TEAL) by up to 2.94% in average performance at the same sparsity levels, across a diverse set of LLM architectures and datasets. These results position WINA as a new performance frontier for training-free sparse activation in LLM inference, advancing training-free sparse activation methods and setting a robust baseline for efficient inference. The source code is available at https://github.com/microsoft/wina.

Autoregressive language models are trained by minimizing the cross-entropy of the model distribution Q relative to the data distribution P -- that is, minimizing the forward cross-entropy, which is equivalent to maximum likelihood estimation (MLE). We have observed that models trained in this way may "over-generalize", in the sense that they produce non-human-like text. Moreover, we believe that reverse cross-entropy, i.e., the cross-entropy of P relative to Q, is a better reflection of how a human would evaluate text generated by a model. Hence, we propose learning with MixCE, an objective that mixes the forward and reverse cross-entropies. We evaluate models trained with this objective on synthetic data settings (where P is known) and real data, and show that the resulting models yield better generated text without complex decoding strategies. Our code and models are publicly available at https://github.com/bloomberg/mixce-acl2023

A number of different architectures and loss functions have been applied to the problem of self-supervised learning (SSL), with the goal of developing embeddings that provide the best possible pre-training for as-yet-unknown, lightly supervised downstream tasks. One of these SSL criteria is to maximize the entropy of a set of embeddings in some compact space. But the goal of maximizing the embedding entropy often depends--whether explicitly or implicitly--upon high dimensional entropy estimates, which typically perform poorly in more than a few dimensions. In this paper, we motivate an effective entropy maximization criterion (E2MC), defined in terms of easy-to-estimate, low-dimensional constraints. We demonstrate that using it to continue training an already-trained SSL model for only a handful of epochs leads to a consistent and, in some cases, significant improvement in downstream performance. We perform careful ablation studies to show that the improved performance is due to the proposed add-on criterion. We also show that continued pre-training with alternative criteria does not lead to notable improvements, and in some cases, even degrades performance.

This paper focuses on task-agnostic prompt compression for better generalizability and efficiency. Considering the redundancy in natural language, existing approaches compress prompts by removing tokens or lexical units according to their information entropy obtained from a causal language model such as LLaMa-7B. The challenge is that information entropy may be a suboptimal compression metric: (i) it only leverages unidirectional context and may fail to capture all essential information needed for prompt compression; (ii) it is not aligned with the prompt compression objective. To address these issues, we propose a data distillation procedure to derive knowledge from an LLM to compress prompts without losing crucial information, and meantime, introduce an extractive text compression dataset. We formulate prompt compression as a token classification problem to guarantee the faithfulness of the compressed prompt to the original one, and use a Transformer encoder as the base architecture to capture all essential information for prompt compression from the full bidirectional context. Our approach leads to lower latency by explicitly learning the compression objective with smaller models such as XLM-RoBERTa-large and mBERT. We evaluate our method on both in-domain and out-of-domain datasets, including MeetingBank, LongBench, ZeroScrolls, GSM8K, and BBH. Despite its small size, our model shows significant performance gains over strong baselines and demonstrates robust generalization ability across different LLMs. Additionally, our model is 3x-6x faster than existing prompt compression methods, while accelerating the end-to-end latency by 1.6x-2.9x with compression ratios of 2x-5x.

Selecting the best data mixture is critical for successful Supervised Fine-Tuning (SFT) of Multimodal Large Language Models. However, determining the optimal mixture weights across multiple domain-specific datasets remains a significant bottleneck due to the combinatorial search space and the high cost associated with even a single training run. This is the so-called Data Mixture Optimization (DMO) problem. On the other hand, model merging unifies domain-specific experts through parameter interpolation. This strategy is efficient, as it only requires a single training run per domain, yet oftentimes leads to suboptimal models. In this work, we take the best of both worlds, studying model merging as an efficient strategy for estimating the performance of different data mixtures. We train domain-specific multimodal experts and evaluate their weighted parameter-space combinations to estimate the efficacy of corresponding data mixtures. We conduct extensive experiments on 14 multimodal benchmarks, and empirically demonstrate that the merged proxy models exhibit a high rank correlation with models trained on actual data mixtures. This decouples the search for optimal mixtures from the resource-intensive training process, thereby providing a scalable and efficient strategy for navigating the complex landscape of mixture weights. Code is publicly available at https://github.com/BerasiDavide/mLLMs_merging_4_DMO.

Data mixing -- determining the ratios of data from different domains -- is a first-order concern for training language models (LMs). While existing mixing methods show promise, they fall short when applied during real-world LM development. We present Olmix, a framework that addresses two such challenges. First, the configuration space for developing a mixing method is not well understood -- design choices across existing methods lack justification or consensus and overlook practical issues like data constraints. We conduct a comprehensive empirical study of this space, identifying which design choices lead to a strong mixing method. Second, in practice, the domain set evolves throughout LM development as datasets are added, removed, partitioned, and revised -- a problem setting largely unaddressed by existing works, which assume fixed domains. We study how to efficiently recompute the mixture after the domain set is updated, leveraging information from past mixtures. We introduce mixture reuse, a mechanism that reuses existing ratios and recomputes ratios only for domains affected by the update. Over a sequence of five domain-set updates mirroring real-world LM development, mixture reuse matches the performance of fully recomputing the mix after each update with 74% less compute and improves over training without mixing by 11.6% on downstream tasks.

Language model performance depends on identifying the optimal mixture of data groups to train on (e.g., law, code, math). Prior work has proposed a diverse set of methods to efficiently learn mixture proportions, ranging from fitting regression models over training runs to dynamically updating proportions throughout training. Surprisingly, we find that no existing method consistently outperforms a simple stratified sampling baseline in terms of average test perplexity. To understand this inconsistency, we unify existing methods into a standard framework, showing they are equivalent to solving a common optimization problem: minimize average loss subject to a method-specific mixing law -- an implicit assumption on the relationship between loss and mixture proportions. This framework suggests that measuring the fidelity of a method's mixing law can offer insights into its performance. Empirically, we find that existing methods set their mixing law parameters inaccurately, resulting in the inconsistent mixing performance we observe. Using this insight, we derive a new online method named Aioli, which directly estimates the mixing law parameters throughout training and uses them to dynamically adjust proportions. Aioli outperforms stratified sampling on 6 out of 6 datasets by an average of 0.27 test perplexity points, whereas existing methods fail to consistently beat stratified sampling, doing up to 6.9 points worse. Moreover, in a practical setting where proportions are learned on shorter runs due to computational constraints, Aioli can dynamically adjust these proportions over the full training run, consistently improving performance over existing methods by up to 12.012 test perplexity points.

Pre-training data mixtures are commonly tuned by running small-scale experiments and extrapolating to the target training budget. When high-quality data is scarce and must be repeated, this extrapolation frequently fails, but the source of the failure has not been isolated. We show that a primary culprit is a repetition mismatch: because high-quality datasets are small, their repetition rate changes as the training budget grows, shifting the optimal mixture in ways that small-scale proxy experiments do not anticipate. A subsampling procedure that matches the target repetition rate controls for this effect. In a two-source setting combining limited high-quality data with web crawl, a single repetition-controlled experiment using only 1/16 of the target tokens recovers a mixture within 0.05 of the optimum for a 757M parameter model, compared to an error of 0.75 without repetition control. Achieving comparable accuracy without repetition control requires three to four horizons, consuming 44 to 94% of the target token budget. With three data sources, the larger mixture space requires more than a single experiment to constrain, but the approach remains effective: at the 757M scale, just two repetition-controlled horizons recover the optimal mixture, outperforming baselines that instead require the full two-source experiments to construct. Our results reveal that repetition dynamics, not scale alone, shape whether small-scale mixture experiments generalize. More broadly, they suggest that data repetition deserves treatment as a first-class variable in mixture optimization, rather than an inconvenient side effect of limited data.

Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem, particularly in the case of high-dimensional discrete distributions. Current approaches typically rely on embedding discrete data into a continuous space and applying neural estimators originally designed for continuous distributions, a process that may not fully capture the discrete nature of the underlying data. We consider Continuous-Time Markov Chains (CTMCs), stochastic processes on discrete state-spaces which have gained popularity due to their generative modeling applications. In this work, we introduce INFO-SEDD, a novel method for estimating information-theoretic quantities of discrete data, including mutual information and entropy. Our approach requires the training of a single parametric model, offering significant computational and memory advantages. Additionally, it seamlessly integrates with pretrained networks, allowing for efficient reuse of pretrained generative models. To evaluate our approach, we construct a challenging synthetic benchmark. Our experiments demonstrate that INFO-SEDD is robust and outperforms neural competitors that rely on embedding techniques. Moreover, we validate our method on a real-world task: estimating the entropy of an Ising model. Overall, INFO-SEDD outperforms competing methods and shows scalability to high-dimensional scenarios, paving the way for new applications where estimating MI between discrete distribution is the focus. The promising results in this complex, high-dimensional scenario highlight INFO-SEDD as a powerful new estimator in the toolkit for information-theoretical analysis.

Continual pre-training is widely used to adapt LLMs to target languages and domains, yet the mixture ratio of training data remains a sensitive hyperparameter that is expensive to tune: they must be fixed before training begins, and a suboptimal choice can waste weeks of compute. In this work, we propose OptiMer, which decouples ratio selection from training: we train one CPT model per dataset, extract each model's distribution vector, which represents the parameter shift induced by that dataset, and search for optimal composition weights post-hoc via Bayesian optimization. Experiments on Gemma 3 27B across languages (Japanese, Chinese) and domains (Math, Code) show that OptiMer consistently outperforms data mixture and model averaging baselines with 15-35 times lower search cost. Key findings reveal that 1) the optimized weights can be interpreted as data mixture ratios, and retraining with these ratios improves data mixture CPT, and 2) the same vector pool can be re-optimized for a given objective without any retraining, producing target-tailored models on demand. Our work establishes that data mixture ratio selection, traditionally a pre-training decision, can be reformulated as a post-hoc optimization over distribution vectors, offering a more flexible paradigm for continual pre-training.

Multimodal reward models are crucial for aligning multimodal large language models with human preferences. Recent works have incorporated reasoning capabilities into these models, achieving promising results. However, training these models suffers from two critical challenges: (1) the inherent noise in preference datasets, which degrades model performance, and (2) the inefficiency of conventional training methods, which ignore the differences in sample difficulty. In this paper, we identify a strong correlation between response entropy and accuracy, indicating that entropy can serve as a reliable and unsupervised proxy for annotation noise and sample difficulty. Based on this insight, we propose a novel Entropy-Guided Training (EGT) approach for multimodal reasoning reward models, which combines two strategies: (1) entropy-guided data curation to mitigate the impact of unreliable samples, and (2) an entropy-guided training strategy that progressively introduces more complex examples. Extensive experiments across three benchmarks show that the EGT-trained model consistently outperforms state-of-the-art multimodal reward models.

