NeurIPS 2026 Papers

Learning dynamics from sparse partial observations presents a fundamental dilemma: the pointwise mean squared error (MSE) training objective may induce local contraction and empirically lead to topological collapse, whereas matching the system's invariant measure preserves global geometry but lacks temporal ordering constraints. To resolve this, we introduce the $\textbf{P}$oincaré $\textbf{R}$eturn $\textbf{I}$nduced $\textbf{M}$easur$\textbf{e}$ $(\textbf{PRIME})$ framework. PRIME bridges this gap by adopting a novel perspective of recurrence-level temporal organization, motivated by the return map and roof time structure of suspension flow representations. Instead of relying on unstable pointwise matching, PRIME refines the learned dynamics by leveraging recurrence-level temporal information, specifically by aligning the empirical graph measure of the induced return map over recurrence blocks. We evaluate our framework on the partially observed Lorenz63 system, sensor-observed Kuramoto-Sivashinsky equation, and flow past a cylinder. PRIME effectively reduces topological collapse across our benchmarks, improving temporal consistency while maintaining or enhancing long-term geometric and spectral fidelity.

Multimodal large language models (MLLMs) leverage object-agnostic tokenization by default, which represents images as flat grids of patch tokens and uniformly discretizes semantically rich foreground regions and information-sparse background areas. This introduces substantial redundancy and constitutes a major source of inference cost. Existing object-level tokenizers could either discard intra-region saliency with predefined region grouping and coarse pooling or limit to a single semantic scale by employing slot attention to the final encoder feature map only. In this paper, we propose a two-stage framework named POST that decouples unsupervised object-centric grouping from language-grounded multimodal reasoning to achieve progressively semantic-aligned object-level visual tokenizers. Specifically, we develop Progressive Slot Attention (PSA) in Stage I to introduce slot attention across multiple layers of a frozen ViT encoder and propagates slot states through a cross-layer refinement chain for learning hierarchical slot--patch correspondences without segmentation supervision. Subsequently, we transfer the learned PSA to the LLaVA pipeline in Stage II for object-level visual tokenization. We design slot-weighted merging to aggregate ViT patch tokens into object-grounded visual tokens and remove low-support slots with adaptive slot pruning. Remarkably, POST eliminates the need for external segmentation models, enables progressive object-centric refinement, and adapts visual token budget to image complexity in visual tokenization. Experimental results show that PSA achieves strong unsupervised object-centric segmentation on PASCAL VOC and COCO. Furthermore, POST is comparable or superior to LLaVA-1.5 on most multimodal benchmarks using only 8.3% visual token budget and improves referring expression comprehension on RefCOCO/+/g. It also outperforms recent patch-level and object-level token compression baselines at comparable budgets.

Streaming reconstruction from monocular image sequences remains challenging, as existing methods typically favor either high-quality rendering or accurate geometry, but rarely both. We present PLANING, an efficient on-the-fly reconstruction framework built on a hybrid representation that loosely couples explicit geometric primitives with neural Gaussians, enabling geometry and appearance to be modeled in a decoupled manner. This decoupling supports an online initialization and optimization strategy that separates geometry and appearance updates, yielding stable streaming reconstruction with substantially reduced structural redundancy. Despite operating online, PLANING improves dense mesh Chamfer-L2 by 18.52% over the offline baseline PGSR, surpasses the streaming baseline ARTDECO by 1.31 dB in PSNR, and reconstructs ScanNetV2 scenes in under 100 seconds, over 5x faster than offline 2D Gaussian Splatting while matching per-scene optimization quality. Beyond reconstruction quality, the structural clarity and computational efficiency of PLANING make it well suited for a broad range of downstream applications, such as enabling large-scale scene modeling and simulation-ready environments for embodied AI.

