NeurIPS 2026 Papers

Echo State Networks (ESNs) are designed to be \emph{stable}—the echo state property makes the reservoir state a well-defined function of the input history—but it remains unclear how \emph{geometrically rich} the reachable reservoir states are and what controls that richness. We give a partition-free, fractal-geometric theory of contractive reservoirs by viewing a quantized-input ESN as a contractive random dynamical system and, equivalently, an iterated function system (IFS). This identifies the reachable set as the IFS attractor and the stationary reservoir-state law under i.i.d.\ inputs as the unique invariant IFS measure. We prove entropy–contraction (entropy–Lyapunov) bounds on the intrinsic dimension of this measure, and in a conformal/similarity regime with standard separation conditions we obtain sharp closed-form dimension laws of the form “input entropy divided by contraction.” These results yield a quantitative \emph{criticality principle}: weakening contraction drives a transition from low-dimensional to full-dimensional state representations at an explicit threshold set by input entropy and contraction rates, providing practical design guidance for tuning leak/spectral radius and input scaling.

Dynamic point cloud pretraining is still dominated by masked reconstruction objectives. However, these objectives inherit two key limitations. Existing methods inject ground-truth tube centers as decoder positional embeddings, causing spatio-temporal positional leakage. Moreover, they supervise inter-frame motion with deterministic proxy targets that systematically discard distributional structure by collapsing multimodal trajectory uncertainty into conditional means. To address these limitations, we propose Diffusion Masked Pretraining (DiMP), a unified self-supervised framework for dynamic point clouds. DiMP introduces diffusion modeling into both positional inference and motion learning. It first applies forward diffusion noise only to masked tube centers, then predicts clean centers from visible spatio-temporal context. This removes positional leakage while preserving visible coordinates as clean temporal anchors. DiMP also reformulates point-wise inter-frame displacement supervision as a DDPM noise-prediction objective conditioned on decoded representations. This design drives the encoder to target the full conditional distribution of plausible motions under a variational surrogate, rather than collapsing to a single deterministic estimate. Extensive experiments demonstrate that DiMP consistently improves downstream accuracy over the backbone alone, with absolute gains of 11.21% on offline action segmentation and 13.65% under causally constrained online inference.

Range-partition entropy is a structural complexity measure used in entropy-sensitive computational geometry. We introduce Differentiable Entropy Regularization (DER), a gradient-optimizable surrogate for the entropy of learned geometric partitions. The paper makes three main contributions. First, we separate the normalized entropy optimized by DER, denoted H_norm(S), from the runtime-scaled entropy H_work(S) = n · H_norm(S) that appears in algorithmic work bounds. Second, for a fixed margin-separated halfspace arrangement, we prove a self-contained soft-to-hard approximation theorem: the soft halfspace-cell entropy converges to the corresponding hard sign-pattern entropy at a rate controlled by margin, temperature, and the number of separators. A connection to optimal range-partition entropy holds when the fixed partition is admissible for the geometric problem and near-optimal in the admissible partition class. Third, we evaluate DER as learned geometric preprocessing for SciPy/Qhull-based convex-hull and Delaunay pipelines. On the evaluated 2D tasks, DER gives up to 4×–5× solver-side speedups and smaller end-to-end gains after preprocessing, with convex-hull area error below 0.2%. We also include a secondary transfer study in ViT-style attention, where the same regularizer induces structured sparsity and improves empirical efficiency. The central contribution is not the entropy formula alone, which resembles soft clustering, but the range-aware differentiable construction, the explicit approximation analysis, and the geometry-first training pipeline.

State estimation is a critical challenge in modeling dynamic systems. Traditional Kalman filters and data-driven methods have shown good results in complex, nonlinear systems. However, most existing methods optimize the posterior without considering prior modeling, which leaves room for improvement in state estimation accuracy, and predict high-dimensional Kalman parameters end-to-end, which lead to unstable training and poor convergence. To address this, we propose Diff-Kalman, which leverages state differences to predict state increments and scaling matrices for correcting both the prediction and update phases of the Kalman filter. Diff-Kalman combines traditional dynamic models with neural networks to adaptively correct system behavior. In the prediction phase, Diff-Kalman utilizes a Transformer-based architecture with self-attention to extract localized patterns from historical states, followed by cross-attention to predict future state increments. These increments are then fused with model-based priors from the dynamic model. In the update phase, a GRU-based Scaling Predictor (GSP) dynamically adjusts the Kalman covariance and gain matrices based on differential residuals, which improves the accuracy and robustness of the estimation. Experimental results on linear MOT trajectories and nonlinear Lorenz dynamics show that Diff-Kalman improves estimation accuracy over representative baselines.

