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Jun 29

Universal Approximation Theorem for a Single-Layer Transformer

Deep learning employs multi-layer neural networks trained via the backpropagation algorithm. This approach has achieved success across many domains and relies on adaptive gradient methods such as the Adam optimizer. Sequence modeling evolved from recurrent neural networks to attention-based models, culminating in the Transformer architecture. Transformers have achieved state-of-the-art performance in natural language processing (for example, BERT and GPT-3) and have been applied in computer vision and computational biology. However, theoretical understanding of these models remains limited. In this paper, we examine the mathematical foundations of deep learning and Transformers and present a novel theoretical result. We review key concepts from linear algebra, probability, and optimization that underpin deep learning, and we analyze the multi-head self-attention mechanism and the backpropagation algorithm in detail. Our main contribution is a universal approximation theorem for Transformers: we prove that a single-layer Transformer, comprising one self-attention layer followed by a position-wise feed-forward network with ReLU activation, can approximate any continuous sequence-to-sequence mapping on a compact domain to arbitrary precision. We provide a formal statement and a complete proof. Finally, we present case studies that demonstrate the practical implications of this result. Our findings advance the theoretical understanding of Transformer models and help bridge the gap between theory and practice.

  • 1 authors
·
Jul 11, 2025

ExpertRAG: Efficient RAG with Mixture of Experts -- Optimizing Context Retrieval for Adaptive LLM Responses

ExpertRAG is a novel theoretical framework that integrates Mixture-of-Experts (MoE) architectures with Retrieval Augmented Generation (RAG) to advance the efficiency and accuracy of knowledge-intensive language modeling. We propose a dynamic retrieval gating mechanism coupled with expert routing, enabling the model to selectively consult an external knowledge store or rely on specialized internal experts based on the query's needs. The paper lays out the theoretical foundations of ExpertRAG, including a probabilistic formulation that treats retrieval and expert selection as latent decisions, and mathematical justifications for its efficiency in both computation and knowledge utilization. We derive formulae to quantify the expected computational cost savings from selective retrieval and the capacity gains from sparse expert utilization. A comparative analysis positions ExpertRAG against standard RAG (with always-on retrieval) and pure MoE models (e.g., Switch Transformer, Mixtral) to highlight its unique balance between parametric knowledge and non-parametric retrieval. We also outline an experimental validation strategy, proposing benchmarks and evaluation protocols to test ExpertRAG's performance on factual recall, generalization, and inference efficiency. The proposed framework, although presented theoretically, is supported by insights from prior work in RAG and MoE, and is poised to provide more factual, efficient, and adaptive generation by leveraging the best of both paradigms. In summary, ExpertRAG contributes a new perspective on scaling and augmenting language models, backed by a thorough analysis and a roadmap for empirical validation.

  • 1 authors
·
Mar 23, 2025

Galvatron: Automatic Distributed Training for Large Transformer Models

Training multi-billion to trillion-parameter language models efficiently on GPU clusters requires leveraging multiple parallelism strategies. We present Galvatron, a novel open-source framework (dubbed 'Optimus-Megatron' in the implementation) that dynamically combines data parallelism, tensor model parallelism, and pipeline parallelism to optimize training throughput. Built atop PyTorch and integrating NVIDIA's Megatron-LM and Microsoft's DeepSpeed, Galvatron automatically selects and adjusts parallelism strategies in real time based on model architecture, hardware, and training dynamics. This paper details Galvatron's key features -- automatic hybrid parallelism selection, layer-wise and phase-wise strategy optimization, and runtime adaptation -- and contrasts them with existing static frameworks. We describe the system's technical stack, including its use of DeepSpeed's ZeRO and NCCL communication, and provide an in-depth implementation overview of its core modules (profilers, strategy selector, parallelism manager). We then illustrate how Galvatron can be seamlessly integrated into existing training pipelines with minimal code modifications, providing companies a plug-and-play solution for efficient large-model training. Finally, we situate Galvatron in context with related efforts (NVIDIA Megatron-LM, Microsoft DeepSpeed, Google GShard, Meta FairScale, etc.), highlighting how it advances the state of the art in distributed deep learning. References to the GitHub repository and relevant literature are provided throughout.

