Large reasoning models (LRMs) like OpenAI-o1 have shown impressive capabilities in natural language reasoning. However, these models frequently demonstrate inefficiencies or inaccuracies when tackling complex mathematical operations. While integrating computational tools such as Code Interpreters (CIs) offers a promising solution, it introduces a critical challenge: a conflict between the model's internal, probabilistic reasoning and the external, deterministic knowledge provided by the CI, which often leads models to unproductive deliberation. To overcome this, we introduce CoRT (Code-Optimized Reasoning Training), a post-training framework designed to teach LRMs to effectively utilize CIs.

We study Transformers through the perspective of optimal control theory, using tools from continuous-time formulations to derive actionable insights into training and architecture design. This framework improves the performance of existing Transformer models while providing desirable theoretical guarantees, including generalization and robustness. Our framework is designed to be plug-and-play, enabling seamless integration with established Transformer models and requiring only slight changes to the implementation. We conduct seven extensive experiments on tasks motivated by text generation, sentiment analysis, image classification, and point cloud classification. Experimental results show that the framework improves the test performance of the baselines, while being more parameter-efficient. On character-level text generation with nanoGPT, our framework achieves a 46\% reduction in final test loss while using 42\% fewer parameters. On GPT-2, our framework achieves a 9.3\% reduction in final test loss, demonstrating scalability to larger models. To the best of our knowledge, this is the first work that applies optimal control theory to both the training and architecture of Transformers. It offers a new foundation for systematic, theory-driven improvements and moves beyond costly trial-and-error approaches.

Web navigation is a unique domain that can automate many repetitive real-life tasks and is challenging as it requires long-horizon sequential decision making beyond typical multimodal large language model (MLLM) tasks. Yet, specialized reward models for web navigation that can be utilized during both training and test-time have been absent until now. Despite the importance of speed and cost-effectiveness, prior works have utilized MLLMs as reward models, which poses significant constraints for real-world deployment. To address this, in this work, we propose the first process reward model (PRM) called Web-Shepherd which could assess web navigation trajectories in a step-level. To achieve this, we first construct the WebPRM Collection, a large-scale dataset with 40K step-level preference pairs and annotated checklists spanning diverse domains and difficulty levels. Next, we also introduce the WebRewardBench, the first meta-evaluation benchmark for evaluating PRMs. In our experiments, we observe that our Web-Shepherd achieves about 30 points better accuracy compared to using GPT-4o on WebRewardBench. Furthermore, when testing on WebArena-lite by using GPT-4o-mini as the policy and Web-Shepherd as the verifier, we achieve 10.9 points better performance, in 10x less cost compared to using GPT-4o-mini as the verifier.

While text-to-image models like GPT-4o-Image and FLUX are rapidly proliferating, they often encounter challenges such as hallucination, bias, and the production of unsafe, low-quality output. To effectively address these issues, it is crucial to align these models with desired behaviors based on feedback from a multimodal judge. Despite their significance, current multimodal judges frequently undergo inadequate evaluation of their capabilities and limitations, potentially leading to misalignment and unsafe fine-tuning outcomes. To address this issue, we introduce MJ-Bench, a novel benchmark which incorporates a comprehensive preference dataset to evaluate multimodal judges in providing feedback for image generation models across six key perspectives: alignment, safety, image quality, bias, composition, and visualization. Specifically, we evaluate a large variety of multimodal judges including smaller-sized CLIP-based scoring models, open-source VLMs, and close-source VLMs on each decomposed subcategory of our preference dataset. Experiments reveal that close-source VLMs generally provide better feedback, with GPT-4o outperforming other judges in average. Compared with open-source VLMs, smaller-sized scoring models can provide better feedback regarding text-image alignment and image quality, while VLMs provide more accurate feedback regarding safety and generation bias due to their stronger reasoning capabilities. Further studies in feedback scale reveal that VLM judges can generally provide more accurate and stable feedback in natural language than numerical scales. Notably, human evaluations on end-to-end and fine-tuned models using separate feedback from these multimodal judges provide similar conclusions, further confirming the effectiveness of MJ-Bench.

The hypothesis that Convolutional Neural Networks (CNNs) are inherently texture-biased has shaped much of the discourse on feature use in deep learning. We revisit this hypothesis by examining limitations in the cue-conflict experiment by Geirhos et al. To address these limitations, we propose a domain-agnostic framework that quantifies feature reliance through systematic suppression of shape, texture, and color cues, avoiding the confounds of forced-choice conflicts. By evaluating humans and neural networks under controlled suppression conditions, we find that CNNs are not inherently texture-biased but predominantly rely on local shape features. Nonetheless, this reliance can be substantially mitigated through modern training strategies or architectures (ConvNeXt, ViTs). We further extend the analysis across computer vision, medical imaging, and remote sensing, revealing that reliance patterns differ systematically: computer vision models prioritize shape, medical imaging models emphasize color, and remote sensing models exhibit a stronger reliance on texture.