Modern automatic-rigging predictors (UniRig, Make-It-Animatable, RigNet) place a skeleton on a 3D mesh in seconds, but the resulting skinning weights animate poorly. Linear-blend skinning (LBS) is non-linear in pose space, so noisy weights amplify into visible candy-wrapper artifacts---the surface twisting and contracting at joint bends---and volume collapse. ARAP-style remedies penalize these symptoms one pose at a time and cannot reach the cross-pose curvature that produces them. We propose \emph{Pose-Interpolation Smoothness} (PIS), a self-supervised, training-free, test-time refiner: minimize the per-vertex gap between the deformation at the SO(3) midpoint of two random poses and the linear average of the two endpoint deformations. The midpoint is obtained by orthogonally projecting the arithmetic mean of the two rotations back onto the rotation group, sidestepping the matrix-logarithm gradient that breaks down near identity and antipodal poses. Because PIS only re-tunes the weights LBS already consumes, it slots into any LBS-based pipeline---generative-3D outputs, automatic-rigging predictions, and the LBS pathways of game engines and AR/VR renderers---without touching shaders. On Objaverse-LVIS Balanced-102 (98 valid models, 51 LVIS categories), PIS reduces fragility (per-vertex deformation variance under random poses), ARAP energy, Jacobian anisotropy, and area distortion by $35.5$\%, $39.3$\%, $19.8$\%, and $43.2$\% on average; $93.9$\% of models improve on all four simultaneously, Wilcoxon $p<10^{-10}$. On the worst-case slice---the top decile of UniRig-initialized fragility, where animation visibly tears---PIS reduces unstable vertices by up to $10.2\times$. Effective bone count and weight entropy are unchanged, and the optimization runs in $\sim$30~s/model on a single H200 GPU.

Large language model (LLM) agents increasingly operate over long and recurring external contexts, like document corpora and code repositories. Across invocations, existing approaches preserve either the agent's trajectory, passive access to raw material, or task-level strategies. None of them preserves what we argue is most needed for repeated same-context workloads: reusable orientation knowledge (e.g., what the context contains, how it is organized, and which entities, constants, and schemas have historically been useful) about the recurring context itself. We introduce **PEEK**, a system that caches and maintains this orientation knowledge as a context map: a small, constant-sized artifact in the agent's prompt that gives it a persistent peek into the external context. The map is maintained by a programmable cache policy with three modules: a Distiller that extracts transferable knowledge from inference-time signals, a Cartographer that translates it into structured edits, and a priority-based Evictor that enforces a fixed token budget. On long-context reasoning and information aggregation, PEEK improves over strong baselines by 6.3–34.0\% while using 93–145 fewer iterations and incurring 1.7–5.8$\times$ lower cost than the state-of-the-art prompt-learning framework, ACE. On context learning, PEEK improves solving rate and rubric accuracy by 6.0–14.0\% and 7.8–12.1\%, respectively, at 1.4$\times$ lower cost than ACE. These gains generalize across LMs and agent architectures, including OpenAI Codex, a production-grade coding agent. Together, these results show that a context map helps long-context LLM agents interact with recurring external contexts more accurately and efficiently.

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 Language Models (LLMs) have demonstrated remarkable capabilities across various domains, including software development, education, and technical assistance. However, a fundamental question remains unresolved: can LLMs reason about physical constraints—the rules governing how abstract computations must map onto real-world hardware? This capability is distinct from, and arguably more demanding than, software generation alone, as it requires grounding language understanding in spatial, electrical, and topological constraints. To address this gap, we introduce PCEval (Physical Computing Evaluation), a benchmark and evaluation protocol for physical computing education that enables fully automatic, execution-based assessment of LLMs across both logical and physical implementation artifacts, without human grading. Our evaluation framework assesses LLMs in generating circuits and producing compatible code across varying levels of project complexity. Through comprehensive testing of 14 leading models, PCEval provides the first reproducible and automatically validated empirical assessment of LLMs' ability to reason about fundamental hardware implementation constraints within a simulation environment. Our findings reveal that while LLMs perform well in code generation and logical circuit design, they struggle significantly with physical breadboard layout creation, particularly in managing proper pin connections and avoiding circuit errors. PCEval advances our understanding of AI assistance in hardware-dependent computing environments and establishes a foundation for developing more effective tools to support physical computing education.

Vision-language-action (VLA) models have made rapid progress in robotic manipulation, yet the policy acts with no sense of the *pace* at which its own execution unfolds—whether it is advancing, stalling, or has quietly gone wrong—especially for long-horizon tasks. Recent methods supply progress through external reward models or as an auxiliary prediction inside the policy, but the signal runs alongside action generation rather than actively shaping it. Moreover, progress is inherently tied to the terminal state, making estimation fragile when the policy lacks an internal awareness of where the task should end. We propose **PACE**, which actively internalizes task progress as a predictive interface bridging commitment and execution, equipping the policy with a calibrated sense of the *pace* at which it advances toward task completion. Specifically, we first equip the VLA with a *foresight anchor*, a predicted terminal representation from observation and instruction, from which progress emerges as a geometric projection. Building on this anchor, the model perceives a compact past–present–future progress state capturing *how much the last step advanced*, *how far execution has come*, and *how far the next step should go*. These predicted progress further actively conditions the action decoder to guide the prediction, while the gap between committed and realized increments provides a built-in consistency check for lightweight failure detection. Experiments across LIBERO, SimplerEnv, and real-world single-arm and bimanual platforms show that PACE achieves 98.7% on LIBERO and 74% on real-world manipulation, with consistent gains especially on long-horizon tasks. Robustness and stable generalization across diverse scenarios further confirm the advantage of internalizing progress within the policy, validating a calibrated sense of execution pace as an effective paradigm for long-horizon robot control.

