NeurIPS 2026 Papers

Looped-in-depth architectures provide an inductive bias toward learning step-by-step procedures for tasks that require compositional reasoning. The effective depth reached by looping determines the quality of the solution. Similar to deep architectures, looped architectures are prone to signal propagation issues as the halting decision is postponed. In this paper, we address these signal propagation issues by using pre-norm layers and residual scaling. Furthermore, we propose ***FPRM***: a Fixed-Point Reasoning Model that uses fixed-point convergence as an end-to-end halting mechanism in a looped architecture. We show that fixed-point halting allows FPRM to adapt its compute to the difficulty of the task. FPRM proves effective on common reasoning benchmarks, namely sudoku, maze, and state tracking.

Masked Generative Models (MGMs) enable parallel decoding and achieve strong performance across modalities, but require full-sequence bidirectional transformers at every step, making training costly and degrading quality under low sampling budgets. Existing work improves efficiency via better samplers or fixed-depth backbones, but does not vary the depth of the denoiser across sampling steps. We introduce Fixed-Point Masked Generative Models (FP-MGMs), which replace part of the denoiser with a fixed-point solver over shared attention layers to enable adaptive depth with fewer parameters. To make it more effective for masked generation, we first introduce a cross-step consistency loss, which aligns hidden representations at neighboring denoising steps and, second, three-state reuse (3SR) which warm-starts the solver using the previous solution by treating unchanged, still-masked, and newly revealed tokens differently. Together, these components define our complete training-to-inference framework for fixed-point masked generation, \emph{CoFRe}. We also show that pre-trained MGMs can be converted into FP-MGMs with short fine-tuning, avoiding full retraining. Across modalities, CoFRe improves the quality and cost trade-off. On OpenWebText, CoFRe reduces parameters by 38.8\%, training time by 11.5\%, and VRAM by 16.9\%, while improving generative perplexity from 830.8 to 101.8 at a budget of $96$ transformer-block forward passes, compared to MDLM. In ImageNette, CoFRe reduces training time by 48.6\% and VRAM by 50.7\%, while improving FID in all sample budgets tested. Overall, CoFRe offers a practical framework for cheaper training and stronger low-budget masked generation.

We introduce \emph{universal transformers}: fixed-parameter architectures that can simulate any transformer in a given class via a suitable input embedding. Analogous to a universal Turing machine, the input embedding encodes a description of the target model while all internal parameters remain fixed. We provide explicit sparse constructions achieving universality when the embedding dimension is sufficiently large, and further show that universality is generic: randomly initialized transformers are universal almost surely, which aligns with recent empirical results of Zhong and Andreas (2024). We empirically validate our theory on the algorithmic tasks of parenthesis balancing and multi-hop reasoning. Our results suggest that much of a transformer’s expressive power may reside in its input representation rather than its learned weights.

Long-context LLM agents often struggle with growing token, memory, and latency costs, making efficient context compression essential for practical deployment. Existing LLM-as-a-compressor methods remain noticeably inferior to using the full context. We find that this gap partly stems from their inability to preserve contextual information effectively. In this work, we revisit context compression from a structural perspective and identify two key bottlenecks in standard LLM-based compressors: limited coordination among compression tokens during information aggregation, and layerwise dilution that weakens useful signals from intermediate hidden states. To address these limitations, we propose **ComprExIT** (Context **Compr**ession via **Ex**plicit **I**nformation **T**ransmission), a new context compression framework based on explicit information transmission. ComprExIT adaptively selects features across frozen LLM layers, then allocates information from anchors to compression slots through a globally coordinated transport plan. Experiments on 12 datasets show that ComprExIT consistently outperforms strong soft-compression baselines, improving average F1 by up to 18.5%, while adding only ~1% trainable parameters and achieving more than 2× faster compression than the fastest baselines. The code will be released upon acceptance.

Modern models can have high average accuracy and benign loss tails while remaining fragile on rare subpopulations. We identify an information-geometric mechanism: after nuisance projection, the task direction can become locally nonidentifiable even when loss and raw Fisher look well behaved. Fisher-Glass certifies this failure by applying CVaR to inverse nuisance-projected task information. We prove a loss--information separation theorem and show that, under a boundary-mass condition, the hidden-environment tail of inverse projected Fisher controls robust classification sample complexity. We then derive stable ridge certificates and repair principles: reserves lift Fisher-null tails, portfolios increase collapse codimension, and tail-transverse influence selects counterfactual repairs by combining Fisher-Glass directionality with loss leverage. Synthetic experiments validate the theory; WILDS/Waterbirds diagnostics show that weakest identifiability need not mean lowest accuracy; and Waterbirds training plus counterfactual repair show that Fisher-Glass controls an identifiability axis complementary to loss.