Cross-entropy (CE) loss is central to deep learning, but existing theory often relies on simplifications—such as squared loss or convex models—that miss key aspects of CE optimization. In this work, we study multi-class CE dynamics using a two-layer linear network with orthogonal inputs, the simplest non-convex setting where the CE implicit bias remains unresolved. This coincides with the unconstrained features model used to study neural collapse (NC). Our analysis is based on a key observation: Hadamard initialization diagonalizes the softmax operator. This allows us to extend the spectral initialization framework that Saxe et al. (2013, 2019) developed for squared loss. We prove convergence to NC under spectral CE training and give the first finite-time analysis in this setting via an explicit Lyapunov function that decreases monotonically to NC despite spurious critical points. We further identify CE-specific phenomena absent under squared loss—coupling, non-monotonic convergence, qualitative dependence on the number of classes, and exponential slowdowns. We also characterize the role of network width and show empirically that spectral dynamics qualitatively model small random initialization.

Recent advances in rectified flow-based image-to-3D generative models have enabled high-fidelity 3D asset generation. Building on this, a growing line of work has exploited these strong 3D priors for training-free stylization, transferring visual attributes from a reference image onto a generated 3D asset. However, existing methods enforce an all-or-nothing paradigm: color and texture are transferred jointly, with no mechanism to control them independently — a limitation we formalize as Disentangled 3D Stylization (Disen3D). To address this, we propose DiDE, the first training-free framework for Disen3D. Key to our approach is the observation that the structured latent space of image-to-3D models is overcomplete with respect to texture: texture information occupies only a small subset of the style-significant channels, leaving a free subspace available for independent color encoding. DiDE exploits this via a channel partition mechanism that processes a content image, a texture reference, and a color reference through dedicated branches and composes both style signals interference-free at every self-attention layer, preserving content geometry throughout. Experiments on Disen3D-Bench, our newly collected multi-reference benchmark, show that DiDE consistently outperforms 2D and 3D stylization baselines in color fidelity, texture transfer, and content preservation.

Vision-Language Models (VLMs) excel at open-world 2D perception but struggle with precise metric spatial reasoning, a key requirement for applications like autonomous driving, navigation, and embodied intelligence. We identify this as a structural limitation: images are 2D projections of the 3D world, inherently suffering from projective ambiguity, while VLM components favor semantic understanding and rely on 2D positional bias, leading to Spatial Collapse. To address this, we propose Despa, a Depth-grounded spatial VLMs that injects depth-based geometric information via Geometric Positional Embedding (GPE) and Depth-aware Rotational Positional Embedding (DoPE). To expose masked limitations in current benchmarks, we construct SpaDataset (1.7M QA pairs) and SpaBench (2,051 QAs), to our knowledge the largest fine-grained training corpus and benchmark suite for metric spatial reasoning. They cover three difficulty levels and ten sub-tasks across diverse settings. The fine-tuned Despa-4B model consistently outperforms general-purpose, closed-source, and specialized VLMs on SpaBench by 27.9% over Qwen3-VL-235B-A22B and 31.1% over GPT-5.2, generalizes to MSMU (66.3%), RefSpatial-U (42.4%), and the multi-frame VSI-Bench (66.0%), and consistently lifts LLaVA-1.5, Qwen2.5-VL, and Qwen3-VL backbones, achieving the performance with only a 4B model. The code will be publicly released.

Monocular depth estimation has improved significantly in recent years, driven by increasingly powerful models and large-scale training data. Predicted depth is increasingly used as an input signal for downstream tasks such as Structure-from-Motion (SfM), visual localization, and SLAM. However, monocular depth estimators (MDEs) are still primarily evaluated in terms of depth accuracy. Standard metrics aggregate errors globally and may not reflect the usefulness of depth for downstream geometric tasks. We therefore propose Depth2Pose, a framework for evaluating MDEs in the context of downstream tasks. By combining depth predictions with feature correspondences in depth-aware geometric solvers, we use relative camera pose estimation accuracy as a task-driven proxy for depth quality. Traditional benchmarks require dense ground truth in the form of per-pixel depth, which is expensive to obtain. In contrast, our formulation requires only camera poses, which can be estimated efficiently, e.g., using Structure-from-Motion pipelines. As a result, our framework can be applied to scenes where ground-truth depth is difficult to obtain, for example due to large scene scale or heavy occlusions (e.g., vegetated environments). Leveraging this, we introduce the D2P dataset, which contains challenging scenes outside the distribution of commonly used training data. We show that methods performing well under standard depth error metrics on existing benchmarks also perform well under our pose-based metric when evaluated on the same datasets, but do not necessarily generalize to our more challenging dataset. Finally, we provide a simple and extensible evaluation framework. The dataset and code are available at kocurvik.github.io/depth2pose.