Single-cell trajectory inference from destructive time-course snapshots is fundamentally ill-posed: neither cross-time cell correspondences nor the continuous paths between snapshots are observed, so the observed snapshot distributions alone do not uniquely determine the underlying dynamics. Existing optimal transport and flow-based methods typically couple cells by Euclidean proximity at observed clock times, which can misalign trajectories when development is asynchronous and cells sampled at the same experimental time occupy different latent pseudotime stages. We propose PACE, a trajectory inference framework that selects geometry-consistent continuous transport dynamics from destructive time-course snapshots through three coupled components. First, PACE constructs a state- and time-dependent anisotropic Riemannian metric that preserves low cost along locally supported tangent directions while penalizing normal velocity components. Second, it alternates between refining cross-time couplings under the induced path-action cost and fitting endpoint-preserving neural bridges between adjacent snapshots. Third, it distills the learned bridge dynamics into a global continuous-time velocity field over cellular states. Across seven controlled and biological datasets covering nine held-out reconstruction experiments, PACE achieves the strongest overall reconstruction performance, reducing MMD, $\mathcal{W}_1$, and $\mathcal{W}_2$ by 23.7\% on average relative to the strongest competing baseline. PACE also improves RNA-velocity alignment by 15.4\% on an embryoid body differentiation benchmark, without requiring explicit cell pairing, lineage tracing, or RNA velocity supervision during training. Code is available at \url{https://anonymous.4open.science/r/PACE-F444/}.

Diffusion large language models (dLLMs) such as LLaDA and Dream now rival autoregressive LLMs in quality while retaining native parallel decoding. To deploy them efficiently, block-wise decoding partitions generation into blocks of size $B$ and commits a fraction of each block before moving on, but $B$ conflates two roles: \emph{how far the model can look ahead} and \emph{how many tokens get committed per step}. Recent accelerators relax this trade-off with indirect heuristics, yet the underlying difficulty is already exposed at every forward pass by the model's per-step confidence. Specifically, the in-window confidence profile exhibits a context-dependent \emph{cliff} (a high plateau, a sigmoidal transition, and a residual floor) that directly encodes how far ahead is safe to look. We propose \textbf{PACE-dLLM}, a decoder that handles the two roles independently. At each step, PACE-dLLM fits the cliff in closed form on the current window's confidences and reads off the next prediction horizon at the cliff's saturation point; a separate confidence threshold decides which tokens are committed. Both rules read the same signal, add a single hyperparameter, and admit a strict-dominance guarantee over fixed-block decoding. Extensive experiments across four reasoning and code benchmarks on two open-source dLLM backbones demonstrate that PACE-dLLM achieves the best average accuracy at a roughly $\mathbf{4.5\times}$ wall-clock speedup over the unaccelerated semi-AR baseline, pushing the Pareto frontier outward.

Large reasoning models (LRMs) have achieved remarkable progress in complex problem-solving tasks. Despite this success, LRMs typically suffer from high computational costs during deployment, highlighting a need for efficient inference. A practical direction is to switch the LRM between thinking and non-thinking modes dynamically. However, such approaches often introduce additional reasoning errors and lack statistical guarantees for the performance loss, which are critical for high-stakes applications. In this work, we propose $\textit{Probably Approximately Correct}$ (PAC) $\textit{Reasoning}$ that controls the performance loss under the user-specified tolerance. Specifically, we construct an upper confidence bound on the performance loss and determine a threshold for switching to the non-thinking model. Theoretically, using the threshold to switch between the thinking and non-thinking modes ensures bounded performance loss in a distribution-free manner. Our experiments on reasoning benchmarks show that the proposed method can save computational budgets and control the user-specified performance loss.