User data confidentiality protection is becoming a rising challenge in the present deep learning research. Without access to data, conventional data-driven model compression faces a higher risk of performance degradation. Recently, some works propose to generate images from a specific pretrained model to serve as training data. However, the inversion process only utilizes biased feature statistics stored in one model and is from low-dimension to high-dimension. As a consequence, it inevitably encounters the difficulties of generalizability and inexact inversion, which leads to unsatisfactory performance. To address these problems, we propose MixMix based on two simple yet effective techniques: (1) Feature Mixing: utilizes various models to construct a universal feature space for generalized inversion; (2) Data Mixing: mixes the synthesized images and labels to generate exact label information. We prove the effectiveness of MixMix from both theoretical and empirical perspectives. Extensive experiments show that MixMix outperforms existing methods on the mainstream compression tasks, including quantization, knowledge distillation, and pruning. Specifically, MixMix achieves up to 4% and 20% accuracy uplift on quantization and pruning, respectively, compared to existing data-free compression work.

In recent years, rapid progress has been made on the problem of single-channel sound separation using supervised training of deep neural networks. In such supervised approaches, a model is trained to predict the component sources from synthetic mixtures created by adding up isolated ground-truth sources. Reliance on this synthetic training data is problematic because good performance depends upon the degree of match between the training data and real-world audio, especially in terms of the acoustic conditions and distribution of sources. The acoustic properties can be challenging to accurately simulate, and the distribution of sound types may be hard to replicate. In this paper, we propose a completely unsupervised method, mixture invariant training (MixIT), that requires only single-channel acoustic mixtures. In MixIT, training examples are constructed by mixing together existing mixtures, and the model separates them into a variable number of latent sources, such that the separated sources can be remixed to approximate the original mixtures. We show that MixIT can achieve competitive performance compared to supervised methods on speech separation. Using MixIT in a semi-supervised learning setting enables unsupervised domain adaptation and learning from large amounts of real world data without ground-truth source waveforms. In particular, we significantly improve reverberant speech separation performance by incorporating reverberant mixtures, train a speech enhancement system from noisy mixtures, and improve universal sound separation by incorporating a large amount of in-the-wild data.

Production deployments in complex systems require ML architectures to be highly efficient and usable against multiple tasks. Particularly demanding are classification problems in which data arrives in a streaming fashion and each class is presented separately. Recent methods with stochastic gradient learning have been shown to struggle in such setups or have limitations like memory buffers, and being restricted to specific domains that disable its usage in real-world scenarios. For this reason, we present a fully differentiable architecture based on the Mixture of Experts model, that enables the training of high-performance classifiers when examples from each class are presented separately. We conducted exhaustive experiments that proved its applicability in various domains and ability to learn online in production environments. The proposed technique achieves SOTA results without a memory buffer and clearly outperforms the reference methods.

Mixture-of-Experts large language models (MoE-LLMs) marks a significant step forward of language models, however, they encounter two critical challenges in practice: 1) expert parameters lead to considerable memory consumption and loading latency; and 2) the current activated experts are redundant, as many tokens may only require a single expert. Motivated by these issues, we investigate the MoE-LLMs and make two key observations: a) different experts exhibit varying behaviors on activation reconstruction error, routing scores, and activated frequencies, highlighting their differing importance, and b) not all tokens are equally important -- only a small subset is critical. Building on these insights, we propose MC-MoE, a training-free Mixture-Compressor for MoE-LLMs, which leverages the significance of both experts and tokens to achieve an extreme compression. First, to mitigate storage and loading overheads, we introduce Pre-Loading Mixed-Precision Quantization, which formulates the adaptive bit-width allocation as a Linear Programming problem, where the objective function balances multi-factors reflecting the importance of each expert. Additionally, we develop Online Dynamic Pruning, which identifies important tokens to retain and dynamically select activated experts for other tokens during inference to optimize efficiency while maintaining performance. Our MC-MoE integrates static quantization and dynamic pruning to collaboratively achieve extreme compression for MoE-LLMs with less accuracy loss, ensuring an optimal trade-off between performance and efficiency. Extensive experiments confirm the effectiveness of our approach. For instance, at 2.54 bits, MC-MoE compresses 76.6% of the model, with only a 3.8% average accuracy loss. During dynamic inference, we further reduce activated parameters by 15%, with a performance drop of less than 0.6%.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

LLMs have boosted progress in many AI applications. Recently, there were attempts to distill the vast knowledge of LLMs into information retrieval systems. Those distillation methods mostly use output probabilities of LLMs which are unavailable in the latest black-box LLMs. We propose Syntriever, a training framework for retrievers using synthetic data from black-box LLMs. Syntriever consists of two stages. Firstly in the distillation stage, we synthesize relevant and plausibly irrelevant passages and augmented queries using chain-of-thoughts for the given queries. LLM is asked to self-verify the synthetic data for possible hallucinations, after which retrievers are trained with a loss designed to cluster the embeddings of relevant passages. Secondly in the alignment stage, we align the retriever with the preferences of LLMs. We propose a preference modeling called partial Plackett-Luce ranking to learn LLM preferences with regularization which prevents the model from deviating excessively from that trained in the distillation stage. Experiments show that Syntriever achieves state-of-the-art performances on benchmark datasets from various domains in nDCG@K. The code is available at https://github.com/kmswin1/Syntriever{https://github.com/kmswin1/Syntriever}.

Discrete diffusion or flow models could enable faster and more controllable sequence generation than autoregressive models. We show that na\"ive linear flow matching on the simplex is insufficient toward this goal since it suffers from discontinuities in the training target and further pathologies. To overcome this, we develop Dirichlet flow matching on the simplex based on mixtures of Dirichlet distributions as probability paths. In this framework, we derive a connection between the mixtures' scores and the flow's vector field that allows for classifier and classifier-free guidance. Further, we provide distilled Dirichlet flow matching, which enables one-step sequence generation with minimal performance hits, resulting in O(L) speedups compared to autoregressive models. On complex DNA sequence generation tasks, we demonstrate superior performance compared to all baselines in distributional metrics and in achieving desired design targets for generated sequences. Finally, we show that our classifier-free guidance approach improves unconditional generation and is effective for generating DNA that satisfies design targets. Code is available at https://github.com/HannesStark/dirichlet-flow-matching.

Knowledge distillation aims to learn a lightweight student network from a pre-trained teacher network. In practice, existing knowledge distillation methods are usually infeasible when the original training data is unavailable due to some privacy issues and data management considerations. Therefore, data-free knowledge distillation approaches proposed to collect training instances from the Internet. However, most of them have ignored the common distribution shift between the instances from original training data and webly collected data, affecting the reliability of the trained student network. To solve this problem, we propose a novel method dubbed ``Knowledge Distillation between Different Distributions" (KD^{3}), which consists of three components. Specifically, we first dynamically select useful training instances from the webly collected data according to the combined predictions of teacher network and student network. Subsequently, we align both the weighted features and classifier parameters of the two networks for knowledge memorization. Meanwhile, we also build a new contrastive learning block called MixDistribution to generate perturbed data with a new distribution for instance alignment, so that the student network can further learn a distribution-invariant representation. Intensive experiments on various benchmark datasets demonstrate that our proposed KD^{3} can outperform the state-of-the-art data-free knowledge distillation approaches.

Instruction tuning is crucial for aligning Large Language Models (LLMs), yet the quality of instruction-following data varies significantly. While high-quality data is paramount, it is often scarce; conversely, abundant low-quality data is frequently discarded, leading to substantial information loss. Existing data augmentation methods struggle to augment this low-quality data effectively, and the evaluation of such techniques remains poorly defined. To address this, we formally define the task of Instruction Distillation: distilling multiple low-quality and redundant inputs into high-quality and coherent instruction-output pairs. Specifically, we introduce a comprehensive data construction pipeline to create MIXTURE, a 144K-sample dataset pairing low-quality or semantically redundant imperfect instruction clusters with their high-quality distillations. We then introduce LM-Mixup, by first performing supervised fine-tuning on MIXTURE and then optimizing it with reinforcement learning. This process uses three complementary reward signals: quality, semantic alignment, and format compliance, via Group Relative Policy Optimization (GRPO). We demonstrate that LM-Mixup effectively augments imperfect datasets: fine-tuning LLMs on its distilled data, which accounts for only about 3% of the entire dataset, not only surpasses full-dataset training but also competes with state-of-the-art high-quality data selection methods across multiple benchmarks. Our work establishes that low-quality data is a valuable resource when properly distilled and augmented with LM-Mixup, significantly enhancing the efficiency and performance of instruction-tuned LLMs.

Neural sentence embedding models for dense retrieval typically rely on binary relevance labels, treating query-document pairs as either relevant or irrelevant. However, real-world relevance often exists on a continuum, and recent advances in large language models (LLMs) have made it feasible to scale the generation of fine-grained graded relevance labels. In this work, we propose BiXSE, a simple and effective pointwise training method that optimizes binary cross-entropy (BCE) over LLM-generated graded relevance scores. BiXSE interprets these scores as probabilistic targets, enabling granular supervision from a single labeled query-document pair per query. Unlike pairwise or listwise losses that require multiple annotated comparisons per query, BiXSE achieves strong performance with reduced annotation and compute costs by leveraging in-batch negatives. Extensive experiments across sentence embedding (MMTEB) and retrieval benchmarks (BEIR, TREC-DL) show that BiXSE consistently outperforms softmax-based contrastive learning (InfoNCE), and matches or exceeds strong pairwise ranking baselines when trained on LLM-supervised data. BiXSE offers a robust, scalable alternative for training dense retrieval models as graded relevance supervision becomes increasingly accessible.

Optimizing data mixtures is essential for unlocking the full potential of large language models (LLMs), yet identifying the optimal composition remains computationally prohibitive due to reliance on heuristic trials or expensive proxy training. To address this, we introduce MergeMix, a novel approach that efficiently determines optimal data mixing ratios by repurposing model merging weights as a high-fidelity, low-cost performance proxy. By training domain-specific experts on minimal tokens and optimizing their merging weights against downstream benchmarks, MergeMix effectively optimizes the performance of data mixtures without incurring the cost of full-scale training. Extensive experiments on models with 8B and 16B parameters validate that MergeMix achieves performance comparable to or surpassing exhaustive manual tuning while drastically reducing search costs. Furthermore, MergeMix exhibits high rank consistency (Spearman ρ> 0.9) and strong cross-scale transferability, offering a scalable, automated solution for data mixture optimization.

