The pursuit of computational efficiency has driven the adoption of low-precision formats for training transformer models. However, this progress is often hindered by notorious training instabilities. This paper provides the first mechanistic explanation for a long-standing and unresolved failure case where training with flash attention in low-precision settings leads to catastrophic loss explosion. Our in-depth analysis reveals that the failure is not a random artifact but caused by two intertwined phenomena: the emergence of similar low-rank representations within the attention mechanism and the compounding effect of biased rounding errors inherent in low-precision arithmetic. We demonstrate how these factors create a vicious cycle of error accumulation that corrupts weight updates, ultimately derailing the training dynamics. To validate our findings, we introduce a minimal modification to the flash attention that mitigates the bias in rounding errors. This simple change stabilizes the training process, confirming our analysis and offering a practical solution to this persistent problem. Code is available at https://github.com/ucker/why-low-precision-training-fails.
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Optimization · Everything Else
The pursuit of computational efficiency has driven the adoption of low-precision formats for training transformer models. However, this progress is often hindered by notorious training instabilities. This paper provides the first mechanistic explanation for a long-standing and unresolved failure case where training with flash attention in low-precision settings leads to catastrophic loss explosion. Our in-depth analysis reveals that the failure is not a random artifact but caused by two intertwined phenomena: the emergence of similar low-rank representations within the attention mechanism and the compounding effect of biased rounding errors inherent in low-precision arithmetic. We demonstrate how these factors create a vicious cycle of error accumulation that corrupts weight updates, ultimately derailing the training dynamics. To validate our findings, we introduce a minimal modification to the flash attention that mitigates the bias in rounding errors. This simple change stabilizes the training process, confirming our analysis and offering a practical solution to this persistent problem. Code is available at https://github.com/ucker/why-low-precision-training-fails.
Deep Learning · Theory
Transformer components such as non-linear activations and normalization are inherently non-injective, suggesting that different inputs could map to the same output and prevent exact recovery of the input from a model’s representations. In this paper, we challenge this view. First, we prove mathematically that transformer language models mapping discrete input sequences to their corresponding sequence of continuous representations are injective and therefore lossless, a property established at initialization and preserved during training. Second, we confirm this result empirically through billions of collision tests on six state-of-the-art language models, and observe no collisions. Third, we operationalize injectivity: we introduce SipIt, the first algorithm that provably and efficiently reconstructs the exact input text from hidden activations, establishing linear-time guarantees and demonstrating exact invertibility in practice. Overall, our work establishes injectivity as a fundamental and exploitable property of language models, with direct implications for transparency, interpretability, and safe deployment.
Reinforcement Learning · Everything Else
Scaling test-time compute has emerged as an effective strategy for improving the performance of large language models. However, existing methods typically allocate compute uniformly across all queries, overlooking variation in query difficulty. To address this inefficiency, we formulate test-time compute allocation as a novel bandit learning problem and propose adaptive algorithms that estimate query difficulty on the fly and allocate compute accordingly. Compared to uniform allocation, our algorithms allocate more compute to challenging queries while maintaining accuracy on easier ones. Among challenging queries, our algorithms further learn to prioritize solvable instances, effectively reducing excessive computing on unsolvable queries. We theoretically prove that our algorithms achieve better compute efficiency than uniform allocation and empirically validate their effectiveness on math and code benchmarks. Specifically, our algorithms achieve up to an 11.10\% performance improvement (15.04\% relative) on the MATH-500 dataset, up to 10.82\% (14.44\% relative) on the AIME25 dataset, and up to an 11.23\% performance improvement (15.29\% relative) on the LiveCodeBench dataset.