A fruitful approach towards understanding generalization in machine learning involves characterizing how models separate generalizable structure from idiosyncratic or even corrupted features of training data. Fisher information has emerged as a diagnostic tool for this separation, leveraging loss geometry to distinguish generalization from memorization. Here we investigate this connection in vision models trained on CIFAR-10 with controlled label noise that can be learned only through memorization. We show that projecting model weights onto the top Fisher eigenvectors decouples general task performance from noisy sample memorization, and we identify the layer in which this decoupling emerges. We show that the same phenomena are present in small transformers trained to perform in-context learning and reproduced in closed form in a simple, analytically solvable linear model. Our results reveal that Fisher information captures aspects of the geometric structure underlying how neural networks allocate capacity between generalization and memorization.

The framework of Online Convex Optimization with Memory captures sequential decision-making settings where the learner's instantaneous loss is affected by their past choices, in addition to the most recent decision. We first give a new first-order regret bound in this framework for potentially non-smooth loss functions, with regret scaling as the square root of the loss of the best decision in hindsight, which can be much better than known regret bounds that explicitly scale with the horizon. In fact, our result holds in a generalized non-differentiable setting, which also captures other decision making problems of interest. We then give a faster gradient-based algorithm that yields an improved first-order regret bound for smooth loss functions. As an application, we consider the recently introduced problem of online nonstochastic control, which involves controlling a linear dynamical system subject to adversarial disturbances to minimize convex cost functions, where our results can be adapted to produce novel first-order regret bounds. This means whenever there is a benchmark controller with small loss in hindsight, our regret bounds are significantly smaller than those present in the literature.

Training robust tool-calling agents requires large-scale trajectory data that is both realistic and verifiable, yet existing datasets still rely heavily on costly human annotation or synthetic pipelines with weak correctness guarantees. In this work, we introduce \projectname, a large-scale synthetic and verifiable dataset for tool-calling agents built on real-world MCP servers. Unlike prior pipelines that first generate tasks and then attempt to solve them, \projectname inverts this process: a strong LLM first self-explores real MCP servers and records reachable execution states, after which natural-language tasks are synthesized backward from observed outcomes. This back-chaining design guarantees task reachability and label correctness by construction. To support scalable offline training and evaluation, we further construct a retrieval-augmented simulator from explored trajectories, enabling reproducible tool execution without relying on live MCP servers. Each instance includes a task description, tool schemas, ground-truth trajectories, ground-truth answers, and tool-call responses for offline replay, and is automatically checked for determinism and semantic consistency. \projectname aggregates thousands of verifiable tasks across diverse real-world MCP servers and supports scalable agent learning without human annotation. Experiments show that models trained on \projectname achieve significant improvements on tau2-Bench and BFCL, demonstrating the effectiveness of realistic, verifiable synthetic data for training generalizable tool-calling agents.

Building on SODA 2026 work Kearns et al. (2026), we study learning in directed acyclic graphs in which each agent observes only a subset of the input coordinates and may use the predictions of its parents as additional features. In the finite-sample protocol, the message sent along each edge is the agent's prediction vector on a shared sample, so the communication cost is linear in the sample size $m$. In this paper we study this model under communication constraints. First, we revisit the finite-sample analysis of the full-message protocol. We identify a gap in the finite-sample proof of Kearns et al. (2026) and develop a different argument that establishes a finite-sample population-risk guarantee along paths satisfying deterministic $M$-coverage. Second, we introduce a shared-sketch protocol in which each agent sends a $k$-dimensional linear sketch of its prediction vector instead of the full $m$-dimensional message, where $k\ll m$. We analyze this protocol through a reduction to least squares on the compressed sample together with an oblivious subspace embedding argument. The resulting bound separates statistics from communication: the statistical term is still governed by the original sample size $m$, while the additional error due to compression is controlled by the sketch dimension $k$. For Gaussian sketches, we obtain an explicit high-probability population-risk bound, showing that row subsampling is not the only possible communication-statistics tradeoff for networked information aggregation.