The progress of composed image retrieval (CIR), a popular research direction in image retrieval, where a combined visual and textual query is used, is held back by the absence of high-quality training and evaluation data. We introduce a new evaluation dataset, i-CIR, which, unlike existing datasets, focuses on an instance-level class definition. The goal is to retrieve images that contain the same particular object as the visual query, presented under a variety of modifications defined by textual queries. Its design and curation process keep the dataset compact to facilitate future research, while maintaining its challenge-comparable to retrieval among more than 40M random distractors-through a semi-automated selection of hard negatives. To overcome the challenge of obtaining clean, diverse, and suitable training data, we leverage pre-trained vision-and-language models (VLMs) in a training-free approach called BASIC. The method separately estimates query-image-to-image and query-text-to-image similarities, performing late fusion to upweight images that satisfy both queries, while down-weighting those that exhibit high similarity with only one of the two. Each individual similarity is further improved by a set of components that are simple and intuitive. BASIC sets a new state of the art on i-CIR but also on existing CIR datasets that follow a semantic-level class definition. Project page: https://vrg.fel.cvut.cz/icir/.

The pretraining data of today's strongest language models is opaque. In particular, little is known about the proportions of various domains or languages represented. In this work, we tackle a task which we call data mixture inference, which aims to uncover the distributional make-up of training data. We introduce a novel attack based on a previously overlooked source of information -- byte-pair encoding (BPE) tokenizers, used by the vast majority of modern language models. Our key insight is that the ordered list of merge rules learned by a BPE tokenizer naturally reveals information about the token frequencies in its training data: the first merge is the most common byte pair, the second is the most common pair after merging the first token, and so on. Given a tokenizer's merge list along with data samples for each category of interest, we formulate a linear program that solves for the proportion of each category in the tokenizer's training set. Importantly, to the extent to which tokenizer training data is representative of the pretraining data, we indirectly learn about the pretraining data. In controlled experiments, we show that our attack recovers mixture ratios with high precision for tokenizers trained on known mixtures of natural languages, programming languages, and data sources. We then apply our approach to off-the-shelf tokenizers released with recent LMs. We confirm much publicly disclosed information about these models, and also make several new inferences: GPT-4o's tokenizer is much more multilingual than its predecessors, training on 39% non-English data; Llama3 extends GPT-3.5's tokenizer primarily for multilingual (48%) use; GPT-3.5's and Claude's tokenizers are trained on predominantly code (~60%). We hope our work sheds light on current design practices for pretraining data, and inspires continued research into data mixture inference for LMs.

We propose a fully data-driven approach to designing mutual information (MI) estimators. Since any MI estimator is a function of the observed sample from two random variables, we parameterize this function with a neural network (MIST) and train it end-to-end to predict MI values. Training is performed on a large meta-dataset of 625,000 synthetic joint distributions with known ground-truth MI. To handle variable sample sizes and dimensions, we employ a two-dimensional attention scheme ensuring permutation invariance across input samples. To quantify uncertainty, we optimize a quantile regression loss, enabling the estimator to approximate the sampling distribution of MI rather than return a single point estimate. This research program departs from prior work by taking a fully empirical route, trading universal theoretical guarantees for flexibility and efficiency. Empirically, the learned estimators largely outperform classical baselines across sample sizes and dimensions, including on joint distributions unseen during training. The resulting quantile-based intervals are well-calibrated and more reliable than bootstrap-based confidence intervals, while inference is orders of magnitude faster than existing neural baselines. Beyond immediate empirical gains, this framework yields trainable, fully differentiable estimators that can be embedded into larger learning pipelines. Moreover, exploiting MI's invariance to invertible transformations, meta-datasets can be adapted to arbitrary data modalities via normalizing flows, enabling flexible training for diverse target meta-distributions.

Optimizing data mixtures for supervised fine-tuning (SFT) of large language models (LLMs) is critical for developing general-purpose models, yet this area remains underexplored. In this paper, we frame data mixing as an optimization problem and introduce a novel method designed to minimize validation loss. Our approach parametrizes the loss by modeling effective data transferred and leveraging scaling laws for fine-tuning. By experimenting with various small-scale data mixtures, we fit these parameters and derive the optimal weights. We provide both mathematical proofs and empirical results demonstrating that our algorithm achieves excellent overall and individual performance across all domains. Through controlled experiments, we show that models trained with our optimized weights perform on par with those using optimal weights determined via grid search, with per-domain loss only 0.66% higher than the best domain loss from grid search on average. Additionally, we show that reweighting popular SFT datasets using our method improves both validation loss and downstream performance. Finally, we discuss how our method can generalize to guide data selection for domain-specific models and provide insights into SFT.

We present SemiOccam, an image recognition network that leverages semi-supervised learning in a highly efficient manner. Existing works often rely on complex training techniques and architectures, requiring hundreds of GPU hours for training, while their generalization ability with extremely limited labeled data remains to be improved. To address these limitations, we construct a hierarchical mixture density classification mechanism by optimizing mutual information between feature representations and target classes, compressing redundant information while retaining crucial discriminative components. Experimental results demonstrate that our method achieves state-of-the-art performance on three commonly used datasets, with accuracy exceeding 95% on two of them using only 4 labeled samples per class, and its simple architecture keeps training time at the minute level. Notably, this paper reveals a long-overlooked data leakage issue in the STL-10 dataset for semi-supervised learning and removes duplicates to ensure reliable experimental results. We release the deduplicated CleanSTL-10 dataset to facilitate fair and reproducible research. Code available at https://github.com/Shu1L0n9/SemiOccam.

Existing pretraining data mixing methods for large language models (LLMs) typically follow a domain-wise methodology, a top-down process that first determines domain weights and then performs uniform data sampling across each domain. However, these approaches neglect significant inter-domain overlaps and commonalities, failing to control the global diversity of the constructed training dataset. Further, uniform sampling within domains ignores fine-grained sample-specific features, potentially leading to suboptimal data distribution. To address these shortcomings, we propose a novel sample-wise data mixture approach based on a bottom-up paradigm. This method performs global cross-domain sampling by systematically evaluating the quality and diversity of each sample, thereby dynamically determining the optimal domain distribution. Comprehensive experiments across multiple downstream tasks and perplexity assessments demonstrate that SampleMix surpasses existing domain-based methods. Meanwhile, SampleMix requires 1.4x to 2.1x training steps to achieves the baselines' performance, highlighting the substantial potential of SampleMix to optimize pre-training data.

Dense retrieval methods have demonstrated promising performance in multilingual information retrieval, where queries and documents can be in different languages. However, dense retrievers typically require a substantial amount of paired data, which poses even greater challenges in multilingual scenarios. This paper introduces UMR, an Unsupervised Multilingual dense Retriever trained without any paired data. Our approach leverages the sequence likelihood estimation capabilities of multilingual language models to acquire pseudo labels for training dense retrievers. We propose a two-stage framework which iteratively improves the performance of multilingual dense retrievers. Experimental results on two benchmark datasets show that UMR outperforms supervised baselines, showcasing the potential of training multilingual retrievers without paired data, thereby enhancing their practicality. Our source code, data, and models are publicly available at https://github.com/MiuLab/UMR

We propose UnMixMatch, a semi-supervised learning framework which can learn effective representations from unconstrained unlabelled data in order to scale up performance. Most existing semi-supervised methods rely on the assumption that labelled and unlabelled samples are drawn from the same distribution, which limits the potential for improvement through the use of free-living unlabeled data. Consequently, the generalizability and scalability of semi-supervised learning are often hindered by this assumption. Our method aims to overcome these constraints and effectively utilize unconstrained unlabelled data in semi-supervised learning. UnMixMatch consists of three main components: a supervised learner with hard augmentations that provides strong regularization, a contrastive consistency regularizer to learn underlying representations from the unlabelled data, and a self-supervised loss to enhance the representations that are learnt from the unlabelled data. We perform extensive experiments on 4 commonly used datasets and demonstrate superior performance over existing semi-supervised methods with a performance boost of 4.79%. Extensive ablation and sensitivity studies show the effectiveness and impact of each of the proposed components of our method.

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

Data-centric training has emerged as a promising direction for improving large language models (LLMs) by optimizing not only model parameters but also the selection, composition, and weighting of training data during optimization. However, existing approaches to data selection, data mixture optimization, and data reweighting are often developed in isolated codebases with inconsistent interfaces, hindering reproducibility, fair comparison, and practical integration. In this paper, we present DataFlex, a unified data-centric dynamic training framework built upon LLaMA-Factory. DataFlex supports three major paradigms of dynamic data optimization: sample selection, domain mixture adjustment, and sample reweighting, while remaining fully compatible with the original training workflow. It provides extensible trainer abstractions and modular components, enabling a drop-in replacement for standard LLM training, and unifies key model-dependent operations such as embedding extraction, inference, and gradient computation, with support for large-scale settings including DeepSpeed ZeRO-3. We conduct comprehensive experiments across multiple data-centric methods. Dynamic data selection consistently outperforms static full-data training on MMLU across both Mistral-7B and Llama-3.2-3B. For data mixture, DoReMi and ODM improve both MMLU accuracy and corpus-level perplexity over default proportions when pretraining Qwen2.5-1.5B on SlimPajama at 6B and 30B token scales. DataFlex also achieves consistent runtime improvements over original implementations. These results demonstrate that DataFlex provides an effective, efficient, and reproducible infrastructure for data-centric dynamic training of LLMs.

Document retrieval is a key stage of standard Web search engines. Existing dual-encoder dense retrievers obtain representations for questions and documents independently, allowing for only shallow interactions between them. To overcome this limitation, recent autoregressive search engines replace the dual-encoder architecture by directly generating identifiers for relevant documents in the candidate pool. However, the training cost of such autoregressive search engines rises sharply as the number of candidate documents increases. In this paper, we find that large language models (LLMs) can follow human instructions to directly generate URLs for document retrieval. Surprisingly, when providing a few {Query-URL} pairs as in-context demonstrations, LLMs can generate Web URLs where nearly 90\% of the corresponding documents contain correct answers to open-domain questions. In this way, LLMs can be thought of as built-in search engines, since they have not been explicitly trained to map questions to document identifiers. Experiments demonstrate that our method can consistently achieve better retrieval performance than existing retrieval approaches by a significant margin on three open-domain question answering benchmarks, under both zero and few-shot settings. The code for this work can be found at https://github.com/Ziems/llm-url.

The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the protection of user data, as individuals may not have given consent for their data to be used in training. To address this concern, recent studies introduce the concept of unlearnable examples, i.e., data instances that appear natural but are intentionally altered to prevent models from effectively learning from them. While existing methods demonstrate empirical effectiveness, they typically rely on heuristic trials and lack formal guarantees. Besides, when unlearnable examples are mixed with clean data, as is often the case in practice, their unlearnability disappears. In this work, we propose a novel approach to constructing unlearnable examples by systematically maximising the Bayes error, a measurement of irreducible classification error. We develop an optimisation-based approach and provide an efficient solution using projected gradient ascent. Our method provably increases the Bayes error and remains effective when the unlearning examples are mixed with clean samples. Experimental results across multiple datasets and model architectures are consistent with our theoretical analysis and show that our approach can restrict data learnability, effectively in practice.

