NeurIPS 2026 Papers

We introduce a unified framework that reinterprets first order optimization on a smooth parameter space as a closed loop controlled dynamical system on a Riemannian manifold. Within this framework, optimizers are specified by a quadruple $(M, g, \Phi, \eta)$ consisting of a Riemannian metric, an internal state transition map, a direction field generator, and a lifting parameter. Classical and modern methods including SGD, Adam, AdamW, Lion and Shampoo are recovered as specific instantiations of this quadruple. The central structural object of the framework is a time indexed family of target submanifolds in the extended state space of parameters, velocities, and internal memory, which we call the Normally Attracting Invariant Manifold (NAIM) family. These submanifolds organize training dynamics into two timescales: a fast contraction of the velocity state onto the current target submanifold, followed by a slow descent along it. Using Riemannian backstepping, we construct a strict Lyapunov function on the extended state space and prove Uniform Ultimate Boundedness (UUB) of the optimization trajectory under a descent alignment assumption and bounded stochastic disturbances. Under the additional Polyak-Lojasiewicz (PL) condition, the Lyapunov function converges linearly to a bounded neighborhood of the optimum, defined as the drift of the target direction field between consecutive iterates after parallel transport. To validate the framework's generativity, we derive three concrete instantiations of the quadruple, each exercising a distinct design axis, and show on geometric diagnostics, image classification benchmarks, and language modeling that their empirical behavior matches the theoretical predictions. The framework casts optimizer design as controller synthesis, complementing heuristic perspectives by providing a constructive template with provable guarantees.

The theory of state tracking in recurrent architectures has predominantly focused on expressive capacity: whether a fixed architecture can theoretically realize a set of symbolic transition rules. We argue that equally important is error control, the dynamics governing hidden-state drift along the directions that distinguish symbolic states. We prove that affine recurrent networks, a class of models encompassing State-Space Models and Linear Attention, cannot correct errors along state-separating subspaces once they preserve state representations. Consequently, practical affine trackers do not learn robust state tracking; rather, they learn finite horizon solutions governed by accumulated state-relevant error. We characterize the mechanics of this failure, showing that tracking remains readable only while the accumulating within-class spread remains small relative to the initial between-class separation. We demonstrate empirically on group state-tracking tasks that this breakdown is predictable: tracking collapses when the distinguishability ratio crosses the readability threshold of the trained decoder. Across trained models, the point of this crossing predicts the horizon at which downstream accuracy fails. These results establish that robust state tracking is determined not only by an architecture's theoretical expressivity but crucially by its error control.

Standard decoding in diffusion language models (DLMs) is controlled through parallel, token-wise unmasking decisions. However, diffusion decoding is inherently a structured, sequence-level process, in which token states evolve under dynamic cross-token dependencies and are therefore poorly captured by purely token-wise unmasking control. Motivated by this mismatch, we view diffusion decoding from a structural perspective, in which iterative denoising progressively gives rise to token subsets that are internally reliable and weakly dependent on the remaining masked positions. We therefore introduce structural commitment, a sequence-level unmasking principle that treats approximately closed token subsets as the basic unmasking units in diffusion decoding. We instantiate this principle with Structural Commitment via Closure Expansion (SCCE), a structure-aware inference-time algorithm that discovers approximate closures and commits high-certainty subsets by unmasking them, with certainty measured by balancing token reliability against external dependency leakage. Empirically, SCCE improves the accuracy–efficiency frontier over local confidence-based unmasking baselines while adding negligible measured per-step overhead in our implementation.

Action chunking is widely used in recent vision–language–action (VLA) systems to mitigate inference latency and improve temporal consistency. Yet, open-loop execution can reduce reactivity and precision, and cross-chunk coherence remains difficult to guarantee. We revisit action chunking through its neurobiological origins and organize current shortcomings around three axes: VLA architecture, representations of sequential actions, and mechanisms for sampling and executing chunks. A case study further illustrates the coherence–reactivity trade-off across representative sampling and execution choices. Building on these observations, we outline brain-inspired directions to improve the reactivity, coherence, and safety of chunking-based VLAs in dynamic and complex tasks beyond quasi-static tabletop manipulation. This position paper aims to broaden how the community thinks about action chunking and to motivate redesigns better aligned with future physical intelligence.

