ICLR 2026 Papers

Current Chain-of-Thought (CoT) verification methods predict reasoning correctness based on outputs (black-box) or activations (gray-box), but offer limited insight into \textit{why} a computation fails. We introduce a white-box method: \textbf{Circuit-based Reasoning Verification (CRV)}. We hypothesize that attribution graphs of correct CoT steps, viewed as \textit{execution traces} of the model's latent reasoning circuits, possess distinct structural fingerprints from those of incorrect steps. By training a classifier on structural features of these graphs, we show that these traces contain a powerful signal of reasoning errors. Our white-box approach yields novel scientific insights unattainable by other methods. (1) We demonstrate that structural signatures of error are highly predictive, establishing the viability of verifying reasoning directly via its computational graph. (2) We find these signatures to be highly domain-specific, revealing that failures in different reasoning tasks manifest as distinct computational patterns. (3) We provide evidence that these signatures are not merely correlational; by using our analysis to guide targeted interventions on individual transcoder features, we successfully correct the model's faulty reasoning. Our work shows that, by scrutinizing a model's computational process, we can move from simple error detection to a deeper, causal understanding of LLM reasoning.

Deep neural networks trained on nonstationary data must balance stability (i.e., retaining prior knowledge) and plasticity (i.e., adapting to new tasks). Standard reinitialization methods, which reinitialize weights toward their original values, are widely used but difficult to tune: conservative reinitializations fail to restore plasticity, while aggressive ones erase useful knowledge. We propose FIRE, a principled reinitialization method that explicitly balances the stability–plasticity tradeoff. FIRE quantifies stability through Squared Frobenius Error (SFE), measuring proximity to past weights, and plasticity through Deviation from Isometry (DfI), reflecting weight isotropy. The reinitialization point is obtained by solving a constrained optimization problem, minimizing SFE subject to DfI being zero, which is efficiently approximated by Newton–Schulz iteration. FIRE is evaluated on continual visual learning (CIFAR-10 with ResNet-18), language modeling (OpenWebText with GPT-0.1B), and reinforcement learning (HumanoidBench with SAC and Atari games with DQN). Across all domains, FIRE consistently outperforms both naive training without intervention and standard reinitialization methods, demonstrating effective balancing of the stability–plasticity tradeoff.

The paradigm of LLM-as-a-judge is emerging as a scalable and efficient alternative to human evaluation, demonstrating strong performance on well-defined tasks. However, its reliability in open-ended tasks with dynamic environments and complex interactions remains unexplored. To bridge the gap, we introduce WebDevJudge, a systematic benchmark for assessing LLM-as-a-judge performance in web development, with support for both non-interactive evaluation based on static observations and continuous interactive evaluation with a dynamic web environment. WebDevJudge comprises human preference labels over paired web implementations, annotated with structured and query-grounded rubrics to ensure high-quality ground truth. Using this benchmark, we comprehensively evaluate various evaluators, including LLMs, MLLMs, and agentic workflows. We systematically investigate the impact of different paradigms and guidance mechanisms. Our experiments reveal a significant gap between LLM judges and human experts. In-depth analysis indicates this gap stems from fundamental model limitations, including failures in recognizing functional equivalence, verifying task feasibility, and mitigating bias. Overall, WebDevJudge presents a significant challenge to LLM-as-a-judge, offering insights to guide future research toward developing more reliable and capable automated evaluators for complicated scenarios.

Contrastive learning has been at the bedrock of unsupervised learning in recent years, allowing training with massive unlabeled data for both task-specific and general (foundation) models. A prototypical loss in contrastive training is InfoNCE and its variants. In this paper we show that the embedding of the features which emerge from InfoNCE training can be well approximated by a multivariate Gaussian distribution. We justify this claim by taking two approaches. First, we show that under certain alignment and concentration assumptions, finite projections of a high dimensional representation approach multivariate Gaussian distribution, as the representation dimensions approach infinity. Next, under less strict assumptions, we show that adding a small regularization term (which vanishes asymptotically) that promotes low feature norm and high feature entropy, we reach similar asymptotic results. We demonstrate experimentally, in a synthetic setting, CIFAR-10 and on pretrained foundation models, that the features indeed follow almost precise Gaussian distribution. One can use the Gaussian model to easily derive analytic expressions in the representation space and to obtain very useful measures, such as likelihood, data entropy and mutual information. Hence, we expect such theoretical grounding to be very useful in various applications involving contrastive learning.

