NeurIPS 2026 论文列表

Tools from random matrix theory have become central to deep learning theory, using spectral information to provide mechanisms for modeling generalization, robustness, scaling, and failure modes. While often capable of modeling empirical behavior, practical computations are limited by matrix size, often imposing a restriction to models that are too small to be realistic. This motivates the inference of properties of larger models from the behavior of smaller ones. Free decompression (FD) is a recently proposed method for extrapolating spectral information across matrix sizes, but its utility is currently limited by strong assumptions that preclude its implementation on more realistic machine learning (ML) models. We use algebraic spectral curve theory to provide a general FD methodology for spectral densities whose Stieltjes transform satisfies an algebraic relation, a modeling assumption that is more likely to hold in practice. This recasts FD as an evolution along spectral curves which can be readily integrated. Our framework enables the expansion of spectral densities that have multiple or multi-modal bulks, that exist at multiple scales, and that contain atoms, all characteristic of real-world data and popular ML models. We demonstrate the efficacy of our framework on models of interest in modern ML, including Hessian and activation matrices associated with neural networks and large-scale diffusion models.

State Space Models (SSMs) compress sequence history into a bounded recurrent state, making the resulting memory law a central architectural choice for long-context performance. Most modern SSMs rely on ODE-based dynamics that lead to exponential forgetting, limiting their ability to retain information over broad temporal ranges. We introduce FRAC, a selective SSM architecture derived from fractional dynamics that replaces this exponential decay with power-law long memory. To make fractional dynamics practical, FRAC approximates the heavy-tailed target kernel with a finite-state, log-spaced sum of exponential modes. This construction turns fractional memory into an efficient recurrent module with parallel training and prefill, while retaining bounded-state autoregressive decoding. Extensive experiments, including 1.3B-parameter language modeling, demonstrate that FRAC consistently improves long-context performance over state-of-the-art SSM baselines while staying competitive on short-context. These results show that fractional dynamics provide a practical and effective prior for long-context SSMs.

Follow the regularized leader (FTRL) is a foundational algorithm in online learning whose regret properties have been extensively studied for decades. However, in stark contrast to mirror descent---and gradient descent in particular---the convergence of FTRL to first-order stationary points in constrained nonconvex optimization was hitherto unresolved. In this paper, we show that continuous-time FTRL can fail to converge even asymptotically in constrained optimization problems; that is, the Karush-Kuhn-Tucker (KKT) gap of FTRL can remain bounded away from zero indefinitely. This is especially surprising in light of the fact that continuous-time FTRL guarantees a monotonic improvement of the objective value. As a result, we establish that non-convergent behavior of no-regret dynamics---which besets general variational inequality problems---can occur even in potential systems. From a technical standpoint, our construction relies on an infinitely differentiable function where the gradient flow dynamics exhibit decelerating oscillations without ever converging pointwise, which we in turn embed into higher-dimensional FTRL dynamics that sustain a perpetually large KKT gap.

Reliable hypothesis testing is the foundation of many empirical scientific claims. Large language model (LLM) agents are increasingly used to automate this process, as they can inspect datasets, generate code, and produce analyses end-to-end. However, we show that they frequently make subtle inferential errors that lead to incorrect conclusions despite correctly executed analyses. Existing benchmarks fail to capture this failure mode, as they rarely assess whether a reported p-value is statistically valid given the assumptions underlying the data. We address this gap by building P-Bench, a benchmark comprising 425 open-ended, realistic hypothesis-testing tasks spanning economics, biology, and medicine. Each task requires an agent to select a statistical method, compute a p-value, and draw a conclusion given only a scientific hypothesis and a dataset. We further introduce Fisher-R1, an open-weight LLM agent trained for rigorous hypothesis testing using synthetic tasks and reinforcement learning. On P-Bench, Fisher-R1-14B substantially improves over its backbone and outperforms strong proprietary and open-source baselines, including GPT-5.4 and DeepSeek-V4-Pro, achieving a 21% average relative improvement in single-trial success over DeepSeek-V4-Pro, with gains up to 26% on the most challenging tasks. Our results demonstrate that current LLM agents lack reliable statistical reasoning for hypothesis testing and that reinforcement learning on tasks with verified statistical reward substantially improves reliability.