We study selective refusal editing as a three-way control problem: induce non-refusal on designated edit prompts while preserving benign behavior and harmful refusals outside the edit set. We introduce Residual Paving, a routed residual editing method for frozen instruction-tuned transformers that separates route selectivity, whether to intervene, from residual-edit capacity, what edit to apply. An early-layer router predicts a scalar gate and expert mixture; when active, prompt-conditioned bottleneck residual experts apply later-layer residual updates while leaving the backbone unchanged. This decomposition supports an oracle-routing diagnostic where only the learned scalar gate is replaced with the held-out edit/keep label, leaving the residual editor and frozen backbone fixed. On the primary Gemma-3-4B-IT held-out split, learned Residual Paving reduces edit refusal from 88.6% to 4.0%, with 95.5% benign distribution preservation and 87.3% harmful distribution preservation. Same-protocol one-direction steering controls are much weaker on edit success, leaving edit refusal at 86.8% for Edit-target ActAdd and 78.9% for DIM-style refusal steering. The remaining failure is off-target harmful-keep degradation: harmful refusal remains below the frozen-base rate, 65.3% vs. 81.6%. Across six backbones, oracle routing improves the keep-side diagnostic score on every reported row, with median gain +12.9 pp, supporting the interpretation that learned route selectivity is the main observed bottleneck. Trajectory diagnostics on two backbones further suggest directed movement toward edit-target continuations rather than generic refusal suppression.

Human vision flexibly extracts part-whole hierarchies from visual scenes, but representing such structures remains a key challenge for neural networks. Inspired by the neural syntax hypothesis in neuroscience, we propose a framework for representing hierarchical part-whole relationships through nested neuronal coherence, characterized by its continuous and distributed nature. Nested neuronal coherence refers to dynamical states where distributed activations are temporally correlated to form cell assembly sequences across timescales, argued to represent neural syntax. Building on this framework, we develop a cortical-inspired hybrid model, Composer, which dynamically achieves emergent nestedness when given images. To evaluate the emergent hierarchy, we create four synthetic datasets and three quantitative metrics, demonstrating the model’s ability to parse scenes of varying complexity. Overall, our work advances a systematic paradigm spanning representation, implementation, and evaluation toward building human-like vision in neural networks.

Generative solvers for combinatorial optimization benefit from additional test-time compute when their refinement states remain aligned with task relaxations. We introduce RAGenCO, a relaxation-aligned test-time scaling framework for generative combinatorial optimization. The central idea is to treat projection onto a task relaxation as a state control primitive: refinement first maintains a projected control state, and only then forms the task-dependent decoder input or expands candidates. For TSP and ATSP, Sinkhorn projection aligns matrix states with the cycle-cover relaxation during refinement and decoding. For MIS and MVC, Bernoulli projection controls refinement on the independent-set side, while raw logits are retained for terminal greedy decoding because their ordering carries the decoder signal. Best-of-$B$ branching then reallocates compute by expanding candidates around aligned control states rather than sampling from unconstrained logits. Because these operations are used only at inference, the diffusion training objective remains unchanged. Under equal runtime budgets, this alignment of control state, decoder input, and branching yields a strong quality-runtime trade-off on TSP and ATSP and competitive results on MIS and MVC.

Diffusion models dominate visual generation, but iterative denoising remains computationally demanding, especially under Classifier-Free Guidance (CFG), which is crucial for high-fidelity generation yet nearly doubles per-step computation. To reduce this burden, recent training-free caching methods reuse intermediate predictions during sampling, yet their single-prediction criteria are misaligned with CFG sampling, where the denoising update is governed by the guided prediction rather than either branch alone. Consequently, such reuse may misestimate the error that actually perturbs sampling, leading to a **branch-guided mismatch**. Moreover, due to error propagation across timesteps, a local guided error may not faithfully reflect the final deviation, inducing a **local-final mismatch**. To address these two mismatches, we propose **RA-CFGCache**, a **R**isk-**A**ligned **Caching** framework for CFG. **RA-CFGCache** introduces CFG-aware Guided-Risk Composition to align caching decisions directly with the guided prediction, and Propagation-Aware Rescaling to calibrate local guided risks against the final generative deviation. Extensive experiments on FLUX.1-dev, Wan2.1-T2V-1.3B, and CogVideoX-2B show that **RA-CFGCache** delivers superior efficiency-fidelity trade-offs over existing training-free caching methods. Moreover, **RA-CFGCache** is compatible with diverse caching strategies and can further enhance their fidelity, e.g., improving PSNR over MagCache from 21.46 to 24.02 under CFG. The code is available at https://anonymous.4open.science/r/RA-CFGCache/.