High-quality instance and panoptic segmentation has traditionally relied on dense instance-level annotations such as masks, boxes, or points, which are costly, inconsistent, and difficult to scale. Unsupervised and weakly-supervised approaches reduce this burden but remain constrained by semantic backbone constraints and human bias, often producing merged or fragmented outputs. We present TRACE (TRAnsforming diffusion Cues to instance Edges), showing that text-to-image diffusion models secretly function as instance edge annotators. TRACE identifies the Instance Emergence Point (IEP) where object boundaries first appear in self-attention maps, extracts boundaries through Attention Boundary Divergence (ABDiv), and distills them into a lightweight one-step edge decoder. This design removes the need for per-image diffusion inversion, achieving 81× faster inference while producing sharper and more connected boundaries. On the COCO benchmark, TRACE improves unsupervised instance segmentation by +5.1 AP, and in tag-supervised panoptic segmentation it outperforms point-supervised baselines by +1.7 PQ without using any instance-level labels. These results reveal that diffusion models encode hidden instance boundary priors, and that decoding these signals offers a practical and scalable alternative to costly manual annotation. **Project Page:** https://shjo-april.github.io/TRACE.

Masked diffusion models (MDMs) for text offer a compelling alternative to traditional autoregressive language models. Parallel generation makes them efficient, but their computational capabilities and the limitations inherent to their parallelism remain largely unexplored. To this end, we characterize what types of reasoning problems MDMs can provably solve and how efficiently. We do this by connecting MDMs to the well-understood reasoning frameworks of chain of thought (CoT) and padded looped transformers (PLTs) in the finite-precision log-width setting: We show that MDMs and polynomially-padded PLTs are, in fact, equivalent in this setting, and that MDMs can solve all problems that CoT-augmented transformers can. Moreover, we showcase classes of problems (including regular languages) for which MDMs are inherently more efficient than CoT transformers, where parallel generation allows for substantially faster reasoning.

Handcrafted optimizers become prohibitively inefficient for complex black-box optimization (BBO) tasks. MetaBBO addresses this challenge by meta-learning to automatically configure optimizers for low-level BBO tasks, thereby eliminating heuristic dependencies. However, existing methods typically require extensive handcrafted training tasks to learn meta-strategies that generalize to target tasks, which poses a critical limitation for realistic applications with unknown task distributions. To overcome the issue, we propose the Adaptive meta Black-box Optimization Model (ABOM), which performs online parameter adaptation using solely optimization data from the target task, obviating the need for predefined task distributions. Unlike conventional metaBBO frameworks that decouple meta-training and optimization phases, ABOM introduces a closed-loop adaptive parameter learning mechanism, where parameterized evolutionary operators continuously self-update by leveraging generated populations during optimization. This paradigm shift enables zero-shot optimization: ABOM achieves competitive performance on synthetic BBO benchmarks and realistic unmanned aerial vehicle path planning problems without any handcrafted training tasks. Visualization studies reveal that parameterized evolutionary operators exhibit statistically significant search patterns, including natural selection and genetic recombination.

Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic Gaussian inputs whose covariance spectrum follows a power law. Unlike the isotropic case, where dynamics collapse to a two-dimensional system, anisotropy yields a qualitatively new regime in which an infinite hierarchy of coupled equations governs the evolution of the summary statistics. We develop a tractable reduction that reveals a three-phase trajectory: (i) fast escape from low alignment, (ii) slow convergence of the summary statistics, and (iii) spectral-tail learning in low-variance directions. From this decomposition, we derive explicit scaling laws for the mean-squared error, showing how spectral decay dictates convergence times and error curves. Experiments confirm the predicted phases and exponents. These results provide the first rigorous characterization of scaling laws in nonlinear regression with anisotropic data, highlighting how anisotropy reshapes learning dynamics.