The Lipschitz constant of neural networks is widely used in robustness, control, generalization bounds, and training stability. As modern neural networks continue to scale, existing methods for Lipschitz estimation are either very time-consuming or overly loose. In this work, we focus on both fast and accurate Lipschitz estimation for large feedforward neural networks. We first reformulate the well-known semidefinite program (SDP) framework into an explicit recursive form, and introduce a key theoretical result, bound backpropagation: the SDP objective has upper and lower bounds that can be propagated backward along the recursive computation graph and depend only on partial variables. Leveraging this property, we decompose the original SDP into a sequence of small subproblems, each minimizing a combination of upper and lower bounds over partial variables. We prove that each subproblem is one-dimensional and convex, enabling fast solution via the secant method. Finally, we present the full FLIP algorithm and its complexity, yielding fast and tight Lipschitz estimation for large feedforward networks. Experiments on both randomly generated and trained networks show that FLIP improves speed and tightness by several orders of magnitude over prior methods, giving the tightest Lipschitz estimates for 100M-parameter networks in 3 seconds.

We study the problem of propagating the mean and covariance of a general multivariate Gaussian distribution through a deep (residual) neural network using layer-by-layer moment matching. We close a longstanding gap by deriving exact moment matching for the probit, GeLU, ReLU (as a limit of GeLU), Heaviside (as a limit of probit), and sine activation functions; for both feedforward and generalized residual layers. On random networks, we find orders-of-magnitude improvements in the KL divergence error metric, up to a millionfold, over popular alternatives. On a variational Bayesian neural network, we show that our method attains hundredfold improvements in KL divergence from Monte Carlo ground truth over a state-of-the-art deterministic inference method. We also give an smooth-distance error bound showing that, under regularity assumptions, moment matching removes the leading low-variance errors and propagates higher-order local accuracy through the layers of a network.

A common failure mode in long-horizon agentic test-time scaling is error propagation, where factual errors or invalid deductions introduced at intermediate steps persist in the agent's belief state and contaminate later reasoning. Existing test-time scaling methods provide limited control over this process, as they often rely on agents to detect their own mistakes, select among flawed trajectories, or refine solutions only after errors have already shaped the reasoning path. We propose ExComm, a communication protocol for exploration-stage agentic test-time scaling. ExComm is motivated by the empirical observation that the majority of intermediate errors in parallel agentic reasoning produce detectable cross-agent factual conflicts. Leveraging the iterative structure of agentic workflows, ExComm periodically audits agent belief states to detect such conflicts, resolves them through a dedicated tool-based verification loop, and returns concise, targeted feedback to the involved agents. Corrections are incorporated through soft belief updates, which append verified feedback rather than overwriting existing beliefs. Furthermore, to prevent collapsing trajectory diversity due to communication, ExComm further introduces a trajectory diversification module that redirects redundant trajectories toward orthogonal strategies. Experiments on AIME 2024, AIME 2025, and GAIA with Gemini-2.5-Flash-Lite and Qwen3.5-4B show that ExComm consistently outperforms strong test-time scaling baselines, achieving average performance gains of 5.7\% and 5.0\% over the best-performing baselines, respectively. Further analyses demonstrate improved error recovery, favorable scaling behavior, stronger diversity than adapted communication baselines, and the best performance-cost trade-off among the evaluated methods.

Foundation models of brain activity aim to learn representations from large-scale neural recordings that generalize across sessions, subjects, species, and downstream tasks. Transformer-based models have emerged as a promising architecture for this goal and begin all with the same first step --- tokenization: transforming sparse binary events into vector representations that downstream networks can consume. In other areas of machine learning, tokenization is its own design problem, distinct from the downstream foundation model. Several mostly implicit tokenization approaches dominate the literature, but their impact on downstream performance has not been systematically evaluated. We propose four explicit desiderata for a neural tokenizer---reconstruction fidelity, downstream utility, cross-instance generalization, and compression---and a framework of metrics spanning seven dimensions, including firing statistics, encoding and decoding, and latent structure and robustness. We assemble a benchmark of ten datasets spanning species, brain areas, recording technologies, and behavioral paradigms, and evaluate a representative set of discrete and continuous tokenizers, both single-neuron and population variants. Across the strategies evaluated, we show how tokenizers trained only on reconstruction can support downstream tasks. Yet reconstruction alone is misleading: reconstruction quality and downstream utility can be sharply dissociated. Our multi-axis framework is a response to this failure mode. These findings highlight tokenization as a critical and underexplored design axis in brain foundation models, and suggest that further progress will require continued systematic study of tokenization strategies.