Efficient attention mechanisms, such as linear and sliding window attention, aim to reduce the computational complexity of Transformers from quadratic to linear. However, their degraded in-context recall often necessitates interleaving full attention layers, leaving the quadratic bottleneck unresolved in long-context processing. To address this, we introduce Orthros attention, which shifts the efficiency paradigm from structural allocation to phase-aware decoupling. As a unified module, it dynamically switches its computation pattern across different phases of sequence processing, enabling linear complexity prefilling and full attention decoding. Our design grants Orthros attention a lower asymptotic complexity compared to vanilla Transformers in prevalent long-context scenarios characterized by heavy prefilling and light decoding. Beyond theoretical formulation and complexity analysis, extensive empirical evaluations demonstrate Orthros's superiority across multiple dimensions. First, we validate its fundamental language modeling capabilities, demonstrating scalability across varying model sizes and strong competitiveness in comprehensive architectural comparisons. Second, Orthros exhibits exceptional conversion feasibility via a data-efficient Transformer-to-Orthros conversion, yielding performance that even surpasses the original Transformer. Finally, Orthros achieves a remarkable $21.9\times$ prefilling speedup over Transformers while avoiding the degradation issues typical of traditional efficient attention mechanisms, evidenced by near-perfect 128K needle-in-a-haystack results and performance on par with strong Transformer baselines on real-world in-context recall tasks. Overall, these advantages in high-performance, flexibility, and efficiency position Orthros as a compelling industrial successor to the Transformer.

Characterizing the relationship between brain anatomical wiring and functional coordination remains a fundamental challenge in computational neuroscience. This difficulty primarily arises because structure-function coupling in the human brain is spatially heterogeneous, often localized to subnetworks, and inherently difficult to align across disparate representational modalities. To address this methodological gap, we introduce $\textbf{O}$rthogonal $\textbf{S}$parse $\textbf{S}$ubgraph $\textbf{A}$lignment ($\textbf{Ossa}$), a principled and interpretable framework designed to identify compact structural cliques that exhibit maximal concordance with functional connectivity (FC) across subjects. Within each FC-derived community, $\textbf{Ossa}$ optimizes an alignment objective over an orthogonal transformation, which absorbs coordinate mismatch between the two connectivity modalities, and a sparse node-selection vector, which identifies the induced structural connectivity (SC) subgraph. Furthermore, we establish theoretical properties for the $\textbf{Ossa}$ estimator, demonstrating its statistical consistency in recovering the true underlying SC clique within each functional community. Extensive empirical evaluations on simulated data, alongside analyses of the Adolescent Brain Cognitive Development (ABCD) baseline and longitudinal cohorts, demonstrate that $\textbf{Ossa}$ successfully recovers aligned structural cliques under latent cross-modal rotations. Ultimately, the proposed methodology significantly improves out-of-sample SC-FC alignment over size-matched baselines and robustly identifies stable, single-core topological structures within human brain networks.

Fine-grained classification in deep taxonomies suffers from representational crowding: large macro-classes dominate the feature space, leaving little angular capacity for fine-grained distinctions, particularly under out-of-distribution (OOD) shifts. Standard hyperbolic spaces offer exponential volume for tree-like data, but embedding an entire taxonomy into a single manifold forces distinct macro-branches to compete for shared angular capacity and entangles their optimization updates. We introduce a geometric architecture that embeds hierarchical taxonomies into a Cartesian product of Lorentz manifolds. Our core mechanism, \textit{Orthogonal Origin Parking} (OOPark), decouples the taxonomy at the root level by assigning an independent Lorentz manifold to each macro-branch and penalizing inactive embeddings that deviate from the manifold origin. We evaluate across four biological OOD tasks/benchmarks (skin lesions, iWildCam, fungi, and plankton) characterised by hierarchical class structure, class imbalance, and domain shift. OOPark generally outperforms standard Euclidean and single-manifold hyperbolic baselines while using 20-dimensional sub-manifolds against Euclidean baselines of up to 512 dimensions, preserving both fine-grained accuracy and global taxonomic fidelity under severe distribution shifts. Code is provided in the supplementary material; a public release will follow upon acceptance.

Precipitation downscaling over complex terrain is essential for resolving water availability, flood risk, and extremes, but current evaluations rarely test whether models learn orographic structure rather than only pixel-wise accuracy. We introduce OroPrecipBench, a km-scale benchmark for orographic precipitation downscaling across five U.S.\ terrain regimes. The benchmark provides a shared-domain dual-track protocol: a perfect-model track that coarsens 3\,km HRRR analyses to isolate controlled super-resolution skill, and an observation-grounded track that downscales 25\,km ERA5 to 4\,km PRISM to test practical robustness under source-target shift. We also introduce PEP-D, a terrain-conditioned diagnostic that measures errors in elevation--precipitation profiles, complementing pointwise, spatial, and extreme-precipitation metrics. Evaluating ten statistical, deterministic deep-learning, and generative baselines shows that strong controlled super-resolution does not reliably translate to real-case or cross-regime downscaling. Models that reduce pixel-wise error can still distort terrain-dependent precipitation and upper-tail rainfall, and terrain-conditioned structure is especially fragile under transfer. OroPrecipBench exposes these failure modes and motivates source-shift-robust, terrain-constrained, and tail-aware downscaling methods. Benchmark is available \href{https://anonymous.4open.science/r/OroPrecipBench-612D}{here}.