The probabilistic diffusion model (DM), generating content by inferencing through a recursive chain structure, has emerged as a powerful framework for visual generation. After pre-training on enormous data, the model needs to be properly aligned to meet requirements for downstream applications. How to efficiently align the foundation DM is a crucial task. Contemporary methods are either based on Reinforcement Learning (RL) or truncated Backpropagation (BP). However, RL and truncated BP suffer from low sample efficiency and biased gradient estimation, respectively, resulting in limited improvement or, even worse, complete training failure. To overcome the challenges, we propose the Recursive Likelihood Ratio (RLR) optimizer, a Half-Order (HO) fine-tuning paradigm for DM. The HO gradient estimator enables the computation graph rearrangement within the recursive diffusive chain, making the RLR's gradient estimator **an unbiased one with lower variance** than other methods. We theoretically investigate the bias, variance, and convergence of our method. Extensive experiments are conducted on image and video generation to validate the superiority of the RLR. Furthermore, we propose a novel prompt technique that is natural for the RLR to achieve a synergistic effect. The implementation is available at https://github.com/RTkenny/RLR-Optimizer.

Language models demonstrate remarkable abilities when pre-trained on large text corpora and fine-tuned for specific tasks, but how and why pre-training shapes the success of the final model remains poorly understood. Notably, although pre-training success is often quantified by cross entropy loss, cross entropy can be poorly predictive of downstream performance. Instead, we provide a theoretical perspective on this relationship through the lens of coverage, which quantifies the probability mass the pre-trained model places on high-quality responses and which is necessary and sufficient for post-training and test-time scaling methods like Best-of-N to succeed. Our main results develop an understanding of the coverage principle, a phenomenon whereby next-token prediction implicitly optimizes toward a model with good coverage. In particular, we uncover a mechanism that explains the power of coverage in predicting downstream performance: coverage generalizes faster than cross entropy, avoiding spurious dependence on problem dependent parameters such as the sequence length. We also study practical algorithmic interventions with provable benefits for improving coverage, including (i) model/checkpoint selection procedures, (ii) gradient normalization schemes, and (iii) test-time decoding strategies.

Semantic associations such as the link between "bird" and "flew" are foundational for language modeling as they enable models to go beyond memorization and instead generalize and generate coherent text. Understanding how these associations are learned and represented in language models is essential for connecting deep learning with linguistic theory and developing a mechanistic foundation for large language models. In this work, we analyze how these associations emerge from natural language data in attention-based language models through the lens of training dynamics. By leveraging a leading-term approximation of the gradients, we develop closed-form expressions for the weights at early stages of training that explain how semantic associations first take shape. Through our analysis, we reveal that each set of weights of the transformer has closed-form expressions as simple compositions of three basis functions--bigram, token-interchangeability, and context mappings--reflecting the statistics in the text corpus and uncover how each component of the transformer captures the semantic association based on these compositions. Experiments on real-world LLMs demonstrate that our theoretical weight characterizations closely match the learned weights, and qualitative analyses further guide us on how our theorem shines light on interpreting the learned association in transformers.

Graph clustering is a fundamental task in data analysis, aiming at grouping nodes with similar characteristics in the graph into clusters. This problem has been widely explored using graph neural networks (GNNs) due to their ability to leverage node attributes and graph topology for effective cluster assignments. However, representations learned through GNNs typically struggle to capture global relationships between nodes via local message-passing mechanisms. Moreover, the redundancy and noise inherently present in the graph data may easily result in node representations lacking compactness and robustness. To address the aforementioned issues, we propose a conjoint framework called CoCo, which captures compactness and consistency in the learned node representations for deep graph clustering. Technically, our CoCo leverages graph convolutional filters to learn robust node representations from both local and global views, and then encodes them into low-rank compact embeddings, thus effectively removing the redundancy and noise as well as uncovering the intrinsic underlying structure. To further enrich the node semantics, we develop a consistency learning strategy based on compact embeddings to facilitate knowledge transfer from the two perspectives. Our experimental findings indicate that our proposed CoCo outperforms state-of-the-art counterparts on various benchmark datasets.