Deep Learning · Attention Mechanisms
Optimizing inference for long-context large language models (LLMs) is increasingly important due to the quadratic compute and linear memory cost of Transformers. Existing approximate inference methods, including key-value (KV) cache dropping, sparse attention, and prompt compression, typically rely on coarse predictions of token or KV pair importance. We unify and extend recent work by introducing a framework for approximate LLM inference that leverages small draft models to more accurately predict token and KV pair importance. We provide novel theoretical and empirical analyses justifying lookahead-based importance estimation techniques. Within this framework, we present: (i) **SpecKV**, the first method to use lookahead with a small draft model to enable precise KV cache dropping; (ii) **SpecPC**, which leverages draft model attention activations to identify and discard less important prompt tokens; and (iii) **SpecKV-PC**, a cascaded compression strategy combining both techniques. Extensive experiments on long-context benchmarks demonstrate that our methods consistently achieve higher accuracy than existing baselines while retaining the same efficiency gains in memory usage, latency, and throughput.
General Machine Learning · Everything Else
Digital quantum computing promises to offer computational capabilities beyond the reach of classical systems, yet its capabilities are often challenged by scarce quantum resources. A critical bottleneck in this context is how to load classical or quantum data into quantum circuits efficiently. Approximate quantum loaders (AQLs) provide a viable solution to this problem by balancing fidelity and circuit complexity. However, most existing AQL methods are either heuristic or provide guarantees only for specific input types, and a general theoretical framework is still lacking. To address this gap, here we reformulate most AQL methods into a unified framework and establish information-theoretic bounds on their approximation error. Our analysis reveals that the achievable infidelity between the prepared state and target state scales linearly with the total entanglement entropy across subsystems when the loading circuit is applied to the target state. In light of this, we develop AQER, a scalable AQL method that constructs the loading circuit by systematically reducing entanglement in target states. We conduct systematic experiments to evaluate the effectiveness of AQER, using synthetic datasets, classical image and language datasets, and a quantum many-body state datasets with up to 50 qubits. The results show that AQER consistently outperforms existing methods in both accuracy and gate efficiency. Our work paves the way for scalable quantum data processing and real-world quantum computing applications.
Deep Learning · Generative Models and Autoencoders
Diffusion models achieve state-of-the-art image quality. However, sampling is costly at inference time because it requires a large number of function evaluations (NFEs). To reduce NFEs, classical ODE numerical methods have been adopted. Yet, the choice of prediction type and integration domain leads to different sampling behaviors. To address these issues, we introduce Dual-Solver, which generalizes multistep samplers through learnable parameters that continuously (i) interpolate among prediction types, (ii) select the integration domain, and (iii) adjust the residual terms. It retains the standard predictor-corrector structure while preserving second-order local accuracy. These parameters are learned via a classification-based objective using a frozen pretrained classifier (e.g., MobileNet or CLIP). For ImageNet class-conditional generation (DiT, GM-DiT) and text-to-image generation (SANA, PixArt-$\alpha$), Dual-Solver improves FID and CLIP scores in the low-NFE regime ($3 \le$ NFE $\le 9$) across backbones.
Applications · Health
Biosignals offer valuable insights into the physiological states of the human body. Although biosignal modalities differ in functionality, signal fidelity, sensor comfort, and cost, they are often intercorrelated, reflecting the holistic and interconnected nature of human physiology. This opens up the possibility of performing the same tasks using alternative biosignal modalities, thereby improving the accessibility, usability, and adaptability of health monitoring systems. However, the limited availability of large labeled datasets presents challenges for training models tailored to specific tasks and modalities of interest. Unsupervised cross-modal knowledge transfer offers a promising solution by leveraging knowledge from an existing modality to support model training for a new modality. Existing methods are typically based on knowledge distillation, which requires running a teacher model alongside student model training, resulting in high computational and memory overhead. This challenge is further exacerbated by the recent development of foundation models that demonstrate superior performance and generalization across tasks at the cost of large model sizes. To this end, we explore a new framework for unsupervised cross-modal knowledge transfer of biosignals by training a lightweight bridge network to align the intermediate representations and enable information flow between foundation models and across modalities. Specifically, we introduce an efficient strategy for selecting alignment positions where the bridge should be constructed, along with a flexible prototype network as the bridge architecture. Extensive experiments across multiple biosignal modalities, tasks, and datasets show that BioX-Bridge reduces the number of trainable parameters by 88-99\% while maintaining or even improving transfer performance compared to state-of-the-art methods.