We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer, allowing deferral rates to be adjusted without retraining. For KL-based ideal distributions, our deferral rules recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior—which incorporates the expert's performance—depending on if the ideal distributions are joint or marginal distributions. Experimentally, our approach is competitive compared to common baselines and more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio learning between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.

As Large Language Models (LLMs) deploy into mission-critical domains (e.g., finance, medicine, and law), output reproducibility has become a strict system requirement. While practitioners use greedy decoding to eliminate algorithmic stochasticity, empirical deployments with 16-bit precisions still exhibit catastrophic output divergence across heterogeneous GPUs. Through SASS-level profiling, we reveal that this inconsistency is fundamentally driven by truncation errors introduced during downcasting at kernel boundaries. However, achieving reproducibility via a global FP32 pipeline incurs prohibitive system penalties: bypassing 16-bit hardware accelerators hurts compute efficiency, while upcasting the KV cache doubles memory overhead. To bridge this gap, we propose Hybrid Error ALleviation (HEAL), a targeted intervention that approximates FP32 precision while resolving hardware constraints through two targeted mechanisms. First, recognizing that floating-point formats underutilize their bit-width for Q, K, V tensors, HEAL applies INT16 quantization that preserves numerical stability without expanding the KV cache footprint. Second, HEAL synthesizes high-precision matrix multiplications via an algebraic error compensation strategy, executing entirely on high-throughput 16-bit Tensor Cores. To evaluate our approach practically, we introduce MCR-Bench, a benchmark targeting reproducibility in mission-critical tasks. HEAL achieves the same level of reproducibility on downstream tasks as the FP32 baseline while reducing the performance overhead by up to 6.7$\times$.

Depth super-resolution (DSR) aims to recover a high-resolution (HR) depth map from its low-resolution (LR) counterpart. With color image guidance, this task is typically formulated as learning the residual between HR and LR in a low-dimensional feature space. However, this additive formulation is insufficient to accurately capture the complex relationship between HR and LR, especially under spatially varying degradations. In this paper, we introduce \textbf{DegBins}, a novel DSR framework that leverages degradation-driven binning to adaptively enhance residual modeling. Specifically, DegBins reformulates the regression-based DSR as a hybrid classification-regression problem, where the residual depth is represented as a linear combination of discrete depth bins weighted by their learned probability distribution, yielding more flexible and expressive representations. Furthermore, DegBins models the degradation relationship between HR and LR in a high-dimensional feature space, enabling adaptive bin range adjustment and probability optimization conditioned on local degradation characteristics. To progressively improve reconstruction quality, DegBins adopts a multi-stage refinement scheme, where each stage performs finer-grained bin partitioning and probability updating based on the former estimation. This coarse-to-fine design facilitates more accurate depth recovery, particularly in regions with severe degradations or complex structural variations. Extensive experiments across five benchmarks demonstrate that DegBins consistently outperforms existing state-of-the-art methods in terms of accuracy, robustness, and generalization.

Turbulence is ubiquitous in engineering, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide computational savings exceeding ten orders of magnitude but introduce unclosed terms requiring modelling (the closure problem). Existing machine-learning (ML) closures suffer distribution shift when trained offline on high-fidelity data, and ML models that bypass the governing equations often have limited capability to generalise. We develop a physics-derived deep learning closure for RANS, the Deep Algebraic Reynolds Stress Model (DARSM), which can be trained on one or two flow cases and generalise across an order of magnitude in Reynolds number, to unseen geometries, and across flow regimes. A neural network maps flow invariants to empirical parameters in an implicit algebraic Reynolds stress equation, derived from the Reynolds stress transport equations under the weak-equilibrium assumption, imposing significant physics-based structure on the ML closure. End-to-end optimisation through the governing PDEs and the coupled implicit closure eliminates distribution shift, but both unrolled and implicit automatic differentiation fail on the stiff coupled solver. We derive adjoint equations that exploit the solver's implicit-explicit structure to enable computationally efficient optimisation. On the canonical square-duct and periodic-hill benchmarks, DARSM reduces test velocity error as compared to the baseline RANS by $2$-$4\times$ across Reynolds number, geometries, and flow regimes, with peak case-level reductions of $12\times$. The model trained on attached, anisotropy-dominated flows (square duct) accurately generalises without retraining to separated flows (periodic hills), a regime change in the underlying turbulence physics. DARSM also outperforms five established ML methods: offline training, tensor-basis neural networks, field-inversion machine learning, DeepONets, and physics-informed neural networks.