We introduce **Gaia2**, a benchmark for evaluating large language model agents in realistic, asynchronous environments. Unlike prior static or synchronous evaluations, Gaia2 introduces scenarios where environments evolve independently of agent actions, requiring agents to operate under temporal constraints, adapt to noisy and dynamic events, resolve ambiguity, and collaborate with other agents. Each scenario is paired with a write-action verifier, enabling fine-grained, action-level evaluation and making Gaia2 directly usable for reinforcement learning from verifiable rewards. Our evaluation of state-of-the-art proprietary and open-source models shows that no model dominates across capabilities: GPT-5 (high) reaches the strongest overall score of 42% pass@1 but fails on time-sensitive tasks, Claude-4 Sonnet trades accuracy and speed for cost, Kimi-K2 leads among open-source models with 21% pass@1. These results highlight fundamental trade-offs between reasoning, efficiency, robustness, and expose challenges in closing the “sim2real” gap. Gaia2 is built on a consumer environment with the open-source **Agents Research Environments** platform and designed to be easy to extend. By releasing Gaia2 alongside the foundational ARE framework, we aim to provide the community with a flexible infrastructure for developing, benchmarking, and training the next generation of practical agent systems.

Modern optimizers like Adam and Muon are central to training large language models, but their reliance on first- and second-order momenta introduces significant memory overhead, which constrains scalability and computational efficiency. In this work, we re-frame the exponential moving average (EMA) used in these momenta as the training of a linear regressor via online gradient flow. Building on this equivalence, we introduce LoRA-Pre, a novel low-rank optimizer designed for efficient pre-training. Specifically, LoRA-Pre reduces the optimizer's memory footprint by decomposing the full momentum matrix into a compact low-rank subspace within the online linear learner, thereby maintaining optimization performance while improving memory efficiency. We empirically validate LoRA-Pre's efficacy by pre-training models from the Llama architecture family, scaling from 60M to 1B parameters. LoRA-Pre achieves the highest performance across all model sizes. Notably, LoRA-Pre demonstrates remarkable rank efficiency, achieving comparable or superior results using only 1/8 the rank of baseline methods. Beyond pre-training, we evaluate LoRA-Pre's effectiveness in fine-tuning scenarios. With the same rank, LoRA-Pre consistently outperforms all efficient fine-tuning baselines. Specifically, compared to standard LoRA, LoRA-Pre achieves substantial improvements of 3.14 points on Llama-3.1-8B and 6.17 points on Llama-2-7B, validating our approach's effectiveness across both pre-training and fine-tuning paradigms.

Reward models (RMs) play a critical role in aligning AI behaviors with human preferences, yet they face two fundamental challenges: (1) Modality Imbalance, where most RMs are mainly focused on text and image modalities, offering limited support for video, audio, and other modalities; and (2) Preference Rigidity, where training on fixed binary preference pairs fails to capture the complexity and diversity of personalized preferences. To address the above challenges, we propose Omni-Reward, a step toward generalist omni-modal reward modeling with support for free-form preferences, consisting of: (1) Evaluation: We introduce Omni-RewardBench, the first omni-modal RM benchmark with free-form preferences, covering nine tasks across five modalities including text, image, video, audio, and 3D; (2) Data: We construct Omni-RewardData, a multimodal preference dataset comprising 248K general preference pairs and 69K instruction-tuning pairs for training generalist omni-modal RMs; (3) Model: We propose Omni-RewardModel, which includes both discriminative and generative RMs, and achieves strong performance on Omni-RewardBench as well as other widely used reward modeling benchmarks.

In this work, we propose FFDP, a set of IO-aware non-GEMM fused kernels supplemented with a distributed framework for image registration at unprecedented scales. Image registration is an inverse problem fundamental to biomedical and life sciences, but algorithms have not scaled in tandem with image acquisition capabilities. Our framework complements existing model parallelism techniques proposed for large-scale transformer training by optimizing non-GEMM bottlenecks and enabling convolution-aware tensor sharding. We demonstrate unprecedented capabilities by performing multimodal registration of a 100μm ex-vivo human brain MRI volume at native resolution – an inverse problem more than 570× larger than a standard clinical datum in about a minute using only 8 A6000 GPUs. FFDP accelerates existing state-of-the-art optimization and deep learning registration pipelines by upto 6 − 7× while reducing peak memory consumption by 20 − 59%. Comparative analysis on a 250μm dataset shows that FFDP can fit upto 64× larger problems than existing SOTA on a single GPU, and highlights both the performance and efficiency gains of FFDP compared to SOTA image registration methods.

