NeurIPS 2026 Papers

Continuous DAG learning formulates combinatorial structure learning as differentiable optimization over weighted adjacency matrices. In these methods, the estimated adjacency matrix depends critically on a sparsity-controlling regularization parameter, whose magnitude governs the recovered graph skeleton. While extensive empirical evidence underscores the centrality of this parameter, existing practice relies on solving a sequence of independent optimization problems over a grid of tuning parameters, which is computationally wasteful, statistically unstable, and provides only a fragmented view of how the adjacency matrix evolves. In this work, we study the regularization path of stationary solutions in continuous DAG learning and propose DAG-flow, an exact path-following framework that compactly encodes the entire family of estimators. We show that for prominent formulations including NOTEARS, GOLEM, and DAGMA, stationary solutions evolve according to a piecewise-smooth matrix-valued dynamical system once the active support is fixed. Our analysis derives the explicit systems governing these branches, identifies the events at which the path changes regime, and clarifies how nonsmooth sparsity and nonconvex acyclicity interact along the path. Unlike grid-based search, DAG-flow exposes the geometry of model variation across regularization levels, which enables the construction of structured candidate graph sets and provides direct insight into edge-level stability. Across synthetic and real benchmarks, our DAG-flow outperforms grid-search baselines at a fraction of the compute and consistently improves structural stability.

Agnostic online learning is classically solved via a reduction to the realizable setting, utilizing Littlestone's Standard Optimal Algorithm (SOA) as a base learner. However, the SOA is computationally intractable to execute even for a single round. To overcome this barrier, recent work in oracle-efficient online learning replaces the SOA with a realizable base learner that accesses the concept class exclusively through an offline empirical risk minimization (ERM) oracle. While such agnostic learners achieve near-optimal expected regret, they suffer from a doubly-exponential oracle complexity of $\mathcal{O}\big(T^{2^{\mathcal{O}(d_\mathrm{LD})}}\big)$, where $d_\mathrm{LD}$ is the Littlestone dimension and $T$ is the number of rounds. In this work, we significantly improve this oracle complexity while relying on an even weaker primitive: a weak-consistency oracle, which merely decides whether a given labeled dataset is realizable. At the core of our approach is an adaptive and dynamic agnostic-to-realizable reduction that actively prunes non-realizable label sequences on the fly. By using the VC dimension ($d_\mathrm{VC}$) to bound the number of dynamically maintained active paths, our algorithm reduces the total query complexity down to $\mathcal{O}(T^{d_\mathrm{VC}+1})$ while perfectly preserving near-optimal expected regret. Crucially, this dynamic pruning also yields a memory reduction over the standard reduction. Furthermore, we formally quantify the regret--oracle complexity tradeoff, providing upper bounds that smoothly interpolate between restricted query budgets and attainable expected regret. We complement these with lower bounds proving that any learner restricted to $Q = o(\sqrt{T})$ queries must suffer an expected regret of $\Omega(T/Q)$.

Wasserstein distributionally robust optimization (DRO) is a prominent paradigm for robust decision-making in the face of distributional uncertainty. Given a nominal data distribution, DRO selects a decision which minimizes the risk for a worst-case data distribution within a prescribed Wasserstein radius $\varepsilon$ of the nominal distribution. In this paper, we investigate the quality of DRO decisions when evaluated on a worst-case distribution within a 2-Wasserstein $\varepsilon$-neighborhood of the nominal distribution, as measured by excess risk or ex-ante regret. Beginning with multivariate linear regression and extending to ridge regression, we first identify the asymptotic complexity of robust decision-making in the $\varepsilon \to 0$ limit, characterized by a problem-specific condition number $\kappa$. In this regime, a wide spectrum of simple algorithms, including DRO, achieve the instance-optimal rate of $O(\kappa \varepsilon^2)$. For fixed $\varepsilon > 0$, we prove that DRO still achieves the minimax rate if the problem is of an appropriate ``low rank''. On the other hand, we identify significant failure modes where DRO is provably suboptimal by dimension-dependent factors. To resolve this, we introduce a new condition number reduction (CNR) procedure which achieves the optimal rate and admits tractable approximation algorithms. We support these theoretical results with numerical experiments comparing the performance of various estimators including DRO and CNR.

Bayesian optimization (BO) is a widely used iterative black-box optimization method that utilizes Gaussian process (GP) surrogate models. In practice, BO is typically terminated after a fixed evaluation budget is exhausted, which can incur unnecessary cost and provides no optimality guarantee on solution quality. Recent research in developing a practical stopping criterion has made empirical progress, yet a theoretically sound stopping criterion remains a work in progress. In this work, we present provably tighter instantaneous regret bounds for GP upper confidence bound (GP-UCB) at any given iteration. Then, we propose stopping criteria for GP-UCB based on this tighter bound that ensures an $\epsilon$-optimal solution with high probability $1-\delta$ upon termination. Numerical experiments are performed to validate and demonstrate the effectiveness and efficiency of our stopping criteria.