Hebbian learning is a biological principle that intuitively describes how neurons adapt their connections through repeated stimuli. However, when applied to machine learning, it suffers serious issues due to the unconstrained updates of the connections and the lack of accounting for feedback mediation. Such shortcomings limit its effective scaling to complex network architectures and tasks. To this end, here we introduce the Structural Projection Hebbian Representation (SPHeRe), a novel unsupervised learning method that integrates orthogonality and structural information preservation through a local auxiliary nonlinear block. The loss for structural information preservation backpropagates to the input through an auxiliary lightweight projection that conceptually serves as feedback mediation while the orthogonality constraints account for the boundedness of updating magnitude. Extensive experimental results show that SPHeRe achieves SOTA performance among unsupervised synaptic plasticity approaches on standard image classification benchmarks, including CIFAR-10, CIFAR-100, and Tiny-ImageNet. Furthermore, the method exhibits strong effectiveness in continual learning and transfer learning scenarios, and image reconstruction tasks show the robustness and generalizability of the extracted features. This work demonstrates the competitiveness and potential of Hebbian unsupervised learning rules within modern deep learning frameworks, demonstrating the possibility of efficient and biologically inspired learning algorithms without the strong dependence on strict backpropagation.

Large Language Models (LLMs) demonstrate human-level or even superior language abilities, effectively modeling syntactic structures, yet the specific computational units responsible remain unclear. A key question is whether LLM behavioral capabilities stem from mechanisms akin to those in the human brain. To address these questions, we introduce the Hierarchical Frequency Tagging Probe (HFTP), a tool that utilizes frequency-domain analysis to identify neuron-wise components of LLMs (e.g., individual Multilayer Perceptron (MLP) neurons) and cortical regions (via intracranial recordings) encoding syntactic structures. Our results show that models such as GPT-2, Gemma, Gemma 2, Llama 2, Llama 3.1, and GLM-4 process syntax in analogous layers, while the human brain relies on distinct cortical regions for different syntactic levels. Representational similarity analysis reveals a stronger alignment between LLM representations and the left hemisphere of the brain (dominant in language processing). Notably, upgraded models exhibit divergent trends: Gemma 2 shows greater brain similarity than Gemma, while Llama 3.1 shows less alignment with the brain compared to Llama 2. These findings offer new insights into the interpretability of LLM behavioral improvements, raising questions about whether these advancements are driven by human-like or non-human-like mechanisms, and establish HFTP as a valuable tool bridging computational linguistics and cognitive neuroscience. This project is available at https://github.com/LilTiger/HFTP.

This paper introduces an approach for training o1-like RAG models that retrieve and reason over relevant information step by step before generating the final answer. Conventional RAG methods usually perform a single retrieval step before the generation process, which limits their effectiveness in addressing complex queries due to imperfect retrieval results. In contrast, our proposed method, CoRAG (Chain-of-Retrieval Augmented Generation), allows the model to dynamically reformulate the query based on the evolving state. To train CoRAG effectively, we utilize rejection sampling to automatically generate intermediate retrieval chains, thereby augmenting existing RAG datasets that only provide the correct final answer. At test time, we propose various decoding strategies to scale the model's test-time compute by controlling the length and number of sampled retrieval chains. Experimental results across multiple benchmarks validate the efficacy of CoRAG, particularly in multi-hop question answering tasks, where we observe more than $10$ points improvement in EM score compared to strong baselines. On the KILT benchmark, CoRAG establishes a new state-of-the-art performance across a diverse range of knowledge-intensive tasks. Furthermore, we offer comprehensive analyses to understand the scaling behavior of CoRAG, laying the groundwork for future research aimed at developing factual and grounded foundation models.

The success of Reinforcement Learning from Human Feedback (RLHF) critically depends on the quality of the reward model. However, while this quality is primarily evaluated through accuracy, it remains unclear whether accuracy fully captures what makes a reward model an effective teacher. We address this question from an optimization perspective. First, we prove that regardless of how accurate a reward model is, if it induces low reward variance, then the RLHF objective suffers from a flat landscape. Consequently, even a perfectly accurate reward model can lead to extremely slow optimization, underperforming less accurate models that induce higher reward variance. We additionally show that a reward model that works well for one language model can induce low reward variance, and thus a flat objective landscape, for another. These results establish a fundamental limitation of evaluating reward models solely based on accuracy or independently of the language model they guide. Experiments using models of up to 8B parameters corroborate our theory, demonstrating the interplay between reward variance, accuracy, and reward maximization rate. Overall, our findings highlight that beyond accuracy, a reward model needs to induce sufficient variance for efficient optimization.

What does it truly mean for a language model to "reason" strategically, and can scaling up alone guarantee intelligent, context-aware decisions? Strategic decision-making requires adaptive reasoning, where agents anticipate and respond to others' actions under uncertainty. Yet, most evaluations of large language models (LLMs) for strategic decision-making often rely heavily on Nash Equilibrium (NE) benchmarks, overlook reasoning depth, and fail to reveal the mechanisms behind model behavior. To address this gap, we introduce a behavioral game-theoretic evaluation framework that disentangles intrinsic reasoning from contextual influence. Using this framework, we evaluate 22 state-of-the-art LLMs across diverse strategic scenarios. We find models like GPT-o3-mini, GPT-o1, and DeepSeek-R1 lead in reasoning depth. Through thinking chain analysis, we identify distinct reasoning styles--such as maximin or belief-based strategies--and show that longer reasoning chains do not consistently yield better decisions. Furthermore, embedding demographic personas reveals context-sensitive shifts: some models (e.g., GPT-4o, Claude-3-Opus) improve when assigned female identities, while others (e.g., Gemini 2.0) show diminished reasoning under minority sexuality personas. These findings underscore that technical sophistication alone is insufficient; alignment with ethical standards, human expectations, and situational nuance is essential for the responsible deployment of LLMs in interactive settings.