The hippocampus contains neurons whose firing correlates with an animal's location and orientation in space. Collectively, these neurons are held to support a cognitive map of the environment, enabling the recall of and navigation to specific locations. Although recent studies have characterised the timelines of spatial neuron development, no unifying mechanistic model has yet been proposed. Moreover, the processes driving the emergence of spatial representations in the hippocampus remain unclear (Tan et al., 2017). Here, we combine computational analysis of postnatal locomotor development with a recurrent neural network (RNN) model of hippocampal function to demonstrate how changes in movement statistics -- and the resulting sensory experiences -- shape the formation of spatial tuning. First, we identify distinct developmental stages in rat locomotion during open-field exploration using published experimental data. Then, we train shallow RNNs to predict upcoming visual stimuli from concurrent visual and vestibular inputs, exposing them to trajectories that reflect progressively maturing locomotor patterns. Our findings reveal that these changing movement statistics drive the sequential emergence of spatially tuned units, mirroring the developmental timeline observed in rats. The models generate testable predictions about how spatial tuning properties mature -- predictions we confirm through analysis of hippocampal recordings. Critically, we demonstrate that replicating the specific statistics of developmental locomotion -- rather than merely accelerating sensory change -- is essential for the emergence of an allocentric spatial representation. These results establish a mechanistic link between embodied sensorimotor experience and the ontogeny of hippocampal spatial neurons, with significant implications for neurodevelopmental research and predictive models of navigational brain circuits.

While achieving exceptional generative quality, modern diffusion, flow, and other matching models suffer from slow inference, as they require many steps of iterative generation. Recent distillation methods address this by training efficient one-step generators under the guidance of a pre-trained teacher model. However, these methods are often constrained to only one specific framework, e.g., only to diffusion or only to flow models. Furthermore, these methods are naturally data-free, and to benefit from the usage of real data, it is required to use an additional complex adversarial training with an extra discriminator model. In this paper, we present \textbf{RealUID}, a unified distillation framework for all matching models that seamlessly incorporates real data into the distillation procedure without GANs. Our \textbf{RealUID} approach offers a simple theoretical foundation that covers previous distillation methods for Flow Matching and Diffusion models, and is also extended to their modifications, such as Bridge Matching and Stochastic Interpolants.

Medical question answering (QA) benchmarks often focus on multiple-choice or fact-based tasks, leaving open-ended answers to real patient questions underexplored. This gap is particularly critical in mental health, where patient questions often mix symptoms, treatment concerns, and emotional needs, requiring answers that balance clinical caution with contextual sensitivity. We present CounselBench, a large-scale benchmark developed with 100 mental health professionals to evaluate and stress-test large language models (LLMs) in realistic help-seeking scenarios. The first component, CounselBench-EVAL, contains 2,000 expert evaluations of answers from GPT-4, LLaMA 3, Gemini, and online human therapists on patient questions from the public forum CounselChat. Each answer is rated across six clinically grounded dimensions, with span-level annotations and written rationales. Expert evaluations show that while LLMs achieve high scores on several dimensions, they also exhibit recurring issues, including unconstructive feedback, overgeneralization, and limited personalization or relevance. Responses were frequently flagged for safety risks, most notably unauthorized medical advice. Follow-up experiments show that LLM judges systematically overrate model responses and overlook safety concerns identified by human experts. To probe failure modes more directly, we construct CounselBench-Adv, an adversarial dataset of 120 expert-authored mental health questions designed to trigger specific model issues. Expert evaluation of 1,080 responses from nine LLMs reveals consistent, model-specific failure patterns. Together, CounselBench establishes a clinically grounded framework for benchmarking LLMs in mental health QA.