We consider the parameter estimation problem in logistic regression with Gaussian design: the estimation of a fixed unknown parameter $\theta^* \in \mathbb{R}^d$ ($\lVert\theta^*\rVert_2\geq$ 1) from $n$ i.i.d. samples $\{(x_i,y_i)\}_{i=1}^n$, where $x_i\sim N(0,I_d)$ and $y_i\mid x_i \sim \mathrm{Bernoulli}$ (1/ (1+exp($-x_i^T$ $\theta^*~$ ))). Our main aim is to characterize the finite-sample estimation performance and convergence behavior of gradient descent (GD) on the maximum likelihood objective (i.e., the logistic loss). Under small $O(1)$ stepsize and $0$ initialization, it is shown that GD linearly converges to a small neighborhood of the true parameter and achieves $\ell_2$ error of order $O(\sqrt{\lVert \theta \rVert_2^5 d/n}).$ This substantially goes beyond existing theoretical results that lack non-asymptotic estimation error rate and exhibit much slower parameter convergence. We also establish a faster local linear convergence to the same statistical error under a large stepsize. The main technical component is to show that the gradient of the logistic loss satisfies a certain approximate invertibility condition (AIC). To that end, we bound the concentration term via covering and peeling arguments, and show that the bias term is a contraction by a delicate eigenvalue analysis of the population Hessian matrices. Finally, we build upon the recent work Matsumoto and Mazumdar (2025) and devise a novel efficient estimator that attains a sharper rate in high dimensions. This indicates that the existing non-asymptotic guarantees exhibit sub-optimal dependence on $\lVert\theta\rVert_2$, and that in many regimes $\Theta(\sqrt{\lVert\theta\rVert_2d/n})$ is the tight estimation error rate. Numerical examples are provided to corroborate our theoretical results for GD.

We study the problem of average reward Multi-Agent Reinforcement Learning (MARL) where agents interact within a network. Each agent in the network conducts local updates with information within its $k$-hop neighborhood and collaboratively maximizes the overall reward of the entire network. We first provide impossibility results in achieving convergence to the global optimal joint policies in our setting. These impossibility results highlight the challenges of decentralized learning with local information in multi-agent systems, namely the issues of multiagency, where each agent independently optimizes its policy, and partial observability, where agents have limited visibility into the global state. Given these challenges which indicate that decentralized policy optimization can generally be certified only up to stationarity, we provide finite-sample convergence guarantees for a decentralized actor-critic algorithm with linear function approximation that converges to an approximate stationary point with small gradient norm. To overcome such impossibility results, we further show that adding fixed-state entropy regularization reshapes the objective landscape which leads to even stronger global convergence guarantees for our proposed actor-critic algorithm.

Exact optimal-decision recovery can be stronger than required when decisions are evaluated at a finite regret tolerance. This paper studies finite-resolution sufficiency under partial linear observations and bounded measurement error. A design is sufficient when every noisy observation fiber admits a single feasible decision with regret at most a prescribed tolerance for all costs in that fiber. We prove a complete finite certificate for insufficiency: an indistinguishable hard tuple of costs with no common low-regret decision. For linear-optimization regret, the required tuple size is controlled by projected cost dimension after quotienting directions that are invisible to regret. For finite cost libraries, this certificate gives exact fixed-design verification and separation. Under coordinatewise noise and a finite query library, query design is exactly set cover over hard tuples; this reduction transfers the standard set-cover greedy guarantee and hardness barrier, and supports an exact delayed-constraint method under exact verification and exact restricted-master solves. Structured cases reduce to polynomial formulations through separability, nested one-dimensional coverage, and interval incidence.

Optimal control of partially observable Markov decision processes (POMDPs), in general, requires a complete history. Traditionally, a belief state is used as a sufficient statistic to control POMDPs. However, being defined over a continuous space, its full representation is impossible with a finite-memory controller. This raises the question we address in this work: what must the available finite memory preserve to achieve near-optimal control performance? We study this question through an information-theoretic converse that gives a fundamental lower bound on the loss of any finite-memory controller. The analysis introduces the concept of a decision witness that characterizes belief states whose confusion would lead to unavoidable loss. Motivated by this bound, we propose RECAP, a constructive quantization method to design representative memory states. We prove upper bounds on the optimality gap of any RECAP codebook, and use the resulting components together with the converse to define the codebook objective. Experiments on 11 POMDP benchmarks demonstrate that RECAP improves over finite-memory representation baselines under the same memory budget.

Estimating the principal eigenpair of a positive operator from stochastic evaluations gives rise to a noisy form of normalized power iteration: each step applies a sampled operator estimate and then renormalizes. We establish finite-time stochastic-approximation guarantees for this procedure, working in Hilbert's projective metric, which is well-suited to the multiplicative geometry of Perron--Frobenius eigenproblems. Our main application is risk-sensitive average-cost reinforcement learning (RL) with exponential utility. In this setting the Bellman equations are multiplicative, and value functions are characterized by nonlinear eigenvalue problems rather than additive fixed points. We cast both policy evaluation and control in this framework, obtaining risk-sensitive TD- and Q-learning algorithms that learn from a single Markovian trajectory. Under explicit positivity, mixing, and linear function approximation assumptions, we prove finite-time bounds on the recovered eigenvector and eigenvalue with $\tilde{O}(\epsilon^{-2})$ sample complexity up to problem-dependent constants. The results cover both tabular and linear function approximation regimes, and through the duality between exponential utility and KL-robust control yield finite-time guarantees for KL-robust average-cost RL as well.

