NeurIPS 2026 Papers

Neural surrogates promise large speedups over classical solvers for physical dynamics but fail silently at sharp dynamical events such as shocks, fronts, and contact. We present hybrid neural world models for physical dynamics: a recipe for training and deploying multi-horizon surrogates in physical state space, where a single network with continuous horizon conditioning is trained with direct supervision against textbook reference solvers to predict any future state at horizon $T$ in one forward pass. Although no part of the training data, loss function, or architecture supervises discontinuity location, the trained surrogate encodes it implicitly, recoverable from its forward passes alone as a per-trajectory error map that concentrates on shocks, fronts, and contacts, and stays small elsewhere. The map is competitive with or better than standard label-free baselines including deep ensembles, learned error heads, gradient-magnitude indicators, and locally-adaptive conformal prediction, while using only a single trained network and requiring no calibration set or governing-equation knowledge. The recipe supports two operating points. Mode 1 runs the surrogate alone for maximum throughput, with same-hardware CPU speedups of $26\times$ to $72\times$ against textbook solvers on the PDE environments. Mode 2 uses the error map to gate a reference-solver fallback, deferring uncertain trajectories and roughly halving the surrogate's residual error at the default operating point. The recipe applies without modification across reaction-diffusion, compressible Euler, and rigid-body collision dynamics.

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose \textbf{HyFAD}, a \textbf{Hy}brid time-frequency \textbf{D}iffusion model with \textbf{F}requency-\textbf{A}ware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at \url{https://anonymous.4open.science/r/HyFAD-0C21/}.

Cluttered indoor environments, where large and heavy objects are scattered across diverse surfaces, require humanoid robots to sequentially navigate, grasp, transport, and accurately place each item at its target location within a single uninterrupted episode. This long-horizon, whole-body loco-manipulation task remains a significant challenge for current methods. Previous approaches often suffer from two main issues: easy-reward bias, where training overemphasizes early transport stages at the expense of later ones, and catastrophic forgetting, where focusing on later stages leads to a decline in earlier-stage performance. In this work, we introduce Humanoid Horizon, a unified policy framework designed to overcome these limitations through three interrelated mechanisms. The Parallel Training Strategy expands $N$ scenes into $S \times N$ concurrent stage streams governed by a shared policy, ensuring all transport stages receive continuous gradient updates and removing the bottleneck of sequential optimization. The Dynamic Starting Mechanism updates each environment's initial state with terminal states from upstream rollouts, gradually broadening transition coverage and enhancing robustness at stage boundaries. Reward Gating sets the reward to zero in later-stage streams if any previously placed object is displaced beyond a set threshold, thus maintaining object placement throughout the episode without extra reward terms. Collectively, these strategies achieve per-stage success rates exceeding 80\% on the LHM-Humanoid benchmark (350 training scenes, 66 held-out scenes), with performance remaining stable even as the number of sequentially transported objects increases beyond two—unlike the sharp drop seen in all baselines. Additionally, we demonstrate that the RL teacher policy can be distilled into a Vision-Language-Action student via DAgger. When provided only with egocentric RGB or depth observations and natural language instructions, the student successfully replicates the teacher's long-horizon, multi-object behaviors, highlighting the potential for perception-driven deployment on real humanoid robots.

Stereo depth estimation of human faces is a prerequisite for various computer vision applications, yet existing stereo benchmarks target outdoor, driving, or large object reconstruction scenarios and lack the anatomical precision and evaluation framework these applications require. We introduce HumanStereo, the first large-scale synthetic stereo dataset dedicated to human faces, comprising 417k stereo pairs from 128 photorealistic avatars across 109 unique stereo configurations and four indoor environments, with dense ground-truth annotations including depth maps, surface normals, segmentation masks, and facial landmarks. We argue that standard evaluation metrics such as $\delta_1$ and RMSE are ill-suited for facial depth estimation, and propose two complementary metrics: task-grounded absolute inlier-ratio (IR) and Landmark 3D Distance Error (L3DE) for metric anatomical accuracy. We benchmark five representative stereo methods: geometrical matchers, RAFT-Stereo, IGEV++, MASt3R, and FoundationStereo. A downstream evaluation on real optometric data for inter-pupillary distance (IPD) measurement, a parameter required in all eyeglass prescription, shows that even the best-performing model remains an order of magnitude above the sub-millimeter accuracy required for clinical deployment.