Phylogenetic inference plays a central role in understanding evolutionary relationships, with applications ranging from tracking pathogen spread to reconstructing the history of life. Conventionally, practitioners obtain posteriors over the phylogenetic tree of species using MCMC methods. However, such likelihood-based methods are only tractable for simple evolutionary models with restrictive assumptions. For more complex and realistic evolutionary models, conventional methods are prohibitively expensive, inaccurate, or even impossible. We instead advocate for a simulation-based inference approach, by using simulated data from an evolutionary model to train a neural network that predicts tree topologies conditioned on sequences. To accurately represent the complex posterior distributions over tree topologies that can arise, we present flexible models that iteratively generate trees using three natural paradigms: top-down, middle-out, and bottom-up. We use a discrete diffusion framework to train these models efficiently on large-scale simulated datasets of phylogenetic trees. For all three generative paradigms, our models fit the data substantially better than the previous state-of-the-art simulation-based method, Phyloformer 2, and obtain more accurate posteriors on real datasets. Finally, our models outperform misspecified conventional methods on data following complex evolutionary processes.

Egocentric action transfer aims to decouple the semantic action from egocentric observations and reproduce them in new visual contexts, enabling scalable world simulation, embodied policy learning, and robotic data generation. Existing approaches to transferring actions rely on condition-guided video generation, which converts the observation video into explicit geometric controls (_e.g._, hand poses or meshes) to drive synthesis. However, these methods introduce geometric estimation errors, making it difficult to preserve physically plausible interactions when transferred to new scenes. Alternatively, motion transfer methods directly extract motion patterns from the observation video, yet motion-level features alone cannot encode rich contact dynamics, frequently leading to severe hand structural collapse and implausible contact layout. To address both limitations, we present EgoACT, a test-time framework for egocentric action transfer that operates directly on the denoising process of video diffusion models without requiring additional geometric estimators. EgoACT uses Velocity-guided Structure Anchoring to stabilize reference-consistent hand-object structure in the early denoising stage, and Sparse Correspondence Calibration to refine reliable local correspondences in the mid-to-late denoising stages. Together, these two components preserve transferable action semantics while improving temporal coherence and interaction realism. We further establish EgoActionBench, a benchmark for evaluating action preservation, visual quality, and hand-object plausibility across diverse egocentric manipulation scenarios. Experiments show that EgoACT generates more coherent and physically plausible interaction videos than strong baselines.

Individualized treatment selection with continuous actions requires accurate causal response estimation in decision-relevant regions, rather than uniformly over the entire action space. Estimating a global causal response surface and then choosing the treatment that maximizes it can therefore be suboptimal, since standard estimation objectives allocate modeling effort according to the observed treatment distribution rather than the regions that determine the optimal decision. While decision-aware approaches have been studied in unconfounded settings, this problem remains underexplored in proximal causal inference, where proxy variables and bridge functions enable identification under suitable assumptions even in the presence of hidden confounding. Despite recent progress, proximal methods have primarily focused on treatment-effect and potential-outcome estimation rather than treatment selection and optimal decision-making. To bridge this gap, we introduce a policy-targeted weighted bridge loss that emphasizes decision-relevant treatment regions while retaining global stabilization. We prove a regret bound showing that the proposed weighted bridge loss controls treatment-selection regret through a weighted ill-posedness constant. We instantiate the framework in decision-aware variants of several proximal bridge solvers, yielding practical algorithms that alternate between weighted bridge estimation, response-surface projection, policy update, and weight refinement. Empirically, we find that decision-aware weighting reduces regret across several bridge solvers, suggesting improved treatment selection in proximal settings.

Decision-focused scenario learning for contextual two-stage stochastic programming has emerged as a promising research direction, but open questions remain. A general theory for when scenario generators can yield optimal decision policies is currently lacking. Many existing methods require strict assumptions on which second-stage data are allowed to be random. Generally, the non-differentiability of the decision-focused objective is a source of difficulty. This paper makes three theoretical contributions, each aiming to remedy one of these challenges. First, we present a comprehensive theory for when scenario generators can induce optimal policies, showing that learning a single out-of-support scenario component is often sufficient. Second, we demonstrate a theoretical and methodological equivalence result between learning different second-stage data components, relaxing assumptions required for applying existing methods. Third, we study log-barrier smoothing enabled training, presenting representability and optimization results. Finally, leveraging the theory, we propose a novel method inspired by interior-point methods from classical optimization, and validate it on standard benchmarks.