Reliable quantum control in the presence of decoherence requires policies that combat the effect of environmental noise on the controlled dynamics. Open quantum systems under continuous monitoring generate classical measurement records whose drift depends on the noise experienced by the system; the records of two evolutions sharing the same decoherence channels differ only in this drift, so Girsanov's theorem yields a closed-form, differentiable estimator of the KL divergence between their trajectory distributions. We instantiate this estimator with two physically motivated reference measures, yielding two regularizers that both drive the system toward states where the effects of decoherence are minimal: the *Wiener KL* (KL_W), which is empirically more effective under certain conditions on the noise model, and the *drift-variance regularizer* (R_DV), which works for all noise models. Both are qualitatively distinct from existing penalties on control fluence or smoothness: they penalize the observable consequences of control on the decoherence channels rather than the control amplitude itself. The regularizers outperform unregularized gradient-based and reinforcement-learning baselines across a range of open quantum systems — including single- and multi-qubit benchmarks and a multi-qubit chain calibrated to a published snapshot of the IBM Kingston processor — along several axes of evaluation: final-state fidelity, robustness to mismatch in the assumed noise model (gains grow from +17 pp at training noise to +27 pp under 2.5× noise mismatch), and occupation of forbidden states. The regularizers reduce infidelity by up to 50%, with ~16% gains on the calibrated IBM Kingston chain. Our code can be found at https://anonymous.4open.science/r/QMaxCal-6E71/.

Large vision model (LVM)-based gait recognition has achieved remarkable performance. However, current LVM-based methods largely rely on 2D image-plane representations and often neglect the underlying 3D structure of the human body. Without 3D structural guidance, 2D representations are sensitive to viewpoint variations. This sensitivity leads to unreliable gait features and limits generalizability in real-world 3D scenarios. To bridge this gap, we propose PuppetGait, a framework that aligns LVM features into a unified 3D canonical body space. The method conceptually manipulates the features like a puppet, adjusting them to a predefined pose and viewpoint. Comprehensive evaluations on CCPG, CCGR-MINI, CASIA-B*, and SUSTech1K show that PuppetGait maintains strong within-domain performance (96.54\% mean Rank-1 on CCPG) while substantially improving cross-domain generalization, reaching 23.22\% Rank-1 on CCPG-to-CCGR-MINI and 63.28\% mean Rank-1 on CCGR-MINI-to-CCPG. Code will be publicly available.

Activation steering controls language model behavior by adding directions to internal representations at inference time, but standard residual-stream steering can fail in stateful dialogue. We identify KV-cache contamination as a key failure mode: steered token states are stored and repeatedly reused, turning a local perturbation into cumulative coherence degradation. Motivated by the stability of prompt-based control, we propose Gated Cropped Attention-Delta steering (GCAD), which extracts steering signals from system-prompt contributions to self-attention and applies them with token-level gating. Across persona-steering experiments, GCAD preserves trait control while substantially improving long-horizon coherence. On the main multi-turn benchmark, GCAD improves average coherence drift from -18.6 to -1.9 and raises turn-10 trait expression from 78.0 to 93.1. These results suggest that activation steering becomes more reliable when interventions follow the prompt-mediated pathways that models already use for behavioral control.

Ambiguous inverse problems often admit multiple clean signals that are consistent with the same observation. In such settings, a sampler should not only produce plausible or measurement-consistent reconstructions, but also allocate probability mass correctly across the alternatives that remain unresolved. We formalize this requirement as \emph{posterior alternative calibration} and introduce mode coverage error (MCE), a finite-alternative diagnostic that measures calibration after pushing the posterior and sampler distributions onto a benchmark-specified alternative label space. This perspective reveals a basic failure mode of point-centered inverse solvers: measurement consistency can be preserved by averaging across alternatives, even when the resulting point lies outside the nonconvex set of valid posterior explanations. We prove that local point-denoising updates can therefore suffer barycentric collapse under weak branch identification, while calibrated local branch probabilities are sufficient to control MCE. Across controlled Gaussian, imbalanced, nullspace, and template-inpainting diagnostics, MCE exposes posterior mass-allocation failures that are missed by residual error, recall, diversity, and confidence. A semantic-label inpainting benchmark with DDIM, DPS, DDNM, RePaint, and clustering-based samplers further shows that practical samplers can recover all specified alternatives while assigning different branch probabilities. These results position MCE as a targeted evaluation axis for finite-alternative ambiguity benchmarks, complementary to reconstruction fidelity and sample quality.