Efficient exploration in high-dimensional decision spaces remains a central challenge for decision-making systems. Humans, in contrast, can navigate large decision spaces with remarkable efficiency. Recent behavioral studies suggest that humans actively reduce dimensionality when facing large decision spaces: they probe candidate feature dimensions, rapidly identify reward-relevant ones, and use them to restrict the effective decision space. Inspired by this mechanism, we propose TDGE (Task-Dimension-Guided Exploration), a human-inspired exploration algorithm, and evaluate its performance in recommendation tasks with contextual bandit backbones. TDGE follows a top-down exploration strategy: it first selects task-relevant feature dimensions, then identifies informative features within those dimensions, and finally recommends concrete items based on the selected features. Experiments on three real-world recommendation datasets, MovieLens-20M, Last.fm, and Amazon, show that TDGE substantially improves exploration efficiency and cold-start adaptation over baseline algorithms. We further provide visualizations of recommendation trajectories showing that TDGE exhibits a human-like dimension-guided exploration process during learning. Code is available at https://anonymous.4open.science/r/Human-inspired-Task-Dimension-Guided-Exploration-for-Efficient-Learning-984B.

We study models for human-AI teaming through the lens of statistical calibration. We assume the team consists of an AI model and human---both of which are calibrated with respect to some partitioning of the feature space---and expose how the calibration assumptions propagate into the teaming framework. In particular, we consider frameworks that either (i) combine human and model predictions or (ii) delegate prediction responsibility to either a human or model. We show via theoretical and empirical results that existing methods for combination do not preserve the human's degree of calibration. Methods for delegation (by the very act of delegation) preserve calibration of the downstream predictors but can place high-capacity demands on the meta-classifier that determines which should predict. This latter result suggests human-AI complementarity and correct delegation place opposite demands on the delegation model.

We propose HuPER, a human-inspired framework that models phonetic perception as adaptive inference over acoustic--phonetic evidence and linguistic knowledge. HuPER first learns an acoustic-grounded phone recognizer from limited human-annotated data and transcript-only speech: canonical G2P transcriptions are treated as auxiliary linguistic cues rather than ground truth, and are corrected into realized phone proxies for self-training. At inference time, HuPER supports multiple perceptual routes: it can rely on bottom-up phone evidence when the signal is clear, incorporate explicit expectations when a reference is available, or use lexical constraints when acoustic evidence is weak. With only 100 hours of training data, HuPER achieves state-of-the-art phonetic feature error rates on five English benchmarks and strong zero-shot transfer to 95 unseen languages. HuPER also improves robustness on weak-evidence and disordered speech, demonstrating the benefit of adaptive, multi-path phonetic perception under diverse acoustic and task conditions. All training data, models, and code are open-sourced. Code and demo are available at https://github.com/HuPER29/HuPER.

Diffusion Maps (DM) is a well studied and popular non-linear dimension reduction algorithm. Surprisingly, while the convergence properties of DM are well understood, the {\em geometric} properties of the embedding, such as reach and smoothness have not yet been studied. Under a set of standard assumptions on a family of submanifolds $\subset \mathbb{R}^D$, we derive a series of geometric properties that are preserved by DM, including almost uniform density, finite polynomial approximation and reach. Leveraging these properties, we establish rigorous bounds on the embedding errors introduced by the DM algorithm, of the order $(\frac{\log n}{n})^{\frac{1}{8d+16}}$. These results offer a solid theoretical foundation for understanding the performance and reliability of DM in practical applications.

Evaluating general-purpose multimodal large language models (MLLMs) for surgical scene understanding remains limited by scarce surgical data and fragmented evaluation protocols. We address these challenges through a two-stage evaluation framework for surgical scene understanding. In Stage I, we introduce SURGKNOWBENCH, a diagnostic benchmark that harmonizes public surgical datasets across procedures and tasks and evaluates proprietary and open-weight MLLMs to map the boundary of pretrained surgical competence. SURGKNOWBENCH reveals that current models retain partial visual priors but remain weak on procedural reasoning and workflow assessment. Building on this failure frontier, and motivated by the scaffolded nature of surgical training, we introduce SURGAGENTGYM, a controlled environment where general-purpose MLLM agents can use bounded knowledge search over SURGWIKI and general-purpose visual grounding for surgical tasks. SURGAGENTGYM evaluates whether generalist agents can improve surgical understanding at inference time through tool-mediated evidence use, without additional surgical training. Our results show that agentic inference narrows the gap mainly for perception-heavy tasks, while fine-grained localization and expert-style assessment remain persistent bottlenecks. This opens a path toward future studies of agentic surgical understanding. We have released the codebase and artifacts.