This work presents a fast and scalable algorithm for incremental learning of Gaussian mixture models. By performing rank-one updates on its precision matrices and determinants, its asymptotic time complexity is of NKD^2 for N data points, K Gaussian components and D dimensions. The resulting algorithm can be applied to high dimensional tasks, and this is confirmed by applying it to the classification datasets MNIST and CIFAR-10. Additionally, in order to show the algorithm's applicability to function approximation and control tasks, it is applied to three reinforcement learning tasks and its data-efficiency is evaluated.

Data quality and diversity are key to the construction of effective instruction-tuning datasets. % With the increasing availability of open-source instruction-tuning datasets, it is advantageous to automatically select high-quality and diverse subsets from a vast amount of data. % Existing methods typically prioritize instance quality and use heuristic rules to maintain diversity. % However, this absence of a comprehensive view of the entire collection often leads to suboptimal results. % Moreover, heuristic rules generally focus on distance or clustering within the embedding space, which fails to accurately capture the intent of complex instructions in the semantic space. % To bridge this gap, we propose a unified method for quantifying the information content of datasets. This method models the semantic space by constructing a label graph and quantifies diversity based on the distribution of information within the graph. % Based on such a measurement, we further introduce an efficient sampling method that selects data samples iteratively to Maximize the Information Gain (MIG) in semantic space. % Experiments on various datasets and base models demonstrate that MIG consistently outperforms state-of-the-art methods. % Notably, the model fine-tuned with 5\% Tulu3 data sampled by MIG achieves comparable performance to the official SFT model trained on the full dataset, with improvements of +5.73\% on AlpacaEval and +6.89\% on Wildbench.

While large language models (LLMs) show promise in scientific discovery, existing research focuses on inference or feedback-driven training, leaving the direct modeling of the generative reasoning process, P(hypothesis|background) (P(h|b)), unexplored. We demonstrate that directly training P(h|b) is mathematically intractable due to the combinatorial complexity (O(N^k)) inherent in retrieving and composing inspirations from a vast knowledge base. To break this barrier, we introduce MOOSE-Star, a unified framework enabling tractable training and scalable inference. In the best case, MOOSE-Star reduces complexity from exponential to logarithmic (O(log N)) by (1) training on decomposed subtasks derived from the probabilistic equation of discovery, (2) employing motivation-guided hierarchical search to enable logarithmic retrieval and prune irrelevant subspaces, and (3) utilizing bounded composition for robustness against retrieval noise. To facilitate this, we release TOMATO-Star, a dataset of 108,717 decomposed papers (38,400 GPU hours) for training. Furthermore, we show that while brute-force sampling hits a ''complexity wall,'' MOOSE-Star exhibits continuous test-time scaling.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

Recent reasoning Large Language Models (LLMs) demonstrate remarkable problem-solving abilities but often generate long thinking traces whose utility is unclear. Our work aims to improve their efficiency, enabling them to reach high performance without overthinking. First, we analyze the entropy of token probabilities in reasoning traces. Across three models, we observe a consistent U-shaped entropy pattern: high entropy on easy problems despite high accuracy, low entropy on problems with medium difficulty, and high entropy on hard problems reflecting uncertainty. Specifically, we notice 22--25\% entropy reduction from easy to medium difficulty regions, suggesting an {overthinking} phenomenon on easy instances. Building on these insights, we introduce DiffAdapt, a lightweight framework that selects Easy/Normal/Hard inference strategies per question based on their difficulty and reasoning trace entropy. Each inference strategy consists of a fixed prompt, temperature and maximum token length. In contrast to existing efficiency optimization methods, our approach does not fine-tune base LLM but a small probe that classifies LLM's final hidden state, allowing inexpensive adaptation. We comprehensively evaluate our method on five models and eight benchmarks. Our method achieves comparable or improved accuracy while reducing token usage by up to 22.4\%, establishing a practical path toward compute-efficient reasoning.

Retrieval-Augmented Generation (RAG) has emerged as the predominant paradigm for grounding Large Language Model outputs in factual knowledge, effectively mitigating hallucinations. However, conventional RAG systems operate under a "retrieve-always" assumption, querying vector databases for every input regardless of query complexity. This static approach incurs substantial computational overhead and inference latency, particularly problematic for high-throughput production deployments. We introduce L-RAG (Lazy Retrieval-Augmented Generation), an adaptive framework that implements hierarchical context management through entropy-based gating. L-RAG employs a two-tier architecture: queries are first processed with a compact document summary, and expensive chunk retrieval is triggered only when the model's predictive entropy exceeds a calibrated threshold, signaling genuine uncertainty. Through experiments on SQuAD 2.0 (N=500) using the Phi-2 model, we demonstrate that L-RAG provides a tunable accuracy-efficiency trade-off: at a conservative threshold (tau=0.5), L-RAG achieves 78.2% accuracy, matching Standard RAG (77.8%), with 8% retrieval reduction; at a balanced threshold (tau=1.0), retrieval reduction increases to 26% with modest accuracy trade-off (76.0%). Latency analysis shows that L-RAG saves 80-210ms per query when retrieval latency exceeds 500ms. Analysis of entropy distributions reveals statistically significant separation (p < 0.001) between correct predictions (H=1.72) and errors (H=2.20), validating entropy as a reliable uncertainty signal. L-RAG offers a practical, training-free approach toward more efficient RAG deployment, providing system architects with a configurable knob to balance accuracy and throughput requirements.

Auto-regressive language models factorize sequence probabilities and are trained by minimizing the negative log-likelihood (NLL) objective. While empirically powerful, a deep theoretical understanding of why this simple objective yields such versatile representations remains elusive. This work introduces a unifying analytical framework using Markov Categories (MCs) to deconstruct the AR generation process and the NLL objective. We model the single-step generation map as a composition of Markov kernels in the category Stoch. This compositional view, when enriched with statistical divergences, allows us to dissect information flow and learned geometry. Our framework makes three main contributions. First, we provide a formal, information-theoretic rationale for the success of modern speculative decoding methods like EAGLE, quantifying the information surplus in hidden states that these methods exploit. Second, we formalize how NLL minimization forces the model to learn not just the next token, but the data's intrinsic conditional stochasticity, a process we analyze using categorical entropy. Third, and most centrally, we prove that NLL training acts as an implicit form of spectral contrastive learning. By analyzing the information geometry of the model's prediction head, we show that NLL implicitly forces the learned representation space to align with the eigenspectrum of a predictive similarity operator, thereby learning a geometrically structured space without explicit contrastive pairs. This compositional and information-geometric perspective reveals the deep structural principles underlying the effectiveness of modern LMs. Project Page: https://github.com/asiresearch/lm-theory

Hard negative mining has become the dominant strategy for training retrievers, yet it faces intrinsic limitations: negatives are bounded by corpus availability, selected by retriever score rather than diagnostic value, and increasingly contaminated by false positives as the retriever improves. LLM-based synthesis offers a principled alternative, where negatives that are unconstrained, targeted, and free from false positive risk. But we show that naively incorporating generated negatives into contrastive learning often degrades retrieval performance. We identify and formalize the root cause as a generative-discriminative gap: LLM generation optimizes for fluent, plausible text, while contrastive learning demands strategic violations of relevance at the decision boundary. Our analysis reveals two compounding failure modes: discriminative-agnostic generation, where the LLM lacks an explicit model of query information needs and defaults to generic or topic-drifted text that provides no contrastive signal; and source-dependent shortcuts, where distributional artifacts enable the model to distinguish negatives by origin rather than relevance, causing gradient drift that actively corrupts optimization. To close this gap, we propose CausalNeg consisting of two main modules: (1) CoT-guided counterfactual perturbation for data construction: decomposes why a document satisfies a query into explicit information requirements, then surgically violates individual requirements to construct negatives with controlled, interpretable hardness. (2) Query-view entropy maximization during training: disperses generated negatives across the similarity spectrum, minimizing the mutual information between source identity and similarity scores to suppress shortcut exploitation. We make our code publicly available at https://github.com/mzhangzhicheng/CausalNeg.

Massive unstructured multimodal streams suffer from high "data entropy," impeding both efficient human knowledge acquisition and high-quality AI post-training. Existing passive annotation paradigms, heavily reliant on heuristic rules or general VLMs, are costly, monotonous, and fail to unlock the deep procedural logic embedded in raw data. We elevate data processing to a learnable capability, proposing a paradigm shift towards Agentic Data Tailoring, which actively refining and structuring data to align with diverse user and downstream intents. To overcome the data scarcity bottleneck in training such high-order capabilities, we design a two-stage pipeline grounding generative semantic synthesis in deterministic Factual Anchors, yielding a large-scale dataset spanning five core physical and digital domains. Building upon this, DataClaw_0-9B model synergizes Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO), achieving robust alignment with complex refinement and tailoring intents. To systematically quantify this capability, we construct DataClaw_0-val, the first benchmark dedicated to data refinement. Crucially, we adopt downstream post-training as the ultimate validation touchstone. Evaluations on video generation, real-world VQA, and GUI navigation confirm that DataClaw_0 delivers high-information-density tailored data, facilitating efficient model adaptation to new tasks under limited training data regimes. Project page: https://czjdsg.github.io/MakeAnyData

The scaling laws hold that a language model grows more capable with more parameters and more training data, and Mixture-of-Experts (MoE) architectures have ridden these laws to remarkable results, activating only a fraction of an enormous stored parameter bank for each token. That success is built on static pretraining data. A deployed model faces a different world, where much of the data that would make it more useful is not in its training set but in the live interaction it is currently handling, such as the facts a user supplies or the corrections they give. A conventional model cannot learn from this data, because its weights are frozen after training. Instead, the knowledge and behaviour supplied at run time are placed in the prompt, by retrieval or instruction, and re-read on every request only to be discarded once the request ends. We ask how an architecture could learn from live interaction by writing it into its weights. Taking inspiration from MoE, we propose the Infinite-Parameter LLM. A compact hypernetwork turns the data given at run time into a low-rank modulation of a shared base network, so the feed-forward weights are generated from live data rather than stored in a fixed bank. Where prior weight generators read the context once and freeze, we carry a Bayesian belief over the generator's latent code and update it online, so the effective weight is re-derived from that evolving belief as the session proceeds rather than fixed after one read. The stored footprint stays fixed, yet the weights the model can compile are effectively infinite. For the knowledge and behaviour supplied at run time, carrying them in the weights rather than the prompt is amortized in compute, frees the context window, persists across turns, and can generalise better than in-context use. We specify an evaluation protocol that tests exactly this against in-context learning and retrieval.