  • 1 authors
·
Mar 13, 2025

One Pass Is Not Enough: Recursive Latent Refinement for Generative Models

Despite remarkable progress, image generation is far from solved. The dominant metric, FID, conflates sample fidelity with mode coverage and is close to being saturated. Yet a model can still exhibit mode collapse while achieving a low FID, since a handful of sharp, near-duplicate images can outscore a model that faithfully covers the full data distribution. We argue that precision and recall are essential complements to FID, and that because FID is already saturated, the more meaningful goal is to improve diversity and coverage. Achieving high recall requires a model that explicitly prioritizes mode coverage, unlike most generative models, which optimize sample fidelity. We introduce RTM, which replaces the single-pass latent mapping in style-based generators with an iterative refinement process, and show that this consistently improves both quality and diversity. Integrated with Implicit Maximum Likelihood Estimation (IMLE), which optimizes mode coverage by design, RTM achieves the highest precision and recall among current state-of-the-art approaches while maintaining competitive FID, with improvements across CIFAR-10, CelebA-HQ at 256x256, and nine few-shot benchmarks. RTM also improves StyleGAN2 and StyleGAN2-ADA on CIFAR-10 and AFHQ-v1 at 512x512, demonstrating that the benefit is not specific to IMLE. Unlike flow-matching baselines that achieve competitive FID at the expense of coverage, recursive refinement improves both quality and diversity simultaneously.

  • 4 authors
·
May 13

Analysis of AdvFusion: Adapter-based Multilingual Learning for Code Large Language Models

Programming languages can benefit from one another by utilizing a language model for software engineering tasks. Full fine-tuning and Parameter Efficient Fine-Tuning (PEFT) of Code Language Models (Code-LMs) has been explored for multilingual knowledge transfer. AdapterFusion is a PEFT architecture that aims to enhance task performance by leveraging information from multiple programming languages, but primarily focuses on the target programming language. In our previous work, we proposed AdvFusion, a novel PEFT-based approach that effectively learns from other programming languages before adapting to the target task. Though previous experiments showed that AdvFusion outperformed AdapterFusion and LoRA, it was applied on pre-trained Code-LMs and was limited to only two tasks, code summarization and method name prediction. In this study, we expanded our work and investigated AdvFusion on Code Large Language Models (Code-LLMs), considering three new tasks: code generation, code translation, and commit message generation. We observed that different Code-LLMs/tasks exhibit different characteristics. In code generation, AdvFusion outperformed AdapterFusion but not other PEFT methods (LoRA, Compacter, and TaskAdapter). In commit message generation, AdapterFusion performed better than AdvFusion, and contrary to code generation, we found that the other PEFT methods do not have better performance. In code translation, AdvFusion performed worse than AdapterFusion overall, with the performance gap marginally widening as the model size increases. However, consistent with code generation, other PEFT methods showed better performance.

  • 5 authors
·
Nov 2, 2025

Data-Driven Forecasting of three-Component Seismograms Using Transformer Architectures

Forecasting seismic waveforms beyond observed data remains challenging due to the nonlinear, dispersive, and multi-scale nature of seismic wave propagation. In this work, we introduce SeismoGPT, a transformer-based autoregressive model designed to forecast three-component seismic waveforms directly in the time domain. Forecasting is formulated as a physically constrained continuation problem in which the model receives waveform context beginning at the P-wave arrival and extending a defined time beyond the S-wave arrival, after which future motion is generated recursively without access to ground-truth samples. Evaluation is performed on synthetic seismograms spanning source depths of 5--100\,km, epicentral distances of 10--90^circ, and magnitudes 3 leq M_w leq 7. To disentangle the effects of context length and prediction horizon, we define three evaluation configurations using a distance-normalized context ratio and fixed prediction horizons of 120 and 240\,s. Across all configurations, the model achieves median normalized cross correlation above 0.93. Analysis of representative forecasts shows that successful predictions preserve both phase coherence and spectral energy distribution. Where failure cases arise, this is primarily due to gradual phase drift during autoregressive rollout rather than unphysical signal generation. These results demonstrate that transformer-based sequence models can learn stable dynamical continuation of seismic wavefields, highlighting the potential of foundation-model approaches for physics-driven time-series forecasting. There are potential applications of this methodology in seismic warning and hazard mitigation, particularly for next-generation gravitational-wave observatories, such as the Einstein Telescope.