In the past year, custom and unreleased math reasoning models reached gold medal performance on the International Mathematical Olympiad (IMO). Similar performance was then reported using large-scale inference on publicly available models but at prohibitive costs (e.g., 3000 per problem). In this work, we present an inference pipeline that attains best-in-class performance on IMO-style math problems at an average inference cost orders of magnitude below competing methods while using only general-purpose off-the-shelf models. Our method relies on insights about grader failure in solver-grader pipelines, which we call the Cognitive Well (iterative refinement converging to a wrong solution that the solver as well as the pipeline's internal grader consider to be basically correct). Our pipeline addresses these failure modes through conjecture extraction, wherein candidate lemmas are isolated from generated solutions and independently verified alongside their negations in a fresh environment (context detachment). On IMO-ProofBench Advanced (PB-Adv), our pipeline achieves 67.1\% performance using Gemini 3.0 Pro with an average cost per question of $\sim$ \$31. This surpasses the performance of the DeepThink IMO gold-winning model, and more than doubles the success rate of the next best publicly accessible pipeline, all at a fraction of the cost.

Foundation models trained on large unlabeled corpora develop emergent capabilities — tasks that go beyond the training objective. We extend this paradigm to multimodal biology with Bonbon, a foundation model for molecular interactions trained on approximately 3.2 trillion tokens of paired protein-ligand sequences. From a single self-supervised objective, Bonbon exhibits four zero-shot emergent capabilities at hierarchical levels of resolution — functional (mechanism of action), residue (binding site localization, including orthosteric/allosteric discrimination), bond (covalent versus non-covalent engagement), and atom (active moiety identification at single-bond resolution). All four capabilities generalize to out-of-distribution proteins. Bonbon was trained on protein-ligand sequences alone, without any task-specific supervision and without structural coordinates. We conducted controlled scaling experiments across four model scales from 42M to 1.6B parameters; every capability evaluated shows a sharp jump at the largest scale on continuous metrics, even as pretraining loss decreases smoothly. This demonstrates that loss-based scaling laws alone are insufficient to predict when zero-shot emergent capabilities become available. The capabilities reported here emerge after training at a 1:2,000 parameter-to-token ratio to accommodate the sparsity of paired biological interaction data. The same frozen representations achieve state-of-the-art binding and affinity predictions at five orders of magnitude greater speed than structure-based methods. In prospective wet-lab validation, Bonbon achieves a 70% hit rate on de novo compounds, discovering novel chemotypes not previously documented as inhibitors for those targets. All of the tested compounds had less than 60% structural similarity to molecules in the training corpus.

Modern distributed optimization methods mostly rely on traditional synchronous approaches, despite substantial recent progress in asynchronous optimization. We revisit Synchronous SGD and its robust variant, called $m$-Synchronous SGD, which can be interpreted as a method with a backup-worker strategy, and theoretically show that they are nearly optimal in many heterogeneous computation and communication scenarios, which is somewhat unexpected. We analyze the synchronous methods under random times and adversarial partial participation of workers, and prove that their time complexities are optimal in many practical regimes, up to logarithmic factors. While synchronous methods are not universal solutions and there exist tasks where asynchronous methods may be necessary, we show that they are sufficient for many modern heterogeneous computation and communication scenarios.

Accurate forecasting of Earth's dynamic systems is vital in geophysics, where neural operators offer a powerful data-driven paradigm. Standard operators often treat the Earth as a flat Euclidean plane, introducing geometric artifacts. In contrast, Spherical Neural Operators (SNOs) resolve this mismatch by operating within the spherical spectral space, naturally adapting to spherical geometries. However, for computational efficiency, existing SNOs typically rely on the rotation equivariance assumption. This assumption simplifies the transitions of physical states into isolated spectral modal evolutions, thereby over-idealizing the Earth as a homogeneous system. To solve this problem, we no longer rely on the rotation equivariance assumption that isolates spectral modal evolution, but directly derive an explicit modal interaction kernel and propose Diagonal Spherical Neural Operators named DIAGNO. DIAGNO explicitly parameterizes cross-modal interactions through spectral modal decomposition, thereby preserving the inherent heterogeneity of Earth dynamics. Furthermore, leveraging the unique diagonal structure of the spherical spectrum, we design inter- and intra-diagonal interaction mechanisms to natively capture essential zonal and meridional dynamics, respecting intrinsic geophysical regularities. Extensive experiments across simulated fluid dynamics and real-world Earth system reanalysis (including atmosphere and ocean) datasets demonstrate DIAGNO’s superior capability, consistently achieving state-of-the-art performance in multi-step forecasting. Beyond this, we validate DIAGNO’s practical analytical value in professional geophysical domains by assessing its fidelity in capturing climatological anomalies and maintaining physical consistency.