Effective de-escalation is critical for law enforcement safety and community trust, yet traditional training methods lack scalability and realism. While Large Language Models (LLMs) enable dynamic, open-ended simulations, their substantial computational footprint renders them impractical for deployment on the lightweight, portable hardware required for immersive field training. Small Language Models (SLMs) offer a viable real-time alternative but suffer from a critical scarcity of high-quality, domain-specific training data. To bridge this gap, we present DeEscalWild, a novel benchmark dataset curated from a multi-stage pipeline of ``in-the-wild`` police-civilian interactions extracted from publicly available video repositories. Starting with 5,000 raw inputs, we employed a rigorous hybrid filtering process combining human-in-the-loop verification with ``LLM-as-a-Judge`` evaluation to distill 1,500 high-fidelity scenarios. The resulting corpus comprises 285,887 dialogue turns, totaling approximately 4.7 million tokens. Extensive experiments demonstrate that SLMs fine-tuned on this data significantly outperform their base counterparts across ROUGE-L, BLEU-4, METEOR, BERTScore, Realism Score, and human evaluation metrics. Notably, our fine-tuned Qwen 2.5 (3B-Instruct) surpasses the general-purpose Gemini 2.5 Flash model when evaluated under equivalent conditions, demonstrating that domain-optimized SLMs can achieve superior performance with a fraction of the computational cost.This work establishes the civilian-response simulation agent and supporting dataset needed for accessible, low-latency de-escalation training at the edge. Code and dataset are available at \url{https://github.com/Hasebul/DeEscalWild-Benchmark-Framework} (code) and \url{https://doi.org/10.7910/DVN/CWMCZI} (dataset).

Cold-start exemplar-free class-incremental learning requires learning a growing set of classes without replay, external pretraining, or a large initial task. Existing cold-start methods typically either train the backbone throughout the stream and compensate for semantic drift, or freeze a backbone after the first task, producing features biased toward the initial classes. These choices also create a computational tension: drift-compensation methods require repeated backbone training and increasingly expensive updates as the task horizon grows, while frozen-backbone methods are cheap but weak under cold start. We study a third option: a feature extractor that is never fit to image data at all. We propose CIRCLE, a class-incremental classifier built from fixed bidirectional two-dimensional reservoir features, adapted from BiRC2D for image classification, and streaming linear discriminant analysis heads. CIRCLE groups multiple random reservoir instantiations into feature ensembles and averages the softmax outputs of independent SLDA heads, yielding a tunable bias-variance tradeoff between richer random features and prediction-level ensembling. Because the feature extractor is fixed and the head admits streaming closed-form updates, CIRCLE performs sample-wise training without replay, task-boundary information, or backbone backpropagation. On CIFAR-100, TinyImageNet, ImageNet-Subset, and ImageNet-1k, CIRCLE is competitive at 10-20 task splits and substantially outperforms strong CS-EFCIL baselines at 50, 100, and 500 task splits, while training much faster than trained-backbone drift-compensation methods. Ablations show that the BiRC2D-style extractor, SLDA head, and balanced feature/prediction ensembling each contribute to the final performance.

Emerging microscopic technologies such as cryo-electron tomography (cryo-ET) provide direct 3D visualization of macromolecules within the cell, enabling analysis of their in situ morphology. This morphology can be regarded as an SE(3)-invariant, denoised volumetric representation of subvolumes extracted from tomograms, termed as subtomograms. Morphology identification from a set of subtomograms is formulated as an inverse problem of estimating a set of template morphologies and per-subtomogram SE(3) transformations with respect to any one of the templates. The existing expectation-maximization-based solution to this end often struggles with high structural heterogeneity and requires manual selection of a large number of hyperparameters. Addressing this issue, we present a novel deep unsupervised learning framework called DUIL. Given a set of subtomograms, DUIL first models their SE(3)-invariant morphological code using a siamese-like neural network with a multi-choice learning module. The learned morphological codes are clustered and used to generate a set of template morphologies through a generator network. The generated templates are used as references to estimate SE(3) transformations for each subtomograms through latent optimization. The subtomograms with identical template morphologies are then aligned and averaged to iteratively refine the templates. Experiments on simulated and real cryo-ET datasets demonstrate clear improvements over prior methods, including the discovery of previously unidentified macromolecular morphologies.