  • 5 authors
·
May 31

Prot2Token: A Unified Framework for Protein Modeling via Next-Token Prediction

The diverse nature of protein prediction tasks has traditionally necessitated specialized models, hindering the development of broadly applicable and computationally efficient Protein Language Models (PLMs). In this work, we introduce Prot2Token, a unified framework that overcomes these challenges by converting a wide spectrum of protein-related predictions, from sequence-level properties and residue-specific attributes to complex inter-protein interactions, into a standardized next-token prediction format. At its core, Prot2Token employs an autoregressive decoder, conditioned on embeddings from pre-trained protein encoders and guided by learnable task tokens, to perform diverse predictions. This architecture uniquely facilitates multi-task learning, enabling a single model to master numerous tasks with improved efficiency. We present extensive experimental validation across a variety of benchmarks, demonstrating Prot2Tokens strong predictive power in different types of protein-prediction tasks. Key results include significant speedups (e.g., near 1000x over AlphaFold2 with MSA) and performance often matching or exceeding specialized approaches. Beyond that, we introduce an auxiliary self-supervised decoder pre-training approach to improve spatially sensitive task performance. Prot2Token thus offers a significant step towards a versatile, high-throughput paradigm for protein modeling, promising to accelerate biological discovery and the development of novel therapeutics. The code is available at https://github.com/mahdip72/prot2token .

  • 9 authors
·
May 26, 2025 2

Bias in the Loop: Auditing LLM-as-a-Judge for Software Engineering

Large Language Models are increasingly used as judges to evaluate code artifacts when exhaustive human review or executable test coverage is unavailable. LLM-judge is increasingly relevant in agentic software engineering workflows, where it can help rank candidate solutions and guide patch selection. While attractive for scale, current practice lacks a principled account of reliability and bias: repeated evaluations of the same case can disagree; small prompt edits can swing outcomes; and seemingly semantics-preserving, human-equivalent perturbations may elicit divergent verdicts. This paper studies LLM-as-a-Judge for code through a measurement-first lens. We analyze two pointwise judging regimes across code generation, code repair task, and test generation, and we systematically probe prompt-induced biases. Our study considers difficulty levels for repeated runs and controlled prompt interventions that isolate one presentation cue at a time, and it evaluates judges using consistency and sensitivity to bias. We find that judge decisions are highly sensitive to prompt biases even when the underlying code snippet is unchanged. Across all three tasks, several biases systematically shift preferences toward the option favored by the prompt, improving accuracy when that option aligns with the gold answer but substantially reducing it otherwise. In some settings, these effects are large enough to change task-level conclusions and alter relative model rankings. These findings show that reported judge performance may reflect prompt artifacts rather than stable assessment ability, posing a direct threat to the validity and reproducibility of code evaluation. We therefore argue that LLM-as-a-Judge studies should report bias sensitivity alongside accuracy and incorporate explicit controls to support more trustworthy model comparison in software engineering.

  • 3 authors
·
Apr 17

Arabic Synonym BERT-based Adversarial Examples for Text Classification

Text classification systems have been proven vulnerable to adversarial text examples, modified versions of the original text examples that are often unnoticed by human eyes, yet can force text classification models to alter their classification. Often, research works quantifying the impact of adversarial text attacks have been applied only to models trained in English. In this paper, we introduce the first word-level study of adversarial attacks in Arabic. Specifically, we use a synonym (word-level) attack using a Masked Language Modeling (MLM) task with a BERT model in a black-box setting to assess the robustness of the state-of-the-art text classification models to adversarial attacks in Arabic. To evaluate the grammatical and semantic similarities of the newly produced adversarial examples using our synonym BERT-based attack, we invite four human evaluators to assess and compare the produced adversarial examples with their original examples. We also study the transferability of these newly produced Arabic adversarial examples to various models and investigate the effectiveness of defense mechanisms against these adversarial examples on the BERT models. We find that fine-tuned BERT models were more susceptible to our synonym attacks than the other Deep Neural Networks (DNN) models like WordCNN and WordLSTM we trained. We also find that fine-tuned BERT models were more susceptible to transferred attacks. We, lastly, find that fine-tuned BERT models successfully regain at least 2% in accuracy after applying adversarial training as an initial defense mechanism.