Social Aspects · Fairness, Equity, Justice and Safety
Large Reasoning Models (LRMs) with long chain-of-thought capabilities, optimized via reinforcement learning with verifiable rewards (RLVR), excel at **objective reasoning** tasks like mathematical problem solving and code generation. However, RLVR is known for degrading generation diversity, which causes LRMs to fall short on **subjective reasoning** that has multiple answers depending on different role perspectives. While recent studies recognize the importance of diversity-enhanced training in objective reasoning, limited attention has been given to subjective tasks. In this paper, we find that subjective reasoning can be improved by introducing perspective diversity and token-level diversity, with the former one providing a coherent scaffolding anchored to a real-world stakeholder group and the latter one broadening the answer search space. We propose MultiRole-R1, a diversity-enhanced training framework featuring an unsupervised data construction pipeline that synthesizes reasoning chains incorporating various role perspectives. It also employs reinforcement learning via Group Relative Policy Optimization with reward shaping, taking diversity as a reward signal in addition to verifiable reward. Training on subjective tasks solely, MultiRole-R1 increases the in-domain and out-of-domain accuracy by 14.1% and 7.64%, and even enhances the performance on advanced math reasoning such as AIME 2024. We further show that diversity is a more consistent indicator of accuracy than reasoning length.
Theory · Learning Theory
Training on Chain-of-Thought (CoT) traces has empirically shown to dramatically improve the capabilities of Large Language Models (LLMs), yet a formal understanding of its power remains limited. In this work, we investigate the role of training on such computational traces from the perspective of language learnability. We introduce a new learning model, identification in the limit with trace, which augments Gold's classic paradigm [Gold'67] by providing the learner not only with examples from a target language but also with computational traces from the machine that accepts them. Our results reveal that access to these traces dramatically enhances the power of the learner. We first prove that with perfect computational traces, the class of all computable languages (those recognizable by Turing Machines) becomes identifiable in the limit. This stands in sharp contrast to Gold's famous impossibility result, which holds even for the simple class of languages that are recognizable by deterministic finite automata. We then analyze the more challenging scenario where the learner has only partial information regarding the computational traces, which are also subject to adversarial corruptions. In this setting, we establish a set of trichotomic results on the amount of error that can be tolerated for the successful identification of language classes across the Chomsky hierarchy.
Deep Learning · Everything Else
Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a core paradigm for enhancing the reasoning capabilities of Large Language Models (LLMs). To address the lack of verification signals at test time after RLVR, prior studies incorporate the training of model's self-verification capabilities into the standard RLVR process, thereby unifying reasoning and verification capabilities within a single LLM. However, previous practice requires the LLM to sequentially generate solutions and self-verifications using two separate prompt templates, which doubles the inference cost per sample and significantly reduces efficiency. In this work, we theoretically reveal that the closed-form solution to the RL objective of self-verification training can be approximately reduced to a remarkably simple form: the true reasoning reward of a solution is equal to its last-token self-rewarding score, which is computed as the difference between the policy model's next-token log-probability assigned to any pre-specified token at the solution's last token and a pre-calculated constant, scaled by the KL coefficient. Based on this insight, we propose LaSeR (Reinforcement Learning with Last-Token Self-Rewarding), an algorithm that simply augments the original RLVR loss with a Mean Squared Error (MSE) loss that aligns the last-token self-rewarding scores with the verifier-based reasoning rewards, and jointly optimizes the reasoning and self-rewarding capabilities of LLMs. The optimized self-rewarding scores serve as auxiliary reward signals in both training and testing to enhance model performance. Notably, our algorithm derives these scores from the predicted next-token probability distribution of the last solution token immediately after solution generation, thereby incurring only the minimal extra cost of at most one additional token inference. Experimental results show that our method not only improves the reasoning performance of the model also equips it with remarkable self-rewarding capability, thereby further boosting its inference-time scaling performance.