Scientific discovery relies on large-scale hypothesis testing. However, the capacity to identify true discoveries while controlling false discovery faces major challenges: obtaining relevant reference data (the null distribution) is resource-intensive, leaving finite-data uncertainty, and the procedure should account for the inherent structure in the hypothesis space, when such structure exists. Here, we present a framework for controlling the false discovery rate for hypotheses with uncertain p-values from finite reference samples within arbitrarily structured hypothesis spaces, requiring only that the structure be represented through a suitable reproducing kernel. We present two decision rules, both proven to control the FDR under any misspecification of the structural information, and show that one strictly dominates the other under correct specification. Furthermore, we suggest a policy for efficient allocation of samples from the hypotheses' null distributions.

The behavior of LLMs does not depend solely on the model itself. Components of the inference system, such as the inference engine, attention backend, and hardware platform, subtly influence how inputs are processed. These components differ in their implementations and thereby induce small numerical deviations across systems when running the same model. While prior work has established the theoretical existence of such deviations, their security implications have remained unexplored. In this paper, we show that these deviations are characteristic of specific components and propagate to observable textual outputs, exposing the inference system to any party that can query the model. Building on this observation, we introduce a fingerprinting method that analyzes the prompt-response behavior of LLMs to identify components of the inference system. Our empirical evaluation demonstrates that the inference engine, attention backend, and underlying hardware platform can be identified reliably, even when the LLM is operated at non-zero temperature. We show that preventing fingerprinting is fundamentally hard, as it would require eliminating numerical differences between hardware and software stacks. We therefore propose partial mitigations and discuss their impact.

Introducing new capabilities to frontier models has long been the goal for posttraining, which relies predominantly on supervised finetuning (SFT) and reinforcement learning (RL) to achieve this. Prevailing wisdom dictates that on-policy RL enables strong generalization on new tasks without losing existing capabilities, while SFT is prone to weak generalization and forgetting. At the same time, SFT enables learning from inherently off-policy expert data, whereas RL must rely on a model's ability to generate positive signal on a new task. In our work, we seek to bridge the strength of on-policy learning with the information signal of off-policy expert traces. To this end, we introduce a Markov chain Monte Carlo (MCMC) sampling algorithm that transforms off-policy traces into more on-policy ones given a reference model for finetuning. Across tasks like scientific skill acquisition, mathematical reasoning, and fact learning, we demonstrate that simple SFT on these boosted off-policy traces can generalize better and forget less than on-policy counterparts. More generally, our approach outlines a principled methodology for model-specific data refinement, suggesting broader utility as a plug-and-play component throughout the post-training pipeline.

Vision-Language-Action (VLA) models have advanced rapidly by leveraging large-scale vision-language priors and robot trajectory data, yet they remain weak at following fine-grained human instructions. We argue that this limitation stems from a fundamental mismatch between language and action supervision in existing robot datasets. Most open-source datasets annotate each trajectory with a goal-oriented task description, while leaving the underlying execution process largely unspecified, including motion trajectories, contact and approach patterns, object state transitions, recovery behavior, and final configurations. Since different choices along these dimensions can lead to substantially different action sequences, coarse task descriptions induce a many-to-one mapping from action trajectories to language, preventing precise action-instruction alignment. To address this problem, we propose FineVLA, a framework for constructing and leveraging fine-grained embodied action instructions for VLA learning. FineVLA includes FineVLA-Tool, a scalable pipeline for data cleaning, temporal alignment, and fine-grained annotation; RoboFine-VLM, a vision-language model for fine-grained robotic action understanding and annotation; RoboFine-Bench, a benchmark for evaluating fine-grained robotic action understanding via VQA and captioning; and FineVLA-Policy, a VLA policy trained with fine-grained instructions on open-source ALOHA robot data. Across benchmark evaluation and policy learning experiments, FineVLA demonstrates that high-density, action-aligned language supervision leads to more controllable and instruction-sensitive robot policies. Our results highlight fine-grained instruction alignment as a critical step toward VLA systems that not only complete tasks, but complete them in the way humans specify.

As revealed by the scaling law of Mixture-of-Experts models, model performance ceases improving once the granularity of the intermediate dimension exceeds the optimal threshold, limiting further gains from single-dimension fine-grained design. To address this bottleneck, we propose FineRMoE (FineR-Grained MoE), an architecture that extends fine-grained expert design to both intermediate and output dimensions, aiming to enhance expert specialization beyond the single-dimension limit. We further introduce a bi-level sparse forward computation paradigm and a specialized routing mechanism to govern the activation. In addition, to obviate the prohibitive cost of pre-training from scratch, we devise a generalized upcycling method to build FineRMoE in a cost-effective manner. Extensive experiments performed under the upcycling paradigm demonstrate the superior performance achieved by FineRMoE across ten standard benchmarks. Compared with the strongest upcycling baseline method, FineRMoE achieves significant parameter and inference efficiency gains.