Dataset distillation has provided a reliable solution for data compression, where models trained on the resulting smaller synthetic datasets achieve performance comparable to those trained on the original datasets. To further improve the performance of synthetic datasets, various training pipelines and optimization objectives have been proposed, greatly advancing the field of dataset distillation. Recent decoupled dataset distillation methods introduce soft labels and stronger data augmentation during the post-evaluation phase and scale dataset distillation up to larger datasets. However, this raises a question: Is accuracy still a reliable metric to fairly evaluate dataset distillation methods? Our empirical findings suggest that the performance improvements of these methods often stem from additional techniques rather than the inherent quality of the images themselves, with even randomly sampled images achieving superior results. Such misaligned evaluation settings severely hinder the development of DD. Therefore, we propose DD-Ranking, a unified evaluation framework, along with new general evaluation metrics to uncover the true performance improvements achieved by different methods. By refocusing on the actual information enhancement of distilled dataset, DD-Ranking provides a more comprehensive and fair evaluation standard for future research advancements.

Mode connectivity studies reveal that high-performing neural networks are often connected by low-loss paths in parameter space. We investigate the analogue of this phenomenon in cooperative multi-agent reinforcement learning (MARL), where a solution is not a single model but a team of decentralized policies. We introduce coordination connectivity, a diagnostic evaluating whether linear interpolation between the actor parameters of two trained policy teams preserves high team return. The resulting coordination barrier measures whether two successful teams are separated by a performance cliff along the joint-policy path. We evaluate this diagnostic on the StarCraft Multi-Agent Challenge (SMAC) across five controlled training histories, isolating the effects of shared initialization, continued training, parameter decoupling, and HAPPO-style separate-actor specialization. Across three SMAC maps and four seeds, policy teams derived from a shared MAPPO checkpoint exhibit near-zero interpolation barriers, even after non-shared specialization. In contrast, interpolation paths involving independently trained HAPPO teams exhibit substantially larger barriers. Mixed-team assembly, single-agent hot-swap, clone-all, role-swap, and weight-space probes further indicate that shared-initialized agents specialize into distinct roles while remaining within a low-barrier coordination component. These results suggest that shared initialization implicitly structures the joint-policy space of cooperative MARL, providing a mode-connectivity-inspired lens for analyzing coordination, specialization, and same-source cross-version team compatibility.

Geometry is invariant to viewpoint, which makes any collection of images a redundant encoding of a single 3D state. Existing feed-forward reconstruction models fail to exploit this: per-view methods emit overlapping, unaligned pointmaps that grow linearly with input count, while global-latent methods commit to a fixed, low-resolution output. We introduce Surflo, which compresses a variable number of unposed RGB views into K latent tokens-one global state-and decodes oriented 3D surface points by independently transporting them from noise onto the surface via flow matching. This frees the output from any fixed grid or token budget: the same latent yields from a few thousand to a million points in a single forward pass. To suppress the local inconsistencies inherent to independent per-point decoding, an inference-time guidance term correlates nearby points by injecting a photometric gradient during ODE integration. Surflo matches or surpasses feed-forward baselines on surface metrics, run an order of magnitude faster than optimization-based methods that require hundreds of views, and is the only feed-forward approach to combine a global latent with arbitrary-resolution decoding.