Recent frontier large language models predominantly rely on Mixture-of-Experts (MoE) architectures. Despite empirical progress, there is still no principled understanding of how hyperparameters should scale with network width $N$, expert width $N_e$, number of experts $M$, sparsity $K$, and depth $L$ to ensure both stability and optimal performance at scale. We take a principled step toward resolving this gap by analyzing three different scaling regimes: (I) co-scaling $N\asymp N_e$, (II) co-scaling $N\asymp M\asymp K$, and (III) full proportional scaling of $N, N_e, M$, and $K$. For each regime, we develop a novel Dynamical Mean Field Theory (DMFT) description of the limiting training dynamics of MoEs that provides a formal foundation for our analysis. Within this framework, we derive the unique parameterization for SGD and Adam satisfying all maximal-update ($\mu$) desiderata. We then show that the resulting $\mu$P prescription induces neither monotonic improvement with scale nor robust learning-rate transfer. We trace these pathologies to scale-dependent observables in the aggregation dynamics, which motivates a refined set of desiderata that we term *maximal scale stability*. Guided by this principle, we derive a *Maximally Scale-Stable Parameterization* (MSSP) for both SGD and Adam in all three scaling regimes, and characterize the corresponding limiting dynamics - qualitatively distinct from the $\mu$P limit - through a separate DMFT analysis. Experiments verify that MSSP robustly recovers learning rate transfer and monotonic improvement with scale across regimes. Combined with existing depth-scaling theory, these results provide a complete scaling prescription for MoE architectures as a function of width, depth, expert width, and number of experts.

Autonomous agents such as Claude Code and Codex now operate for hours or even days. Understanding their runtime behavior has become critical for downstream tasks such as diagnosing inefficiencies, fixing bugs, and ensuring better oversight. A primary way to gain this understanding is analyzing the reasoning trajectories and execution traces these agents generate. Yet such data remains in unstructured natural-language form, making it difficult for humans to interpret at scale. We introduce ACT*ONOMY (a combination of Action and Taxonomy, pronounced /ækˈtɑːnəmi/), a taxonomy for describing and analyzing agent behavior at runtime. has two components: (1) the taxonomy itself, developed through Grounded Theory and structured as a three-level hierarchy of 10 actions, 46 subactions, and 120 leaf categories; and (2) an open repository that hosts the living taxonomy, provides an automated analysis pipeline that applies it to agent trajectories analysis, and defines an extension protocol for community contributions. Our experiments show that ACT*ONOMY can compare behavioral profiles across agents and characterize a single agent's behavior across diverse trajectories, surfacing patterns indicative of failure modes. By providing a shared vocabulary, ACT*ONOMY helps researchers, agent designers, and end users interpret agent behavior more consistently, enabling better oversight and control.

Scaling robot policy learning is bottlenecked by the cost of collecting demonstrations: datasets at modern scale require thousands of skilled-operator hours on dedicated robot hardware. The language description paired with these demonstrations does not face the same bottleneck---a single short task label is cheap, but it also leaves implicit spatial relations, object interactions, embodiment state, and subgoal structure that the pixels already contain. We treat \emph{language density} as a cheap lever for amplifying signal in a fixed demonstration corpus; whereas prior dense-language work in robotics commits to a single caption style, we instead ask which kind of dense language helps each task and learn to deliver it at deployment. We realize this as \textbf{DeMiAn} (\textbf{De}nse \textbf{M}ult\textbf{i}-aspect \textbf{A}nnotatio\textbf{n}) in two stages. First, an automatic VLM pipeline re-labels each segment of an existing demonstration along four complementary aspects---\emph{physical motion}, \emph{scene composition}, \emph{arm pose}, and segment-level \emph{reasoning}---each surfacing a distinct kind of structure that a one-line task label omits. Second, a small learned \emph{instructor}, trained via supervised fine-tuning, maps the natural language task description and an initial scene snapshot to a task-appropriate annotation and runs asynchronously alongside the action policy, hiding generation latency behind the rollout. Applied to over 1M robot manipulation and 50K EgoVerse human-egocentric videos, with no new demonstrations collected, DeMiAn delivers four findings on a VLA action policy and a video-based world-action model: i) the learned instructor lifts RoboCasa success by 5 points over the no-annotation baseline, within 3 points of a per-task oracle; (ii) that oracle is non-trivial---no fixed aspect dominates, and peak performance requires selecting the right annotation aspect per task; (iii) the trained system extends usefully to composite tasks under subgoal-driven prompt switching, and to OOD scenes and objects; and (iv) dense annotation improves the compute-performance frontier in both mid-training and post-training, making re-annotation a practical scaling lever for robot policy learning.