The rapid rise of AI has seen the coexistence of open-weight models and closed-source, API-based deployment, each with its own strengths and limitations. A growing share of deployment scenarios needs both local, customizable execution and owner-side accountability, yet neither extreme serves them well. Such scenarios include on-prem enterprise use with sensitive data, edge and offline robotics, and local fine-tuning or retrieval-augmented generation. This position paper argues that the middle regime between closed APIs and open-weight release deserves a principled deployment-level primitive of its own, and proposes OML—Open, Monetizable, Loyal—as a starting point for that primitive. An OML-formatted artifact aims to be simultaneously Open (open-weight and locally executable), Monetizable (usage is accountable to the owner), and Loyal (owner-declared use constraints are enforceable). Throughout, "open" refers to open-weight, locally executable artifacts rather than to fully open-source release, and "loyal" refers to owner-declared use constraints rather than to remote control over a running model. We articulate the desirable properties and threat model for OML, survey theoretical and practical constructions across software, hardware, and cryptographic primitives, and outline an end-to-end deployment protocol together with market-based and policy alternatives. We then describe OML 1.0, a low-overhead instantiation based on AI-native fingerprinting, and characterize the regime in which it provides meaningful guarantees. We close with a research agenda calling on the ML, cryptography, systems, and mechanism-design communities to refine the primitives needed to make OML deployable at scale.

AI video generation is moving beyond general generation, which relies on exhaustive prompt-engineering and "cherry-picking", towards fine-grained, controllable generation and high-fidelity post-processing. In professional AI-assisted filmmaking, the core requirement is the ability to perform precise, targeted modifications. A key task is video instance insertion, which requires precise spatial-temporal placement, physically consistent scene interaction (e.g., shadows and reflections), and the faithful preservation of original dynamics - all achieved under minimal user effort. In this paper, we propose PISCO, a video diffusion model for precise video instance insertion with arbitrary sparse keyframe control. PISCO allows users to specify a single keyframe, start-and-end keyframes, or sparse keyframes at arbitrary timestamps, and automatically propagates object appearance, motion, and interaction. To stabilize generation under sparse conditioning, we introduce Variable-Information Guidance and Distribution-Preserving Temporal Masking, complemented by geometry-aware conditioning. We further construct PISCO-Bench, a benchmark with verified instance annotations and paired clean background videos, and evaluate performance using both reference-based and reference-free perceptual metrics. Experiments demonstrate that PISCO consistently outperforms existing baselines and scales effectively as additional control signals are provided.

Pose and motion priors play a crucial role in humanoid robotics. Although such priors have been widely studied in human motion recovery (HMR) domain with a range of models, their adoption for humanoid robots remains limited, largely due to the scarcity of high-quality humanoid motion data. In this work, we introduce Pose Distance Fields for Humanoid Robots (PDF-HR), a lightweight prior that represents the robot pose distribution as a continuous and differentiable manifold. Given an arbitrary pose, PDF-HR predicts its distance to a large corpus of retargeted robot poses, yielding a smooth measure of pose plausibility that is well suited for optimization and control. PDF-HR can be integrated as a reward shaping term, a regularizer, or a standalone plausibility scorer across diverse pipelines. We evaluate PDF-HR on various humanoid tasks, including single-trajectory motion tracking, general motion tracking, style-based motion mimicry, and general motion retargeting. Experiments show that this plug-and-play prior consistently and substantially strengthens strong baselines.