When primed with only a handful of training samples, very large, pretrained language models such as GPT-3 have shown competitive results when compared to fully-supervised, fine-tuned, large, pretrained language models. We demonstrate that the order in which the samples are provided can make the difference between near state-of-the-art and random guess performance: essentially some permutations are "fantastic" and some not. We analyse this phenomenon in detail, establishing that: it is present across model sizes (even for the largest current models), it is not related to a specific subset of samples, and that a given good permutation for one model is not transferable to another. While one could use a development set to determine which permutations are performant, this would deviate from the true few-shot setting as it requires additional annotated data. Instead, we use the generative nature of language models to construct an artificial development set and based on entropy statistics of the candidate permutations on this set, we identify performant prompts. Our method yields a 13% relative improvement for GPT-family models across eleven different established text classification tasks.

Large Language Models (LLMs) have achieved impressive performance through Supervised Fine-tuning (SFT) on diverse instructional datasets. When training on multiple capabilities simultaneously, the mixture training dataset, governed by volumes of data from different domains, is a critical factor that directly impacts the final model's performance. Unlike many studies that focus on enhancing the quality of training datasets through data selection methods, few works explore the intricate relationship between the compositional quantity of mixture training datasets and the emergent capabilities of LLMs. Given the availability of a high-quality multi-domain training dataset, understanding the impact of data from each domain on the model's overall capabilities is crucial for preparing SFT data and training a well-balanced model that performs effectively across diverse domains. In this work, we introduce IDEAL, an innovative data equilibrium adaptation framework designed to effectively optimize volumes of data from different domains within mixture SFT datasets, thereby enhancing the model's alignment and performance across multiple capabilities. IDEAL employs a gradient-based approach to iteratively refine the training data distribution, dynamically adjusting the volumes of domain-specific data based on their impact on downstream task performance. By leveraging this adaptive mechanism, IDEAL ensures a balanced dataset composition, enabling the model to achieve robust generalization and consistent proficiency across diverse tasks. Experiments across different capabilities demonstrate that IDEAL outperforms conventional uniform data allocation strategies, achieving a comprehensive improvement of approximately 7% in multi-task evaluation scores.

Although existing neural retrieval models reveal promising results when training data is abundant and the performance keeps improving as training data increases, collecting high-quality annotated data is prohibitively costly. To this end, we introduce a novel noisy self-training framework combined with synthetic queries, showing that neural retrievers can be improved in a self-evolution manner with no reliance on any external models. Experimental results show that our method improves consistently over existing methods on both general-domain (e.g., MS-MARCO) and out-of-domain (i.e., BEIR) retrieval benchmarks. Extra analysis on low-resource settings reveals that our method is data efficient and outperforms competitive baselines, with as little as 30% of labelled training data. Further extending the framework for reranker training demonstrates that the proposed method is general and yields additional gains on tasks of diverse domains.Source code is available at \url{https://github.com/Fantabulous-J/Self-Training-DPR}

To support reliable long-term interaction in complex environments, LLM agents require memory systems that efficiently manage historical experiences. Existing approaches either retain full interaction histories via passive context extension, leading to substantial redundancy, or rely on iterative reasoning to filter noise, incurring high token costs. To address this challenge, we introduce SimpleMem, an efficient memory framework based on semantic lossless compression. We propose a three-stage pipeline designed to maximize information density and token utilization: (1) Semantic Structured Compression, which applies entropy-aware filtering to distill unstructured interactions into compact, multi-view indexed memory units; (2) Recursive Memory Consolidation, an asynchronous process that integrates related units into higher-level abstract representations to reduce redundancy; and (3) Adaptive Query-Aware Retrieval, which dynamically adjusts retrieval scope based on query complexity to construct precise context efficiently. Experiments on benchmark datasets show that our method consistently outperforms baseline approaches in accuracy, retrieval efficiency, and inference cost, achieving an average F1 improvement of 26.4% while reducing inference-time token consumption by up to 30-fold, demonstrating a superior balance between performance and efficiency. Code is available at https://github.com/aiming-lab/SimpleMem.

Hard-parameter sharing is a common strategy to train a single model jointly across diverse tasks. However, this often leads to task interference, impeding overall model performance. To address the issue, we propose a simple yet effective Supervised Mixture of Experts (S-MoE). Unlike traditional Mixture of Experts models, S-MoE eliminates the need for training gating functions by utilizing special guiding tokens to route each task to its designated expert. By assigning each task to a separate feedforward network, S-MoE overcomes the limitations of hard-parameter sharing. We further apply S-MoE to a speech-to-text model, enabling the model to process mixed-bandwidth input while jointly performing automatic speech recognition (ASR) and speech translation (ST). Experimental results demonstrate the effectiveness of the proposed S-MoE, achieving a 6.35% relative improvement in Word Error Rate (WER) when applied to both the encoder and decoder.

Mutual information maximization has emerged as a powerful learning objective for unsupervised representation learning obtaining state-of-the-art performance in applications such as object recognition, speech recognition, and reinforcement learning. However, such approaches are fundamentally limited since a tight lower bound of mutual information requires sample size exponential in the mutual information. This limits the applicability of these approaches for prediction tasks with high mutual information, such as in video understanding or reinforcement learning. In these settings, such techniques are prone to overfit, both in theory and in practice, and capture only a few of the relevant factors of variation. This leads to incomplete representations that are not optimal for downstream tasks. In this work, we empirically demonstrate that mutual information-based representation learning approaches do fail to learn complete representations on a number of designed and real-world tasks. To mitigate these problems we introduce the Wasserstein dependency measure, which learns more complete representations by using the Wasserstein distance instead of the KL divergence in the mutual information estimator. We show that a practical approximation to this theoretically motivated solution, constructed using Lipschitz constraint techniques from the GAN literature, achieves substantially improved results on tasks where incomplete representations are a major challenge.

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

The performance of modern language models depends critically on pretraining data composition. Yet existing data selection methods rely on auxiliary classifiers for document scoring or mixture optimization, adding computational overhead and dependence on labeled data. We propose WebGraphMix, a lightweight data selection framework that computes structural centrality scores over the Common Crawl host-level web graph and uses them to vary the proportion of central versus peripheral documents in the pretraining mixture. We hypothesize that central hosts expose models to reusable abstractions, while peripheral hosts encode specialized, long-tail knowledge. WebGraphMix computes centrality scores efficiently at web scale, requiring no model training, labeled data, or downstream supervision. We integrate WebGraphMix into the DataComp-LM pipeline and train models at 400M and 1B parameter scales with 8B and 28B tokens respectively, evaluating on 23 tasks ranging from factual knowledge to symbolic reasoning. Our experiments show that central and peripheral web regions encode complementary capabilities. Mixture combining both at a ratio of 1:1 achieves 41.4% on average, compared to 39.8% for uniform sampling. Combining structural scores with document-level quality classifier scores further improves performance to 43.8%. These findings demonstrate that web graph topology is a meaningful axis for pretraining data curation, capturing information that is largely orthogonal to existing content-based approaches.

Large language models (LLMs) have revolutionized the field of natural language processing, extending their strong capabilities into multi-modal domains. Thus, it is vital to define proper and diversified metrics for the evaluation of LLMs. In this paper, we introduce matrix entropy, a novel metric rooted in information theory and geometry principles to quantify the data compression proficiency in LLMs. It reflects the model's ability to extract relevant information and eliminate unnecessary elements, thereby providing insight into the language model's intrinsic capability. Specifically, we demonstrate its applicability in both single-modal (language) and multi-modal settings. For language models, our findings reveal that the matrix entropy of representations follows a scaling law type reduction when the model scales up, serving as a complement to the traditional loss scaling law. For the multi-modal setting, we also propose an evaluation method based on matrix entropy for assessing alignment quality and we find that modern large multi-modal models exhibit great alignment performance.

Pretraining large language models effectively requires strategic data selection, blending and ordering. However, key details about data mixtures especially their scalability to longer token horizons and larger model sizes remain underexplored due to limited disclosure by model developers. To address this, we formalize the concept of two-phase pretraining and conduct an extensive systematic study on how to select and mix data to maximize model accuracies for the two phases. Our findings illustrate that a two-phase approach for pretraining outperforms random data ordering and natural distribution of tokens by 3.4% and 17% on average accuracies. We provide in-depth guidance on crafting optimal blends based on quality of the data source and the number of epochs to be seen. We propose to design blends using downsampled data at a smaller scale of 1T tokens and then demonstrate effective scaling of our approach to larger token horizon of 15T tokens and larger model size of 25B model size. These insights provide a series of steps practitioners can follow to design and scale their data blends.

The advancement of transformer neural networks has significantly elevated the capabilities of sentence similarity models, particularly in creating effective vector representations of natural language inputs. However, these models face notable challenges in domain-specific contexts, especially in highly specialized scientific sub-fields. Traditional methods often struggle in this regime, either overgeneralizing similarities within a niche or being overly sensitive to minor differences, resulting in inaccurate text classification and subpar vector representation. In an era where retrieval augmentation and search are increasingly crucial, precise and concise numerical representations are essential. In this paper, we target this issue by assembling niche datasets using co-citations as a similarity metric, focusing on biomedical domains. We employ two key strategies for fine-tuning state-of-the-art models: 1. Domain-specific Fine-Tuning, which tailors pretrained models to a single domain, and 2. Universal Applicability with Mixture of Experts (MoE), adapting pretrained models with enforced routing for multiple domains simultaneously. Our training approach emphasizes the use of abstracts for faster training, incorporating Multiple Negative Rankings loss for efficient contrastive learning. Notably, our MoE variants, equipped with N experts, achieve the efficacy of N individual models, heralding a new era of versatile, One-Size-Fits-All transformer networks for various tasks. This methodology marks significant advancements in scientific text classification metrics and holds promise for enhancing vector database search and compilation.

Long-term memory enables large language model agents to tackle complex tasks through historical interactions. However, existing frameworks encounter a fundamental dilemma between compressing redundant information efficiently and maintaining precise retrieval for downstream tasks. To bridge this gap, we propose MemFly, a framework grounded in information bottleneck principles that facilitates on-the-fly memory evolution for LLMs. Our approach minimizes compression entropy while maximizing relevance entropy via a gradient-free optimizer, constructing a stratified memory structure for efficient storage. To fully leverage MemFly, we develop a hybrid retrieval mechanism that seamlessly integrates semantic, symbolic, and topological pathways, incorporating iterative refinement to handle complex multi-hop queries. Comprehensive experiments demonstrate that MemFly substantially outperforms state-of-the-art baselines in memory coherence, response fidelity, and accuracy.

Mixture of Experts (MoE) architectures have significantly increased computational efficiency in both research and real-world applications of large-scale machine learning models. However, their scalability and efficiency under memory constraints remain relatively underexplored. In this work, we present joint scaling laws for dense and MoE models, incorporating key factors such as the number of active parameters, dataset size, and the number of experts. Our findings provide a principled framework for selecting the optimal MoE configuration under fixed memory and compute budgets. Surprisingly, we show that MoE models can be more memory-efficient than dense models, contradicting conventional wisdom. To derive and validate the theoretical predictions of our scaling laws, we conduct over 280 experiments with up to 2.7B active parameters and up to 5B total parameters. These results offer actionable insights for designing and deploying MoE models in practical large-scale training scenarios.