As powerful AI systems reach and sometimes surpass the abilities of human experts across a range of cognitively demanding tasks, the problem of accurate oversight and supervision of these systems has become increasingly urgent. One promising approach is AI debate, which seeks to leverage a debate between two powerful AIs to break complex questions down into simpler claims that can be easily judged directly. Theoretical work on debate has formalized this intuition in the language of computational complexity theory, where the goal is to design protocols (i.e. rules of the debate game) that provide rigorous guarantees on correctness for judging solutions to complex problems with limited supervision. Specifically, the current best protocol has been shown to work for all problems that have sufficiently-stable decompositions into subproblems. In this paper we design a new protocol for this same class of problems that improves on the prior work in several ways. First, correctness holds in a worst-case rather than an average-case sense. Second, honesty and correctness is a dominant-strategy equilibrium for both debaters, rather than a Stackelberg equilibrium. Finally, we prove black-box lower bounds, showing that our new protocol is instance-wise optimal. That is, no protocol for this class of problems can outperform ours while making only black-box queries to human judgments. We obtain these results by relating the notion of stable problem decompositions to the concept of fractional block sensitivity from query complexity.

Feature learning is widely viewed as the mechanism that distinguishes neural networks from fixed-kernel methods, yet its effect on the underlying function space remains poorly understood. We aim to precisely characterize how the function space (e.g., RKHS) endowed by a two-layer neural network during gradient descent training. We prove that, in a high-dimensional proportional regime, the post-update feature distribution is well approximated by a target-dependent spiked Gaussian covariance, yielding a deformed kernel that can be written as the original isotropic kernel evaluated on geometrically transformed inputs. This characterization enables a spectral analysis of the corresponding integral operator. We prove that the global eigenvalue decay rate is preserved, while the spike selectively alters the leading eigenspaces. For ReLU activations, we derive an explicit perturbative expansion showing that feature learning boosts the eigenvalue of the linear eigenfunction aligned with the target direction and mixes the top radial eigenfunction with a target-aligned quadratic harmonic. These results provide a precise function-space description of early feature learning: gradient descent does not merely rescale a static kernel, but induces a data-adaptive deformation that preferentially enriches directions aligned with the teacher signal.

While reinforcement learning (RL) successfully enhances reasoning in large language models, its role in fostering compositional generalization (the ability to synthesize novel skills from known components) is often conflated with mere length generalization. To this end, we study what RL post-training teaches models about skill composition and how the composition structure affects the skill trasnfer. We focus on the \countdown{} task (given $n$ numbers and a target, form an expression that evaluates to the target) and analyze model solutions using expression trees, where each subtree corresponds to a reusable subtask and thus can be viewed as a ``skill.'' Tracking tree shapes and their success rates over training, we find: (i) out-of-distribution (OOD) generalization to larger $n$ and to unseen tree shapes, indicating compositional reuse of subtasks; (ii) the order of skill acquisition depends upon the composition structure---models master shallow balanced trees (workload is balanced between subtasks) before deep unbalanced ones, with persistent fragility on right-heavy structures for a fixed composition depth. Our diagnostic reveals what is learned, in what order, and where generalization fails, clarifying how RL-only post-training induces OOD generalization beyond what standard metrics such as pass@k reveal. To study the implication of our findings for more real-world tasks, we present a preliminary study on formal theorem proving.