  • 4 authors
·
Feb 5, 2024

HoloPASWIN: Robust Inline Holographic Reconstruction via Physics-Aware Swin Transformers

In-line digital holography (DIH) is a widely used lensless imaging technique, valued for its simplicity and capability to image samples at high throughput. However, capturing only intensity of the interference pattern during the recording process gives rise to some unwanted terms such as cross-term and twin-image. The cross-term can be suppressed by adjusting the intensity of reference wave, but the twin-image problem remains. The twin-image is a spectral artifact that superimposes a defocused conjugate wave onto the reconstructed object, severely degrading image quality. While deep learning has recently emerged as a powerful tool for phase retrieval, traditional Convolutional Neural Networks (CNNs) are limited by their local receptive fields, making them less effective at capturing the global diffraction patterns inherent in holography. In this study, we introduce HoloPASWIN, a physics-aware deep learning framework based on the Swin Transformer architecture. By leveraging hierarchical shifted-window attention, our model efficiently captures both local details and long-range dependencies essential for accurate holographic reconstruction. We propose a comprehensive loss function that integrates frequency-domain constraints with physical consistency via a differentiable angular spectrum propagator, ensuring high spectral fidelity. Validated on a large-scale synthetic dataset of 25,000 samples with diverse noise configurations (speckle, shot, read, and dark noise), HoloPASWIN demonstrates effective twin-image suppression and robust reconstruction quality.

  • 2 authors
·
Mar 5

REASONING COMPILER: LLM-Guided Optimizations for Efficient Model Serving

While model serving has unlocked unprecedented capabilities, the high cost of serving large-scale models continues to be a significant barrier to widespread accessibility and rapid innovation. Compiler optimizations have long driven substantial performance improvements, but existing compilers struggle with neural workloads due to the exponentially large and highly interdependent space of possible transformations. Although existing stochastic search techniques can be effective, they are often sample-inefficient and fail to leverage the structural context underlying compilation decisions. We set out to investigate the research question of whether reasoning with large language models (LLMs), without any retraining, can leverage the context-aware decision space of compiler optimizations to significantly improve sample efficiency. To that end, we introduce a novel compilation framework (dubbed REASONING COMPILER) that formulates optimization as a sequential, context-aware decision process guided by a large language model and structured Monte Carlo tree search (MCTS). The LLM acts as a proposal mechanism, suggesting hardware-informed transformations that reflect the current program state and accumulated performance feedback. MCTS incorporates the LLM-generated proposals to balance exploration and exploitation, facilitating a structured, context-sensitive traversal of the expansive compiler optimization space. By achieving substantial speedups with markedly fewer samples than leading neural compilers, our approach demonstrates the potential of LLM-guided reasoning to transform the landscape of compiler optimization.

  • 5 authors
·
Feb 3

GlucoFM: A Dual-Stream Foundation Model for Continuous Glucose Monitoring

Continuous glucose monitoring (CGM) provides a dense view of daily metabolic physiology, yet existing generic time-series and CGM-specific foundation models often encode glucose traces as entangled single-stream sequences, leaving the distinct temporal structure of glycemic dynamics only implicitly modeled. We present GlucoFM, a lightweight CGM foundation model that aligns irregular recordings to a 24-hour chronological grid, preserves observation masks, and decomposes glucose dynamics into slow physiological state and transient event streams, capturing low-frequency glycemic baselines and short-term deviations that may reflect acute physiological responses or sensor artifacts. GlucoFM is pretrained on 109,066 hours of unlabeled CGM recordings from 477 subjects with two complementary objectives: masked contextual latent prediction over fused daily representations and temporal dynamics prediction over state and event streams. Across four diverse cohorts and seven clinical prediction tasks, GlucoFM achieves the strongest subject-disjoint linear-probing performance among evaluated baselines, improving average PR-AUC by 4.1 points over the best CGM-specific foundation model. Its gains are most pronounced on core metabolic outcomes, leading PR-AUC on all diabetes-risk and β-cell dysfunction tasks and on 3 of 4 insulin-resistance tasks. GlucoFM also achieves the best overall cross-dataset transfer performance and strong few-shot adaptation among evaluated methods, and consistent gains when aggregating multiple days for subject-level prediction, highlighting physiology-aware decomposition as an effective inductive bias for transferable CGM representation learning.