In this paper, we tackle the problem of discovering new classes in unlabeled visual data given labeled data from disjoint classes. Existing methods typically first pre-train a model with labeled data, and then identify new classes in unlabeled data via unsupervised clustering. However, the labeled data that provide essential knowledge are often underexplored in the second step. The challenge is that the labeled and unlabeled examples are from non-overlapping classes, which makes it difficult to build the learning relationship between them. In this work, we introduce OpenMix to mix the unlabeled examples from an open set and the labeled examples from known classes, where their non-overlapping labels and pseudo-labels are simultaneously mixed into a joint label distribution. OpenMix dynamically compounds examples in two ways. First, we produce mixed training images by incorporating labeled examples with unlabeled examples. With the benefits of unique prior knowledge in novel class discovery, the generated pseudo-labels will be more credible than the original unlabeled predictions. As a result, OpenMix helps to prevent the model from overfitting on unlabeled samples that may be assigned with wrong pseudo-labels. Second, the first way encourages the unlabeled examples with high class-probabilities to have considerable accuracy. We introduce these examples as reliable anchors and further integrate them with unlabeled samples. This enables us to generate more combinations in unlabeled examples and exploit finer object relations among the new classes. Experiments on three classification datasets demonstrate the effectiveness of the proposed OpenMix, which is superior to state-of-the-art methods in novel class discovery.

Several post-training quantization methods have been applied to large language models (LLMs), and have been shown to perform well down to 8-bits. We find that these methods break down at lower bit precision, and investigate quantization aware training for LLMs (LLM-QAT) to push quantization levels even further. We propose a data-free distillation method that leverages generations produced by the pre-trained model, which better preserves the original output distribution and allows quantizing any generative model independent of its training data, similar to post-training quantization methods. In addition to quantizing weights and activations, we also quantize the KV cache, which is critical for increasing throughput and support long sequence dependencies at current model sizes. We experiment with LLaMA models of sizes 7B, 13B, and 30B, at quantization levels down to 4-bits. We observe large improvements over training-free methods, especially in the low-bit settings.

Distributed dense word vectors have been shown to be effective at capturing token-level semantic and syntactic regularities in language, while topic models can form interpretable representations over documents. In this work, we describe lda2vec, a model that learns dense word vectors jointly with Dirichlet-distributed latent document-level mixtures of topic vectors. In contrast to continuous dense document representations, this formulation produces sparse, interpretable document mixtures through a non-negative simplex constraint. Our method is simple to incorporate into existing automatic differentiation frameworks and allows for unsupervised document representations geared for use by scientists while simultaneously learning word vectors and the linear relationships between them.

State-of-the-art flow models achieve remarkable quality but require slow, iterative sampling. To accelerate this, flow maps can be distilled from pre-trained teachers, a procedure that conventionally requires sampling from an external dataset. We argue that this data-dependency introduces a fundamental risk of Teacher-Data Mismatch, as a static dataset may provide an incomplete or even misaligned representation of the teacher's full generative capabilities. This leads us to question whether this reliance on data is truly necessary for successful flow map distillation. In this work, we explore a data-free alternative that samples only from the prior distribution, a distribution the teacher is guaranteed to follow by construction, thereby circumventing the mismatch risk entirely. To demonstrate the practical viability of this philosophy, we introduce a principled framework that learns to predict the teacher's sampling path while actively correcting for its own compounding errors to ensure high fidelity. Our approach surpasses all data-based counterparts and establishes a new state-of-the-art by a significant margin. Specifically, distilling from SiT-XL/2+REPA, our method reaches an impressive FID of 1.45 on ImageNet 256x256, and 1.49 on ImageNet 512x512, both with only 1 sampling step. We hope our work establishes a more robust paradigm for accelerating generative models and motivates the broader adoption of flow map distillation without data.

No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are often referenced in support of the notion that individual problems require specially tailored inductive biases. While virtually all uniformly sampled datasets have high complexity, real-world problems disproportionately generate low-complexity data, and we argue that neural network models share this same preference, formalized using Kolmogorov complexity. Notably, we show that architectures designed for a particular domain, such as computer vision, can compress datasets on a variety of seemingly unrelated domains. Our experiments show that pre-trained and even randomly initialized language models prefer to generate low-complexity sequences. Whereas no free lunch theorems seemingly indicate that individual problems require specialized learners, we explain how tasks that often require human intervention such as picking an appropriately sized model when labeled data is scarce or plentiful can be automated into a single learning algorithm. These observations justify the trend in deep learning of unifying seemingly disparate problems with an increasingly small set of machine learning models.

Recent advancements in large language models (LLMs) have allowed the augmentation of information retrieval (IR) pipelines with synthetic data in various ways. Yet, the main training paradigm remains: contrastive learning with binary relevance labels and the InfoNCE loss, where one positive document is compared against one or more negatives. This objective treats all documents that are not explicitly annotated as relevant on an equally negative footing, regardless of their actual degree of relevance, thus (a) missing subtle nuances that are useful for ranking and (b) being susceptible to annotation noise. To overcome this limitation, in this work we forgo real training documents and annotations altogether and use open-source LLMs to directly generate synthetic documents that answer real user queries according to several different levels of relevance. This fully synthetic ranking context of graduated relevance, together with an appropriate list-wise loss (Wasserstein distance), enables us to train dense retrievers in a way that better captures the ranking task. Experiments on various IR datasets show that our proposed approach outperforms conventional training with InfoNCE by a large margin. Without using any real documents for training, our dense retriever significantly outperforms the same retriever trained through self-supervision. More importantly, it matches the performance of the same retriever trained on real, labeled training documents of the same dataset, while being more robust to distribution shift and clearly outperforming it when evaluated zero-shot on the BEIR dataset collection.

Retrieval-augmented generation integrates the capabilities of large language models with relevant information retrieved from an extensive corpus, yet encounters challenges when confronted with real-world noisy data. One recent solution is to train a filter module to find relevant content but only achieve suboptimal noise compression. In this paper, we propose to introduce the information bottleneck theory into retrieval-augmented generation. Our approach involves the filtration of noise by simultaneously maximizing the mutual information between compression and ground output, while minimizing the mutual information between compression and retrieved passage. In addition, we derive the formula of information bottleneck to facilitate its application in novel comprehensive evaluations, the selection of supervised fine-tuning data, and the construction of reinforcement learning rewards. Experimental results demonstrate that our approach achieves significant improvements across various question answering datasets, not only in terms of the correctness of answer generation but also in the conciseness with 2.5% compression rate.

Entropy-based pruning has been proposed as an effective method for compressing Chain-of-Thought (CoT) reasoning with negligible accuracy loss. We test the robustness of low- and high-entropy CoT step selection methods across various models and reasoning tasks, showing that entropy offers no advantage over random pruning in any evaluated setting. Moving from sentences to tokens, we then show that retaining low-entropy tokens seems effective only on mathematical benchmarks. We find this is due to the inherently low-entropy nature of numeric tokens, which also convey semantic content in such problems. Finally, we demonstrate that patching a subset of a few CoT tokens with their original activations recovers near-perfect full-trace performance, providing causal evidence that task information is not concentrated in a small set of CoT tokens identifiable by heuristics, but rather distributed across the full reasoning chain.

Mixture-of-Experts (MoE) models scale efficiently by activating only a subset of experts per token, offering a computationally sparse alternative to dense architectures. While prior post-training optimizations, such as inter- and intra-expert pruning, reduce memory usage they provide limited gains in inference-time compute efficiency. Moreover, existing MoE architectures typically activate a fixed number of experts uniformly across all layers, resulting in redundant computation and suboptimal performance. In this work, we first demonstrate that MoE pruning strategies improve only the memory footprint but do not significantly improve inference performance on GPU using optimized frameworks such as vLLM. To address this, we introduce LExI, a data-free optimization technique that determines the optimal number of active experts per layer in a pretrained MoE model. LExI leverages only the model weights to estimate the relative importance of each layer and adaptively assigns the number of active experts accordingly per layer. Experiments on state-of-the-art language and vision MoE benchmarks demonstrate that LExI significantly outperforms traditional MoE pruning approaches in terms of inference efficiency with negligible accuracy loss. For example, using LExI, Qwen1.5-MoE achieves the same throughput on Nvidia H100 GPU with 10% better accuracy than traditional expert pruning.

Comprehensive evaluation of Large Language Models (LLMs) is an open research problem. Existing evaluations rely on deterministic point estimates generated via greedy decoding. However, we find that deterministic evaluations fail to capture the whole output distribution of a model, yielding inaccurate estimations of model capabilities. This is particularly problematic in critical contexts such as unlearning and alignment, where precise model evaluations are crucial. To remedy this, we introduce the first formal probabilistic evaluation framework for LLMs. Namely, we propose novel metrics with high probability guarantees concerning the output distribution of a model. Our metrics are application-independent and allow practitioners to make more reliable estimates about model capabilities before deployment. Our experimental analysis reveals that deterministic evaluations falsely indicate successful unlearning and alignment, whereas our probabilistic evaluations better capture model capabilities. We show how to overcome challenges associated with probabilistic outputs in a case study on unlearning by introducing (1) a novel loss based on entropy optimization, and (2) adaptive temperature scaling. We demonstrate that our approach significantly enhances unlearning in probabilistic settings on recent benchmarks. Overall, our proposed shift from point estimates to probabilistic evaluations of output distributions represents an important step toward comprehensive evaluations of LLMs. Code available at https://www.cs.cit.tum.de/daml/probabilistic-unlearning/.

The scaling of Large Language Models (LLMs) is increasingly limited by data quality. Most methods handle data mixing and sample selection separately, which can break the structure in code corpora. We introduce UniGeM, a framework that unifies mixing and selection by treating data curation as a manifold approximation problem without training proxy models or relying on external reference datasets. UniGeM operates hierarchically: Macro-Exploration learns mixing weights with stability-based clustering; Micro-Mining filters high-quality instances by their geometric distribution to ensure logical consistency. Validated by training 8B and 16B MoE models on 100B tokens, UniGeM achieves 2.0times data efficiency over a random baseline and further improves overall performance compared to SOTA methods in reasoning-heavy evaluations and multilingual generalization.

Large language models (LLMs) are increasingly being used to generate synthetic datasets for the evaluation and training of downstream models. However, prior work has noted that such generated data lacks diversity. In this paper, we propose Voyager, a novel principled approach to generate diverse datasets. Our approach is iterative and directly optimizes a mathematical quantity that optimizes the diversity of the dataset using the machinery of determinantal point processes. Furthermore, our approach is training-free, applicable to closed-source models, and scalable. In addition to providing theoretical justification for the working of our method, we also demonstrate through comprehensive experiments that Voyager significantly outperforms popular baseline approaches by providing a 1.5-3x improvement in diversity.