Applications · Language, Speech and Dialog
Alignment training has tradeoffs: it helps language models (LMs) gain in reasoning and instruction following but might lose out on skills such as creativity and calibration, where unaligned base models are better at. We aim to make the best of both worlds through model collaboration, where different models in the training pipeline collaborate and complement each other. Since LM responses feature interleaving skills that favor different models, we propose Switch Generation, where pretrained and aligned model versions take turns to ``speak'' in a response sequence. Specifically, we train a switcher LM by learning from outcomes of choosing different models to generate the next segment across diverse queries and contexts. At inference time, the switcher LM guides different model checkpoints to dynamically generate the next segment where their strengths are most needed. Extensive experiments with 8 model collaboration baselines and 18 datasets show that 1) model collaboration consistently outperforms individual models on 16 out of 18 tasks, and 2) Switch Generation further outperforms baselines by 12.9% on average. Further analysis reveals that Switch Generation discovers compositional skills to solve problems where individual models struggle and generalizes to unseen models and tasks, reusing and repurposing by-products in expensive model training pipelines that are otherwise discarded.
Accurate cell instance segmentation is foundational for digital pathology analysis. Existing methods based on contour detection and distance mapping still face significant challenges in processing complex and dense cellular regions. Graph coloring-based methods provide a new paradigm for this task, yet the effectiveness of this paradigm in real-world scenarios with dense overlaps and complex topologies has not been verified. Addressing this issue, we release a large-scale dataset GBC-FS 2025, which contains highly complex and dense sub-cellular nuclear arrangements. We conduct the first systematic analysis of the chromatic properties of cell adjacency graphs across four diverse datasets and reveal an important discovery: most real-world cell graphs are non-bipartite, with a high prevalence of odd-length cycles (predominantly triangles). This makes simple 2-coloring theory insufficient for handling complex tissues, while higher-chromaticity models would cause representational redundancy and optimization difficulties. Building on this observation of complex real-world contexts, we propose Disco (Densely-overlapping Cell Instance Segmentation via Adjacency-aware Collaborative Coloring), an adjacency-aware framework based on the “divide and conquer” principle. It uniquely combines a data-driven topological labeling strategy with a constrained deep learning system to resolve complex adjacency conflicts. First, “Explicit Marking” strategy transforms the topological challenge into a learnable classification task by recursively decomposing the cell graph and isolating a “conflict set.” Second, “Implicit Disambiguation” mechanism resolves ambiguities in conflict regions by enforcing feature dissimilarity between different instances, enabling the model to learn separable feature representations. Disco achieves a significant 7.08\% improvement in the PQ metric on the GBC-FS 2025 dataset and an average improvement of 2.72% across all datasets. Furthermore, the predicted “Conflict Map” serves as a novel tool for interpreting topological complexity, offering new potential for data-driven pathology research.
Social Aspects · Accountability, Transparency and Interpretability
Uncovering the opacity of diffusion-based generative models is urgently needed, as their applications continue to expand while their underlying procedures largely remain a black box. With a critical question -- how can the diffusion generation process be interpreted and understood? -- we proposed *Patronus*, an interpretable diffusion model that incorporates a prototypical network to encode semantics in visual patches, revealing *what* visual patterns are learned and *where* and *when* they emerge throughout denoising. This interpretability of Patronus provides deeper insights into the generative mechanism, enabling the detection of shortcut learning via unwanted correlations and the tracing of semantic emergence across timesteps. We evaluate *Patronus* on four natural image datasets and one medical imaging dataset, demonstrating both faithful interpretability and strong generative performance. With this work, we open new avenues for understanding and steering diffusion models through prototype-based interpretability. Our code is available at [nina-weng.github.io/patronus.github.io](https://nina-weng.github.io/patronus.github.io/).