Large vision-language models have significantly advanced GUI agents, enabling executable interaction across web, mobile, and desktop interfaces. Yet these gains largely rely on a forgiving \emph{region-tolerant} paradigm, where many nearby pixels inside the same component remain valid. Precise geometric construction breaks this assumption: actions must land on points in continuous canvas space rather than tolerant regions. Because geometric primitives carry ontological dependencies, a local coordinate error can induce cascading topological failures that distort downstream objects and invalidate the final construction. We identify this regime as \emph{precision-sensitive GUI tasks}, requiring point-level accuracy, geometry-aware verification, and robustness to dependency-driven error propagation. To benchmark it, we introduce \textsc{PAGE} Bench, with 4{,}906 problems and over 224K process-supervised, pixel-level GUI actions. We further propose \textsc{PAGER}, a topology-aware agent that decomposes construction into dependency-structured planning and pixel-level execution. Pixel-grounded supervised tuning establishes executable action grammar, while precision-aligned reinforcement learning mitigates rollout-induced exposure bias through state-conditioned geometric feedback. Experiments reveal a pronounced ``Semantic-Execution Gap'': general multimodal models can exceed 88\% Action Type Accuracy yet remain below 6\% Task Success. \textsc{PAGER} closes this gap, delivering $4.1\times$ higher Task Success than the strongest evaluated general baseline and raising Step Success Rate from below 9\% for GUI-specialized agents to over 62\%, establishing a new state of the art for point-precise GUI control.

We consider a variant of the partially observed online control problem where there are _multiple sensors_ which provide noisy linear measurements of the system. In our setting, the system state evolves according to a discrete-time linear dynamical system. The objective is to design an algorithm which minimizes regret relative to the best _single-sensor_ policy (within a restricted class) in hindsight. When the system and process noise is stochastic and the costs are quadratic in the control and _unobserved state_, we design an algorithm that achieves $\mathcal{O}(\mathrm{poly}\log(S)\sqrt{n})$ regret over time horizon $n$ relative to our benchmark policy class if there are $S$ sensors. Notably, this regret guarantee is with respect to the _state costs_, which are never fully observed. When the system and process noise is chosen by an oblivious adversary, and the cost functions are convex-Lipschitz (or subquadratic) functions of the control and _observations_, then a similar $\mathcal{O}(\mathrm{poly}\log(S)\sqrt{n})$ regret is achievable. While our work is the first, to our knowledge, to study this generalization of the online control problem, we remark that a na\"ive application of known results in the partially observed online control literature have regret scaling $\mathcal{O}(\mathrm{poly}(S)\sqrt{n})$, exponentially worse than our regret scaling in terms of dependence on the number of sensors. Our algorithm is based on the Follow-The-Regularized-Leader framework, and our analysis carefully exploits the $\ell_1$ geometry of the policy class.

Offline reinforcement learning (RL) offers a promising route for developing plasma controllers from historical tokamak data, since online trial-and-error on real devices is costly and risky. However, progress in this direction remains difficult to measure due to the lack of a standardized offline RL benchmark for realistic multi-actuator, long-horizon plasma control problems in nuclear fusion. We introduce RL4F, an Offline Reinforcement Learning Benchmark for Plasma Control in Nuclear Fusion, providing closed-loop evaluation environments and baseline comparisons across four full-profile tracking tasks: rotation, density, temperature, and pressure. The dynamics function underlying the evaluation environment is built from historical discharge data from DIII-D, a real-world Tokamak. We evaluate a broad set of imitation learning and offline RL baselines under a unified protocol. We find that offline model-based RL methods obtain the best average performance on most objectives, although no single method dominates all tasks, highlighting the importance of dynamics modeling in complex, long-horizon plasma control tasks. To foster further research, we open-source the codebase, datasets, and evaluation framework, providing a benchmark not only for the fusion community but also for algorithm development in offline RL. Our data and code are available at https://anonymous.4open.science/r/Anonymous-B71F

Conformal risk control is an emerging framework for the safe deployment of machine learning models with finite-sample guarantees. To accommodate a broader class of risk notions, quantile risk control extends this framework to quantile-based risk measures. However, existing methods either suffer from excessive conservatism or lack rigorous finite-sample guarantees. To address these limitations, we introduce Occupancy-based Quantile Risk Control (OQRC), a novel method that provides tight risk control bounds with finite-sample validity. Our key idea is to formulate risk control as a finite-occupancy problem by partitioning the loss space with the ordered calibration losses. Specifically, we estimate the distribution of test losses across the resulting bins and upper-bound the risk by the maximum loss attained within each bin. We then select the parameter $\lambda$ such that this upper bound does not exceed a predefined threshold $\alpha$ with high probability $1-\delta$. Theoretically, we establish a finite-sample guarantee showing that OQRC yields tight risk control bounds that converge to the optimal bounds at a provable rate of $\mathcal{O}_p(n^{-1/2})$. Extensive experiments demonstrate the effectiveness of our method, reducing the risk gap by up to 78.64\% on common benchmarks.