Adapting large language models (LLMs) to specific domains often faces a critical bottleneck: the scarcity of high-quality, human-curated data. While large volumes of unchecked data are readily available, indiscriminately using them for fine-tuning risks introducing noise and degrading performance. Strategic data selection is thus crucial, requiring a method that is both accurate and efficient. Existing approaches, categorized as similarity-based and direct optimization methods, struggle to simultaneously achieve these goals. In this paper, we introduce LAMDAS (LLM As an iMplicit classifier for domain-specific DAta Selection), a novel approach that leverages the pre-trained LLM itself as an implicit classifier, thereby bypassing explicit feature engineering and computationally intensive optimization process. LAMDAS reframes data selection as a one-class classification problem, identifying candidate data that "belongs" to the target domain defined by a small reference dataset. Extensive experimental results demonstrate that LAMDAS not only exceeds the performance of full-data training using a fraction of the data but also outperforms nine state-of-the-art (SOTA) baselines under various scenarios. Furthermore, LAMDAS achieves the most compelling balance between performance gains and computational efficiency compared to all evaluated baselines.

Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models that present the intriguing possibility of providing general-purpose prediction methods, even in this mixture setting. In this work, we investigate the hypothesis that transformers can learn an optimal predictor for mixtures of regressions. We construct a generative process for a mixture of linear regressions for which the decision-theoretic optimal procedure is given by data-driven exponential weights on a finite set of parameters. We observe that transformers achieve low mean-squared error on data generated via this process. By probing the transformer's output at inference time, we also show that transformers typically make predictions that are close to the optimal predictor. Our experiments also demonstrate that transformers can learn mixtures of regressions in a sample-efficient fashion and are somewhat robust to distribution shifts. We complement our experimental observations by proving constructively that the decision-theoretic optimal procedure is indeed implementable by a transformer.

Large language models (LLMs), despite their impressive performance across a wide range of tasks, often struggle to balance two competing objectives in open-ended text generation: fostering diversity and creativity while preserving logical coherence. Existing truncated sampling techniques, including temperature scaling, top-\p (nucleus) sampling, and min-\p sampling, aim to manage this trade-off. However, they exhibit limitations, particularly in the effective incorporation of the confidence of the model into the corresponding sampling strategy. For example, min-\p sampling relies on a single top token as a heuristic for confidence, eventually underutilizing the information of the probability distribution. Toward effective incorporation of the confidence of the model, in this paper, we present **top-H** decoding. We first establish the theoretical foundation of the interplay between creativity and coherence in truncated sampling by formulating an **entropy-constrained minimum divergence** problem. We then prove this minimization problem to be equivalent to an **entropy-constrained mass maximization** (ECMM) problem, which is NP-hard. Finally, we present top-H decoding, a computationally efficient greedy algorithm to solve the ECMM problem. Extensive empirical evaluations demonstrate that top-H outperforms the state-of-the-art (SoTA) alternative of min-\p sampling by up to **25.63%** on creative writing benchmarks, while maintaining robustness on question-answering datasets such as GPQA, GSM8K, and MT-Bench. Additionally, an *LLM-as-judge* evaluation confirms that top-H indeed produces coherent outputs even at higher temperatures, where creativity is especially critical. In summary, top-H advances SoTA in open-ended text generation and can be *easily integrated* into creative writing applications. The code is available at https://github.com/ErfanBaghaei/Top-H-Decoding.

Reinforcement learning with verifiable rewards (RLVR) has demonstrated superior performance in enhancing the reasoning capability of large language models (LLMs). However, this accuracy-oriented learning paradigm often suffers from entropy collapse, which reduces policy exploration and limits reasoning capabilities. To address this challenge, we propose an efficient reinforcement learning framework that leverages entropy signals at both the semantic and token levels to improve reasoning. From the data perspective, we introduce semantic entropy-guided curriculum learning, organizing training data from low to high semantic entropy to guide progressive optimization from easier to more challenging tasks. For the algorithmic design, we adopt non-uniform token treatment by imposing KL regularization on low-entropy tokens that critically impact policy exploration and applying stronger constraints on high-covariance portions within these tokens. By jointly optimizing data organization and algorithmic design, our method effectively mitigates entropy collapse and enhances LLM reasoning. Experimental results across 6 benchmarks with 3 different parameter-scale base models demonstrate that our method outperforms other entropy-based approaches in improving reasoning.

The performance of large language models (LLMs) is significantly affected by the quality and composition of their pre-training data, which is inherently diverse, spanning various domains, sources, and topics. Effectively integrating these heterogeneous data sources is crucial for optimizing LLM performance. Previous research has predominantly concentrated on domain-based data mixing, often neglecting the nuanced topic-level characteristics of the data. To address this gap, we propose a simple yet effective topic-based data mixing strategy that utilizes fine-grained topics generated through our topic modeling method, DataWeave. DataWeave employs a multi-stage clustering process to group semantically similar documents and utilizes LLMs to generate detailed topics, thereby facilitating a more nuanced understanding of dataset composition. Our strategy employs heuristic methods to upsample or downsample specific topics, which significantly enhances LLM performance on downstream tasks, achieving superior results compared to previous, more complex data mixing approaches. Furthermore, we confirm that the topics Science and Relationships are particularly effective, yielding the most substantial performance improvements. We will make our code and datasets publicly available.

In this work, we present a naive initialization scheme for word vectors based on a dense, independent co-occurrence model and provide preliminary results that suggest it is competitive and warrants further investigation. Specifically, we demonstrate through information-theoretic minimum description length (MDL) probing that our model, EigenNoise, can approach the performance of empirically trained GloVe despite the lack of any pre-training data (in the case of EigenNoise). We present these preliminary results with interest to set the stage for further investigations into how this competitive initialization works without pre-training data, as well as to invite the exploration of more intelligent initialization schemes informed by the theory of harmonic linguistic structure. Our application of this theory likewise contributes a novel (and effective) interpretation of recent discoveries which have elucidated the underlying distributional information that linguistic representations capture from data and contrast distributions.

Deep neural networks have demonstrated remarkable performance in supervised learning tasks but require large amounts of labeled data. Self-supervised learning offers an alternative paradigm, enabling the model to learn from data without explicit labels. Information theory has been instrumental in understanding and optimizing deep neural networks. Specifically, the information bottleneck principle has been applied to optimize the trade-off between compression and relevant information preservation in supervised settings. However, the optimal information objective in self-supervised learning remains unclear. In this paper, we review various approaches to self-supervised learning from an information-theoretic standpoint and present a unified framework that formalizes the self-supervised information-theoretic learning problem. We integrate existing research into a coherent framework, examine recent self-supervised methods, and identify research opportunities and challenges. Moreover, we discuss empirical measurement of information-theoretic quantities and their estimators. This paper offers a comprehensive review of the intersection between information theory, self-supervised learning, and deep neural networks.

Wild Test-Time Adaptation (WTTA) is proposed to adapt a source model to unseen domains under extreme data scarcity and multiple shifts. Previous approaches mainly focused on sample selection strategies, while overlooking the fundamental problem on underlying optimization. Initially, we critically analyze the widely-adopted entropy minimization framework in WTTA and uncover its significant limitations in noisy optimization dynamics that substantially hinder adaptation efficiency. Through our analysis, we identify region confidence as a superior alternative to traditional entropy, however, its direct optimization remains computationally prohibitive for real-time applications. In this paper, we introduce a novel region-integrated method ReCAP that bypasses the lengthy process. Specifically, we propose a probabilistic region modeling scheme that flexibly captures semantic changes in embedding space. Subsequently, we develop a finite-to-infinite asymptotic approximation that transforms the intractable region confidence into a tractable and upper-bounded proxy. These innovations significantly unlock the overlooked potential dynamics in local region in a concise solution. Our extensive experiments demonstrate the consistent superiority of ReCAP over existing methods across various datasets and wild scenarios.

In recent years, advances in the large-scale pretraining of language and text-to-image models have revolutionized the field of machine learning. Yet, integrating these two modalities into a single, robust model capable of generating seamless multimodal outputs remains a significant challenge. To address this gap, we present the Joint Autoregressive Mixture (JAM) framework, a modular approach that systematically fuses existing text and image generation models. We also introduce a specialized, data-efficient instruction-tuning strategy, tailored for mixed-modal generation tasks. Our final instruct-tuned model demonstrates unparalleled performance in generating high-quality multimodal outputs and represents the first model explicitly designed for this purpose.

Despite the significant breakthrough of Mixture-of-Experts (MoE), the increasing scale of these MoE models presents huge memory and storage challenges. Existing MoE pruning methods, which involve reducing parameter size with a uniform sparsity across all layers, often lead to suboptimal outcomes and performance degradation due to varying expert redundancy in different MoE layers. To address this, we propose a non-uniform pruning strategy, dubbed Differentiable Expert Pruning (DiEP), which adaptively adjusts pruning rates at the layer level while jointly learning inter-layer importance, effectively capturing the varying redundancy across different MoE layers. By transforming the global discrete search space into a continuous one, our method handles exponentially growing non-uniform expert combinations, enabling adaptive gradient-based pruning. Extensive experiments on five advanced MoE models demonstrate the efficacy of our method across various NLP tasks. Notably, DiEP retains around 92\% of original performance on Mixtral 8times7B with only half the experts, outperforming other pruning methods by up to 7.1\% on the challenging MMLU dataset.

A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

With the rise of reasoning language models and test-time scaling methods as a paradigm for improving model performance, substantial computation is often required to generate multiple candidate sequences from the same prompt. This enables exploration of different reasoning paths toward the correct solution, however, allocates the same compute budget for each prompt. Grounded on the assumption that different prompts carry different degrees of complexity, and thus different computation needs, we propose EAGer, a training-free generation method that leverages model uncertainty through token-wise entropy distribution to reduce redundant computation and concurrently improve overall performance. EAGer allows branching to multiple reasoning paths only in the presence of high-entropy tokens, and then reallocates the saved compute budget to the instances where exploration of alternative paths is most needed. We find that across multiple open-source models on complex reasoning benchmarks such as AIME 2025, EAGer can reallocate the budget without accessing target labels, achieving the best efficiency-performance trade-off in terms of reasoning length and Pass@k. When target labels are accessible, EAGer generates up to 65% fewer tokens (hence saving compute) and achieves up to 37% improvement in Pass@k compared to the Full Parallel Sampling.