Large Language Models (LLMs) have achieved remarkable success in software engineering tasks when trained with executable runtime environments, particularly in resolving GitHub issues. However, such runtime environments are often unavailable in other domains, especially cybersecurity, where challenge configurations and execution contexts are ephemeral or restricted. We present Cyber-Zero, the first runtime-free framework for synthesizing high-quality agent trajectories to train cybersecurity LLMs. Cyber-Zero leverages publicly available CTF writeups and employs persona-driven LLM simulation to reverse-engineer runtime behaviors and generate realistic, long-horizon interaction sequences without actual environments. Using trajectories synthesized by Cyber-Zero, we train LLM-based agents that achieve up to 13.1% absolute performance gains over baseline models on three prominent CTF benchmarks: InterCode-CTF, NYU CTF Bench, and Cybench. Our best model, Cyber-Zero-32B, establishes new state-of-the-art performance among open-weight models, matching the capabilities of proprietary systems like DeepSeek-V3-0324 and Claude-3.5-Sonnet while offering superior cost-effectiveness, and demonstrating that runtime-free trajectory synthesis can effectively democratize the development of state-of-the-art cybersecurity agents.
General Machine Learning · Causality
Unmeasured confounding is a fundamental obstacle to causal inference from observational data. Latent-variable methods address this challenge by imputing unobserved confounders, yet many lack explicit model-based identification guarantees and are difficult to extend to richer causal structures. We propose Confounder Imputation with Stochastic Neural Networks (CI-StoNet), which parameterizes the conditional structure of a causal directed acyclic graph using a stochastic neural network and imputes latent confounders via adaptive stochastic-gradient Hamiltonian Monte Carlo. Under SUTVA and overlap, and assuming that the structural components of the data-generating process are well approximated by a capacity-controlled sparse deep neural network class, we establish model identification and consistent estimation of the mean potential outcome under a fixed intervention within this class. Although the latent confounder is identifiable only up to reparameterizations that preserve the joint treatment–outcome distribution, the causal estimand is invariant across this observationally equivalent class. We further characterize the effect of overlap on estimation accuracy. Empirical results on simulated and benchmark datasets demonstrate accurate performance, and the framework extends naturally to proxy-variable and multiple-cause settings with overlap diagnostics and bootstrap-based uncertainty quantification.
Deep Learning · Generative Models and Autoencoders
To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite their shared goal, these models have disparate algorithms, theoretical structures, and tradeoffs: discrete diffusion has the most natural domain, Gaussian diffusion has more mature algorithms, and diffusion on the simplex in principle combines the strengths of the other two but in practice suffers from a numerically unstable stochastic processes. Ideally we could see each of these models as instances of the same underlying framework, and enable practitioners to switch between models for downstream applications. However previous theories have only considered connections in special cases. Here we build a theory unifying all three methods of discrete diffusion as different parameterizations of the same underlying process: the Wright-Fisher population genetics model. In particular, we find simplicial and Gaussian diffusion as two large-population limits. Our theory formally connects the likelihoods and hyperparameters of these models and leverages decades of mathematical genetics literature to unlock stable simplicial diffusion. Finally, we relieve the practitioner of balancing model trade-offs by demonstrating it is possible to train a single model that can perform diffusion in any of these three domains at test time. Our experiments show that Wright-Fisher simplicial diffusion is more stable and outperforms previous simplicial diffusion models on conditional DNA generation. We also show that we can train models on multiple domains at once that are competitive with models trained on any individual domain.