  • 14 authors
·
May 28 1

$π_{0.7}$: a Steerable Generalist Robotic Foundation Model with Emergent Capabilities

We present a new robotic foundation model, called π_{0.7}, that can enable strong out-of-the-box performance in a wide range of scenarios. π_{0.7} can follow diverse language instructions in unseen environments, including multi-stage tasks with various kitchen appliances, provide zero-shot cross-embodiment generalization, for example enabling a robot to fold laundry without seeing the task before, and perform challenging tasks such as operating an espresso machine out of the box at a level of performance that matches much more specialized RL-finetuned models. The main idea behind π_{0.7} is to use diverse context conditioning during training. This conditioning information, contained in the prompt, makes it possible to steer the model precisely to perform many tasks with different strategies. It is conditioned not just on a language command that describes what it should do, but on additional multimodal information that also describes the manner or strategy in which it should do it, including metadata about task performance and subgoal images. This enables π_{0.7} to use very diverse data, including demonstrations, potentially suboptimal (autonomous) data including failures, and data from non-robot sources. Our experiments evaluate π_{0.7} across numerous tasks with multiple robot platforms, on tasks that require speed and dexterity, language following, and compositional task generalization.

  • 88 authors
·
Apr 23

Competition-Level Code Generation with AlphaCode

Programming is a powerful and ubiquitous problem-solving tool. Developing systems that can assist programmers or even generate programs independently could make programming more productive and accessible, yet so far incorporating innovations in AI has proven challenging. Recent large-scale language models have demonstrated an impressive ability to generate code, and are now able to complete simple programming tasks. However, these models still perform poorly when evaluated on more complex, unseen problems that require problem-solving skills beyond simply translating instructions into code. For example, competitive programming problems which require an understanding of algorithms and complex natural language remain extremely challenging. To address this gap, we introduce AlphaCode, a system for code generation that can create novel solutions to these problems that require deeper reasoning. In simulated evaluations on recent programming competitions on the Codeforces platform, AlphaCode achieved on average a ranking of top 54.3% in competitions with more than 5,000 participants. We found that three key components were critical to achieve good and reliable performance: (1) an extensive and clean competitive programming dataset for training and evaluation, (2) large and efficient-to-sample transformer-based architectures, and (3) large-scale model sampling to explore the search space, followed by filtering based on program behavior to a small set of submissions.

  • 26 authors
·
Feb 8, 2022

From Knowledge to Action: Outcomes of the 2025 Large Language Model (LLM) Hackathon for Applications in Materials Science and Chemistry

Large language models (LLMs) are rapidly changing how researchers in materials science and chemistry discover, organize, and act on scientific knowledge. This paper analyzes a broad set of community-developed LLM applications in an effort to identify emerging patterns in how these systems can be used across the scientific research lifecycle. We organize the projects into two complementary categories: Knowledge Infrastructure, systems that structure, retrieve, synthesize, and validate scientific information; and Action Systems, systems that execute, coordinate, or automate scientific work across computational and experimental environments. The submissions reveal a shift from single-purpose LLM tools toward integrated, multi-agent workflows that combine retrieval, reasoning, tool use, and domain-specific validation. Prominent themes include retrieval-augmented generation as grounding infrastructure, persistent structured knowledge representations, multimodal and multilingual scientific inputs, and early progress toward laboratory-integrated closed-loop systems. Together, these results suggest that LLMs are evolving from general-purpose assistants into composable infrastructure for scientific reasoning and action. This work provides a community snapshot of that transition and a practical taxonomy for understanding emerging LLM-enabled workflows in materials science and chemistry.

  • 353 authors
·
May 3