Evaluating Computer Use Agents (CUAs) on interactive environments is fraught with methodological pitfalls that the field has yet to systematically address. We show that a 1MB replay script that blindly executes a recorded action sequence without ever observing the screen outperforms frontier models on prominent static benchmarks, and prove that its expected success rate is exactly equal to the source agent's pass@k in deterministic environments. We trace this and other failures to two root causes: non-principled environment design (static, unsandboxed, or unreliably verified environments) and non-principled evaluation methodology (naïve aggregation and misuse of pass@k for stateful UI interactions). To address the first, we propose PRISM, five design principles for CUA environments (privileged verification, realistic environments, integrity-checked configurations, sandboxed execution, and multifactorial variability) and instantiate them in DigiWorld, a benchmark of 15 realistic sandboxed mobile applications able to evaluate agents in over 3.2 million verified unique configurations. To address the second, we develop an aggregation framework pairing Wilson score intervals with hierarchical bootstrap, producing confidence intervals that correctly account for the nested structure of CUA benchmarks, as we empirically demonstrate. All together, we show that principled environment design and rigorous evaluation methodology are not optional refinements but prerequisites for meaningful CUA research.

SO(3) equivariant graph neural networks have become the dominant paradigm for atomistic foundation models, achieving high accuracy and data efficiency by building rotational symmetry directly into the architecture. Yet the computational cost of their higher-order tensor operations creates a tough trade-off between model accuracy and inference efficiency. In this paper, we propose a structural pruning method for SO(3) equivariant atomistic foundation models to bridge this accuracy-efficiency gap. The pruning is applied along the channel and order dimensions, with each irreducible representation kept or removed as a complete block, thereby retaining SO(3) equivariance. Starting from a large checkpoint, the pruned model substantially reduces the inference cost while retaining higher accuracy than an independently trained small model. The pruned MACE-MP model outperforms the official from-scratch trained small model on 7 of 9 metrics on the Matbench Discovery leaderboard. In terms of efficiency, compressed MACE-MP and MACE-OFF models contain 1.5$\times$ to 4$\times$ fewer parameters and require 2.5$\times$ to 4$\times$ less pre-training compute than training a small model from scratch. For downstream applications, fine-tuning the pruned model reduces energy and force errors by 70.1\% and 34.4\% compared to training task-specific models from scratch across eight representative downstream datasets. We demonstrate that the method generalizes to other SO(3) equivariant architectures (SevenNet, eSCN) and can be combined with quantization and knowledge distillation for further gains.

Diffusion models achieve state-of-the-art image synthesis, with their generative trajectories fundamentally exhibit a spectral bias, resolving low-frequency global structures early and high-frequency fine details later. Conventional stochastic differential equation (SDE) solvers fail to account for this dynamic, naively injecting uniform white noise throughout the entire process and misusing the finite energy budget. In this work, we establish a mathematical framework that reconsiders SDE inference as a targeted, frequency-decoupled energy transfer. Leveraging this framework, we introduce Colored Noise Sampling (CNS), a novel, training-free stochastic solver. Rather than injecting uniform white noise, CNS utilizes a dynamic, timestep- and frequency-dependent schedule that more-efficiently allocates injected energy toward structurally unresolved frequency bands. By actively exploiting the model's inherent spectral bias, CNS systematically steers the generated distribution toward the true data manifold. Extensive experiments demonstrate that CNS significantly outperforms standard ODE and SDE baselines as a strictly plug-and-play, inference-time sampler substitution across diverse architectures (SiT, JiT, FLUX). Compared to standard sampling on ImageNet-256, CNS achieves substantial unguided FID reductions, improving from 8.26 to 6.27 on SiT-XL/2, 32.39 to 26.69 on JiT-B/16, and 11.88 to 8.31 on JiT-H/16, while yielding consistent relative FID improvements with Classifier-Free Guidance.

Recent text-only models demonstrate remarkable reasoning capabilities. Extending these to visual domains requires vision-language models to translate images into text descriptions. However, current models, trained to produce captions for human readers, often omit the precise details that reasoning systems require. This creates an interface mismatch: reasoners often fail not due to reasoning limitations but because they lack access to critical visual information. We propose Adaptive-Clarification Reinforcement Learning (AC-RL), which, through interaction, teaches vision models what information reasoners need. Our key insight is that clarification requests during training reveal information gaps; by penalizing success that requires clarification, we create pressure for comprehensive initial captions that enable the reasoner to solve the problem in a single pass. AC-RL improves average accuracy by $4.4$ points over pretrained baselines across seven visual reasoning benchmarks, and analysis shows it would cut clarification requests by up to $44$\% if those were allowed. By treating clarification as a form of implicit supervision, AC-RL demonstrates that vision-language interfaces can be effectively learned through interaction alone, without requiring explicit annotations.