Applications · Robotics
The acquisition of robotic skills via reinforcement learning (RL) is crucial for advancing embodied intelligence, but designing effective reward functions for complex tasks remains challenging. Recent methods using large language models (LLMs) can generate reward functions from language instructions, but they often produce overly goal-oriented rewards that neglect state exploration, causing robots to get stuck in local optima. Traditional RL addresses this by adding exploration bonuses, but these are typically generic and inefficient, wasting resources on exploring task-irrelevant areas. To address these limitations, we propose Policy-grounded Synergy of Reward Shaping and Exploration (PoRSE), a novel and unified framework that guides LLMs to generate task-aware reward functions while constructing an abstract affordance space for efficient exploration bonuses. Given the vast number of possible reward-bonus combinations, it is impractical to exhaustively train a policy from scratch for each configuration to identify the best one. Instead, PoRSE employs an in-policy-improvement grounding process, dynamically and continuously generating and filtering out reward-bonus pairs along the policy improvement process. This approach accelerates skill acquisition and fosters a mutually reinforcing relationship between reward shaping, exploration and policy enhancement through close feedback. Experiments show that PoRSE is highly effective, achieving significant improvement in average returns across all robotic tasks compared to previous state-of-the-art methods. It also achieves initial success in two highly challenging manipulation tasks, marking a significant breakthrough.
As LLMs are increasingly deployed in real-world applications, ensuring their ability to refuse malicious prompts, especially jailbreak attacks, is essential for safe and reliable use. Recently, activation steering has emerged as an effective approach for enhancing LLM safety by adding a refusal direction vector to internal activations of LLMs during inference, which will further induce the refusal behaviors of LLMs. However, indiscriminately applying activation steering fundamentally suffers from the trade-off between safety and utility, since the same steering vector can also lead to over-refusal and degraded performance on benign prompts. Although prior efforts, such as vector calibration and conditional steering, have attempted to mitigate this trade-off, their lack of theoretical grounding limits their robustness and effectiveness. To better address the trade-off between safety and utility, we present a theoretically grounded and empirically effective activation steering method called AlphaSteer. Specifically, it considers activation steering as a learnable process with two principled learning objectives: utility preservation and safety enhancement. For utility preservation, it learns to construct a nearly zero vector for steering benign data, with the null-space constraints. For safety enhancement, it learns to construct a refusal direction vector for steering malicious data, with the help of linear regression. Experiments across multiple jailbreak attacks and utility benchmarks demonstrate the effectiveness of AlphaSteer, which significantly improves the safety of LLMs without compromising their general capabilities. Our codes are available at \url{https://anonymous.4open.science/r/AlphaSteer-929C/}.
Computer Vision · Image and Video Generation
Generative models, such as diffusion and autoregressive approaches, have demonstrated impressive capabilities in editing natural images. However, applying these tools to scientific charts rests on a flawed assumption: a chart is not merely an arrangement of pixels but a visual representation of structured data governed by a graphical grammar. Consequently, chart editing is not a pixel-manipulation task but a structured transformation problem. To address this fundamental mismatch, we introduce \textit{FigEdit}, a large-scale benchmark for scientific figure editing comprising over 30,000 samples. Grounded in real-world data, our benchmark is distinguished by its diversity, covering 10 distinct chart types and a rich vocabulary of complex editing instructions. The benchmark is organized into five distinct and progressively challenging tasks: single edits, multi edits, conversational edits, visual-guidance-based edits, and style transfer. Our evaluation of a range of state-of-the-art models on this benchmark reveals their poor performance on scientific figures, as they consistently fail to handle the underlying structured transformations required for valid edits. Furthermore, our analysis indicates that traditional evaluation metrics (e.g., SSIM, PSNR) have limitations in capturing the semantic correctness of chart edits. Our benchmark demonstrates the profound limitations of pixel-level manipulation and provides a robust foundation for developing and evaluating future structure-aware models. By releasing \textit{FigEdit}, we aim to enable systematic progress in structure-aware figure editing, provide a common ground for fair comparison, and encourage future research on models that understand both the visual and semantic layers of scientific charts.