We propose a structure learning method for directed acyclic graph (DAG) models of zero-inflated multivariate count data. Although causal structure learning with zero-inflated Poisson models is identifiable, existing algorithms rely on local search over the DAG space, leading to poor scalability and a tendency to converge to suboptimal solutions. To address these limitations, we develop a novel order-based scoring framework that searches over variable orderings rather than directly over DAGs. Building on this framework, we further extend the method to multiple heterogeneous datasets by identifying a shared variable ordering while allowing each dataset to have its own edge set. We implement a stochastic hill climbing algorithm with a random-to-random (R2R) proposal operator to efficiently explore the ordering space. Simulation studies show that the proposed method outperforms competing approaches and improves graph estimation accuracy under increasing heterogeneity when a shared causal ordering is preserved. We apply the method to single-nucleus RNA sequencing data from a major depressive disorder study.

Flow-based generative models have emerged as an efficient alternative to diffusion models. We study the sample complexity of learning a target distribution in Wasserstein distance via flow matching, which learns a velocity field transporting a base distribution to the target. Under standard assumptions on the network architecture and data distribution, we show that any squared-loss flow-matching variant including rectified flow with bounded derivatives achieves $\widetilde{O}(\varepsilon^{-2})$ sample complexity with the Wasserstein guarantee taking the form $W_2 \le K(\varepsilon + C\sqrt{\varepsilon_{app}})$, where $\varepsilon_{app}$ is the approximation error of the network class. This improves upon existing $\widetilde{O}(\varepsilon^{-4})$ guarantees and does not require the Polyak \L{}ojasiewicz condition assumed in prior work. Instead, we exploit a structural property of the squared-loss objective - it induces an approximate Bernstein condition that directly ties the variance of the excess loss to the excess risk up to additive approximation-error. This condition enables a localized Rademacher complexity analysis yielding fast $O(1/n)$ rates. The flow-matching schedule enters only through the Lipschitz constant of the pointwise loss, which we characterize explicitly for standard schedules.

Masked Diffusion Models (MDMs) are trained under an objective that is symmetric over decoding orders, but at sampling time a single order must be committed to. A common task in such models is to evaluate the log-probability of a candidate sequence, either as a downstream score or to rank a finite pool of candidates. We observe that this evaluation depends substantially on the decoding order chosen, even though the training objective averages over orders. For both a model trained on closed-form Probabilistic Context-Free Grammar (PCFG) data and a pre-trained MDM on OpenWebText, the per-order log-probability rankings of fixed candidate pools disagree on most inputs. We characterize this phenomenon and propose Order-Marginalized Scoring (OMS), a simple Monte-Carlo (MC) estimator of the order-marginalized log-likelihood $\tilde \mu(x)=E_\sigma[\log p_\sigma(x)]$. We use it in two complementary algorithms: a reranker over a fixed candidate pool, and a stochastic best-of-$N$ decoder that combines adaptive position selection with $\tilde\mu$-reranking. On Sudoku, the decoder substantially raises exact-match accuracy over the strongest single-order baseline from $65.3$% to $94.7$%. On a zero-shot protein-stability benchmark, the reranker improves Spearman correlation between log-probability scores and experimental folding stabilities over a per-order baseline by $0.07$. These results suggest that OMS is a useful alternative to per-order scoring for order-agnostic problems.

We study online alignment of large language models under misspecified preference feedback, where the observed preference oracle deviates from an ideal but unknown ground-truth oracle. The online LLM alignment problem is a bi-level reinforcement problem due to the coupling between data collection and policy updates. Recently, the problem has been reduced to a tractable single-level objective in the SAIL (Self-Improving Efficient Online Alignment) framework. In this paper, we introduce a pointwise oracle uncertainty set in this problem and formulate an oracle-robust online alignment objective as a worst-case optimization problem. For log-linear policies, we show that this robust objective admits an exact closed-form decomposition into the original loss function plus an explicit sensitivity penalty. We develop projected stochastic composite updates for the resulting weakly convex objective and prove $\widetilde{O}(\varepsilon^{-2})$ oracle complexity for reaching approximate stationarity.