Recent works have demonstrated that transformers can be trained to recover sparse, binary cryptographic secrets in the Learning With Errors (LWE) problem, a foundational problem that underlies many post-quantum cryptographic schemes. However, as architectures have evolved to efficient encoder-only models, the mechanism by which these models recover the cryptographic secret has become more opaque. In this paper, we present the first layer-wise and embedding-level mechanistic interpretability analysis of encoder-only transformers trained on LWE samples. We reveal a surprising phenomenon: despite achieving near-zero exact prediction accuracy on the training objective, the models successfully recover the secret by bypassing the standard predictive pathways. We use dimensionality reduction, causal intervention, and linear probing and find that the secret is implicitly present in the positional embedding. Building on this mechanistic understanding, we introduce an architectural intervention that applies $L_1$ sparsity regularization directly to the positional embeddings. This modification forces the model to explicitly isolate the latent secret, transforming the computationally expensive post-hoc secret recovery process into a direct, human-interpretable parameter inspection. Our findings provide fundamental insights into how transformers allocate representational capacity when faced with high-noise, structured combinatorial problems.

In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space. In deep learning, this idea is known as the linear representation hypothesis and underpins many interpretability and control methods based on linear probes, from concept detection to activation steering. Yet while prior work has studied whether such directions should exist \textit{after} training, the dynamics of how they emerge \textit{during} training remain poorly understood. Here, we develop a framework to study the alignment of concept directions during training -- a process we call "abstraction". In a minimal linear network setting, we obtain exact solutions for the full trajectory of abstraction. These solutions reveal key analytic principles governing abstraction: (i) data and target geometry jointly determine terminal abstraction, (ii) abstraction improves with network depth, and (iii) initialization scale controls the maximum abstraction reached during training. Extending our theory to nonlinear networks, we analyze how the choice of nonlinearity affects abstraction dynamics: erf networks approximate the linear theory, while abstraction in ReLU networks depends less on target geometry and more on input geometry. Across both, we prove a striking attenuation law: both nonlinearities weaken abstraction in activations relative to preactivations. We find evidence for this law in open models (DINOv3, Gemma 4) and apply our theory to improve linear probe generalization in LLMs. Together, our results provide a dynamical theory of abstraction with implications for interpretability and control.

Predicting how a person's first-person view will evolve (what action will follow, what plan completes a task, whether an in-progress shot will score) is fundamentally under-specified: the same context admits many plausible futures, and a model trained to minimize prediction error is forced to hedge or average across them, getting it wrong either way. Two findings shape our approach. First, the future camera trajectory, the path the head carves through space, lets the model commit to one of those futures: it carries the operator's intent in a form fine enough to determine how an action will unfold, substantially outperforming language as a conditioning signal. Second, this same intent makes the trajectory itself partially predictable from the context at hand, enough that trajectory need not be observed at test time to recover most of the gain. We instantiate these findings as TrajPilot, a model that predicts candidate future trajectories from egocentric context and uses them to pilot action prediction in an action-aligned embedding space where language shapes the structure but is never used as a conditioning input. TrajPilot beats VLM and structured-planner baselines on procedural planning across Ego-Exo4D atomic, Ego-Exo4D Keystep, Ego4D GoalStep, and EgoPER, with the trajectory advantage widening with horizon (exactly where prior planners collapse) and holding under RGB-only camera-pose estimation. With the goal masked at inference, the same model performs goal-free anticipation, beating VLM baselines on Ego-Exo4D atomic and extending to EPIC-Kitchens-100 and basketball shot-outcome prediction.

Using prompted language models as classifiers enables classification in domains with limited training data, but misses some of the robustness and performance benefits that fine-tuning can bring. We study whether training on multiple classification tasks, each with its own prompt, improves performance on new domains with new classification prompts. We show that such training partially generalizes to adjacent domains, improving classification performance on tasks that are unseen during training. However, we identify specific edge cases where the finetuned models fail to follow prompts, such as when the classification prompt changes completely while the data domain remains the same as during training. We show that classification training can be mixed with general instruction following training, and that (when done well), such training keeps the benefits of classification training and mitigates its generalization failures. Surprisingly, we see that this no-thinking supervised classification training can generalize to with-thinking classification and summarization, suggesting that no-thinking classification training might be instrumentally useful in building other kinds of classifiers and monitoring systems.