This paper introduces the counter-intuitive generalization results of overfitting pre-trained large language models (LLMs) on very small datasets. In the setting of open-ended text generation, it is well-documented that LLMs tend to generate repetitive and dull sequences, a phenomenon that is especially apparent when generating using greedy decoding. This issue persists even with state-of-the-art LLMs containing billions of parameters, trained via next-token prediction on large datasets. We find that by further fine-tuning these models to achieve a near-zero training loss on a small set of samples -- a process we refer to as hyperfitting -- the long-sequence generative capabilities are greatly enhanced. Greedy decoding with these Hyperfitted models even outperform Top-P sampling over long-sequences, both in terms of diversity and human preferences. This phenomenon extends to LLMs of various sizes, different domains, and even autoregressive image generation. We further find this phenomena to be distinctly different from that of Grokking and double descent. Surprisingly, our experiments indicate that hyperfitted models rarely fall into repeating sequences they were trained on, and even explicitly blocking these sequences results in high-quality output. All hyperfitted models produce extremely low-entropy predictions, often allocating nearly all probability to a single token.

Learned sparse retrieval, which can efficiently perform retrieval through mature inverted-index engines, has garnered growing attention in recent years. Particularly, the inference-free sparse retrievers are attractive as they eliminate online model inference in the retrieval phase thereby avoids huge computational cost, offering reasonable throughput and latency. However, even the state-of-the-art (SOTA) inference-free sparse models lag far behind in terms of search relevance when compared to both sparse and dense siamese models. Towards competitive search relevance for inference-free sparse retrievers, we argue that they deserve dedicated training methods other than using same ones with siamese encoders. In this paper, we propose two different approaches for performance improvement. First, we introduce the IDF-aware FLOPS loss, which introduces Inverted Document Frequency (IDF) to the sparsification of representations. We find that it mitigates the negative impact of the FLOPS regularization on search relevance, allowing the model to achieve a better balance between accuracy and efficiency. Moreover, we propose a heterogeneous ensemble knowledge distillation framework that combines siamese dense and sparse retrievers to generate supervisory signals during the pre-training phase. The ensemble framework of dense and sparse retriever capitalizes on their strengths respectively, providing a strong upper bound for knowledge distillation. To concur the diverse feedback from heterogeneous supervisors, we normalize and then aggregate the outputs of the teacher models to eliminate score scale differences. On the BEIR benchmark, our model outperforms existing SOTA inference-free sparse model by 3.3 NDCG@10 score. It exhibits search relevance comparable to siamese sparse retrievers and client-side latency only 1.1x that of BM25.

We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.

Large Language Models (LLMs) have achieved state-of-the-art performance across various language tasks but pose challenges for practical deployment due to their substantial memory requirements. Furthermore, the latest generative models suffer from high inference costs caused by the memory bandwidth bottleneck in the auto-regressive decoding process. To address these issues, we propose an efficient weight-only quantization method that reduces memory consumption and accelerates inference for LLMs. To ensure minimal quality degradation, we introduce a simple and effective heuristic approach that utilizes only the model weights of a pre-trained model. This approach is applicable to both Mixture-of-Experts (MoE) and dense models without requiring additional fine-tuning. To demonstrate the effectiveness of our proposed method, we first analyze the challenges and issues associated with LLM quantization. Subsequently, we present our heuristic approach, which adaptively finds the granularity of quantization, effectively addressing these problems. Furthermore, we implement highly efficient GPU GEMMs that perform on-the-fly matrix multiplication and dequantization, supporting the multiplication of fp16 or bf16 activations with int8 or int4 weights. We evaluate our approach on large-scale open source models such as OPT-175B and internal MoE models, showcasing minimal accuracy loss while achieving up to 3.65 times higher throughput on the same number of GPUs.

A significant use case of instruction-finetuned Large Language Models (LLMs) is to solve question-answering tasks interactively. In this setting, an LLM agent is tasked with making a prediction by sequentially querying relevant information from the user, as opposed to a single-turn conversation. This paper explores sequential querying strategies that aim to minimize the expected number of queries. One such strategy is Information Pursuit (IP), a greedy algorithm that at each iteration selects the query that maximizes information gain or equivalently minimizes uncertainty. However, obtaining accurate estimates of mutual information or conditional entropy for LLMs is very difficult in practice due to over- or under-confident LLM probabilities, which leads to suboptimal query selection and predictive performance. To better estimate the uncertainty at each iteration, we propose Conformal Information Pursuit (C-IP), an alternative approach to sequential information gain based on conformal prediction sets. More specifically, C-IP leverages a relationship between prediction sets and conditional entropy at each iteration to estimate uncertainty based on the average size of conformal prediction sets. In contrast to conditional entropy, we find that conformal prediction sets are a distribution-free and robust method of measuring uncertainty. Experiments with 20 Questions show that C-IP obtains better predictive performance and shorter query-answer chains compared to previous approaches to IP and uncertainty-based chain-of-thought methods. Furthermore, extending to an interactive medical setting between a doctor and a patient on the MediQ dataset, C-IP achieves competitive performance with direct single-turn prediction while offering greater interpretability.

Dataset Distillation (DD) seeks to create a compact dataset from a large, real-world dataset. While recent methods often rely on heuristic approaches to balance efficiency and quality, the fundamental relationship between original and synthetic data remains underexplored. This paper revisits knowledge distillation-based dataset distillation within a solid theoretical framework. We introduce the concepts of Informativeness and Utility, capturing crucial information within a sample and essential samples in the training set, respectively. Building on these principles, we define optimal dataset distillation mathematically. We then present InfoUtil, a framework that balances informativeness and utility in synthesizing the distilled dataset. InfoUtil incorporates two key components: (1) game-theoretic informativeness maximization using Shapley Value attribution to extract key information from samples, and (2) principled utility maximization by selecting globally influential samples based on Gradient Norm. These components ensure that the distilled dataset is both informative and utility-optimized. Experiments demonstrate that our method achieves a 6.1\% performance improvement over the previous state-of-the-art approach on ImageNet-1K dataset using ResNet-18.

Data mixing decides how to combine different sources or types of data and is a consequential problem throughout language model training. In pretraining, data composition is a key determinant of model quality; in continual learning and adaptation, it governs what is retained and acquired. Yet existing data mixing methods address only one phase of this lifecycle at a time: some require smaller proxy models tied to a single training phase, others assume a fixed domain set, and continual learning lacks principled guidance altogether. We argue that data mixing is fundamentally an online decision making problem -- one that recurs throughout training and demands a single, unified solution. We introduce OP-Mix (On-Policy Mix), a data mixing algorithm that operates across the entire language model training lifecycle. Our main insight is that candidate data mixtures can be cheaply simulated by interpolating between low-rank adapters trained directly on the current model, eliminating separate proxy models and ensuring the search is always grounded in the model's actual learning dynamics. Across pretraining, continual midtraining, and continual instruction tuning, OP-Mix consistently finds near-optimal mixtures while using a fraction of the compute of the baselines. In pretraining, OP-Mix improves upon training without mixing by 6.3% in average perplexity. For continual learning, OP-Mix matches the performance of both retraining and on-policy distillation while using 66% and 95% less overall compute, respectively. OP-Mix suggests a different view of language model training: not a sequence of distinct phases, but a single continuous process of learning from data.

As language models grow ever larger, so do their vocabularies. This has shifted the memory footprint of LLMs during training disproportionately to one single layer: the cross-entropy in the loss computation. Cross-entropy builds up a logit matrix with entries for each pair of input tokens and vocabulary items and, for small models, consumes an order of magnitude more memory than the rest of the LLM combined. We propose Cut Cross-Entropy (CCE), a method that computes the cross-entropy loss without materializing the logits for all tokens into global memory. Rather, CCE only computes the logit for the correct token and evaluates the log-sum-exp over all logits on the fly. We implement a custom kernel that performs the matrix multiplications and the log-sum-exp reduction over the vocabulary in flash memory, making global memory consumption for the cross-entropy computation negligible. This has a dramatic effect. Taking the Gemma 2 (2B) model as an example, CCE reduces the memory footprint of the loss computation from 24 GB to 1 MB, and the total training-time memory consumption of the classifier head from 28 GB to 1 GB. To improve the throughput of CCE, we leverage the inherent sparsity of softmax and propose to skip elements of the gradient computation that have a negligible (i.e., below numerical precision) contribution to the gradient. Experiments demonstrate that the dramatic reduction in memory consumption is accomplished without sacrificing training speed or convergence.

Large language models (LLMs) effectively generate fluent text when the target output follows natural language patterns. However, structured prediction tasks confine the output format to a limited ontology, causing even very large models to struggle since they were never trained with such restrictions in mind. The difficulty of using LLMs for direct prediction is exacerbated in few-shot learning scenarios, which commonly arise due to domain shift and resource limitations. We flip the problem on its head by leveraging the LLM as a tool for data augmentation rather than direct prediction. Our proposed Mixture of Soft Prompts (MSP) serves as a parameter-efficient procedure for generating data in a controlled manner. Denoising mechanisms are further applied to improve the quality of synthesized data. Automatic metrics show our method is capable of producing diverse and natural text, while preserving label semantics. Moreover, MSP achieves state-of-the-art results on three benchmarks when compared against strong baselines. Our method offers an alternate data-centric approach for applying LLMs to complex prediction tasks.

Recent advances in large language models highlighted the excessive quadratic cost of self-attention. Despite the significant research efforts, subquadratic attention methods still suffer from inferior performance in practice. We hypothesize that dynamic, learned content-based sparsity can lead to more efficient attention mechanisms. We present Mixture of Sparse Attention (MoSA), a novel approach inspired by Mixture of Experts (MoE) with expert choice routing. MoSA dynamically selects tokens for each attention head, allowing arbitrary sparse attention patterns. By selecting k tokens from a sequence of length T, MoSA reduces the computational complexity of each attention head from O(T^2) to O(k^2 + T). This enables using more heads within the same computational budget, allowing higher specialization. We show that among the tested sparse attention variants, MoSA is the only one that can outperform the dense baseline, sometimes with up to 27% better perplexity for an identical compute budget. MoSA can also reduce the resource usage compared to dense self-attention. Despite using torch implementation without an optimized kernel, perplexity-matched MoSA models are simultaneously faster in wall-clock time, require less memory for training, and drastically reduce the size of the KV-cache compared to the dense transformer baselines.

In this work, we aim to connect two research areas: instruction models and retrieval-based models. While instruction-tuned Large Language Models (LLMs) excel at extracting information from text, they are not suitable for semantic retrieval. Similarity search over embedding vectors allows to index and query vectors, but the similarity reflected in the embedding is sub-optimal for many use cases. We identify the task of retrieving sentences based on abstract descriptions of their content. We demonstrate the inadequacy of current text embeddings and propose an alternative model that significantly improves when used in standard nearest neighbor search. The model is trained using positive and negative pairs sourced through prompting an a large language model (LLM). While it is easy to source the training material from an LLM, the retrieval task cannot be performed by the LLM directly. This demonstrates that data from LLMs can be used not only for distilling more efficient specialized models than the original LLM, but also for creating new capabilities not immediately possible using the original model.