We study principal-agent problems in which a principal commits to an outcome-dependent payment scheme (i.e., a contract) in order to induce an agent to take a costly action leading to a favorable outcome. We consider the online extension of the classical (one-shot) principal-agent problem, in which the principal repeatedly interacts with agents by proposing contracts over multiple rounds. The principal has no information about the agents and, crucially, does not observe their actions. As a result, the principal must learn an optimal contract using only the realized outcomes observed at each round. We focus on the setting with binary-actions and single-dimensional agent types, where the agent's private type represents their cost per unit-of-effort. For adversarial-type sequences, we provide tight $\widetilde\Theta(T^{2/3})$ regret guarantees. Remarkably, this rate is completely independent of the number of outcomes $m$. The upper bound is based on two key components: 1) a reduction to one-dimensional threshold optimization problem and 2) a non-uniform discretization to handle the non-Lipschitz nature of the problem. Moreover, in the case of a single (fixed) hidden type, we show that it is possible to improve the rates and provide a tight $\widetilde\Theta(\sqrt{T})$ regret bound. Our algorithm is based on an explore-then-commit strategy where we first approximately learn the hidden type via a stochastic binary search, and then we commit to a ``robustified'' near-optimal contract.

We present Register Anything Model (RAM), a unified model for generalizable 3D point cloud registration that robustly estimates 6-DoF transformations across diverse domains spanning sensors and environments. Existing registration methods are typically tailored to a single domain, with carefully tuned architectures and hyperparameters, and thus degrade markedly when applied to novel domains. We bridge this gap by training a single model on diverse data from indoor, outdoor, and object domains. A central challenge is the severe geometric discrepancy across domains, i.e., differences in scene scale, sensor noise, point density, and structural patterns, which hinders processing with a unified point-based model. To address this, we introduce a geometry-aware normalization strategy that jointly voxelizes and normalizes point clouds into a standarized geometric space, adaptively based on their geometric properties to preserve salient local structures while standardizing resolution. Built on this normalization, RAM follows a hierarchical coarse-to-fine paradigm, and employs an efficient geometric transformer that models local geometric consistency instead of over all points. This design mitigates discretization noise introduced by voxelization, and improves computational efficiency. Extensive experiments on $12$ benchmarks demonstrate state-of-the-art performance in terms of inlier ratio and registration recall. Notably, our method outperforms the counterparts trained on each separate domain, showing superior generalization capability. Code and models will be released upon publication.

Direct Preference Optimization (DPO) has recently been applied to medical image segmentation, since comparing candidate masks is substantially cheaper than producing new dense pixel-level annotations, making pairwise preference signals an appealing source of supervision. However, existing work derives preferences from ground-truth masks, leaving open whether the approach is sound under the imperfect feedback available in practice. In our analysis of this reformulation, we identify that candidate masks tend to agree over most of the image and differ only in localized regions, yet standard DPO averages the preference signal over the full spatial domain. This couples update strength to disagreement area, diluting small correct refinements and amplifying large misranked differences. Crucially, this bias even degrades performance even under oracle preferences derived from ground truth. We propose Region-Normalized DPO (RN-DPO), which normalizes the likelihood ratio over the disagreement region between candidate masks, removing this coupling. We further provide a systematic empirical study of preference-based segmentation fine-tuning under controlled noisy judges, analyzing the effects of mining strategies, judge types, and reliability regimes. Across two medical segmentation benchmarks, multiple judge configurations, and two backbone architectures, RN-DPO consistently improves over vanilla DPO and robust DPO variants, with gains persisting under noiseless oracle preferences.

Visual Geometry Grounded Transformer (VGGT) recovers dense 3D scene structure from multi-view images in one forward pass, but quadratic cross-frame attention limits its scalability. Existing training-free accelerators reduce computation uniformly along one axis, missing layer heterogeneity. Our spectral, probing, and causal analyses reveal three regimes: shallow layers lack cross-view structure, middle layers drive cross-view alignment, and deep layers are redundant for dense geometry yet their cross-frame attention remains essential for pose. RegimeVGGT applies layer-wise U-shaped compression along two axes: Saliency-Guided Banded Merging protects geometry- and edge-salient tokens, while Selectively Protected K/V Downsampling preserves cross-frame spatial coverage and the pose-critical path through a phase-shifted spatial grid, a reference-frame anchor, and uncompressed camera/register tokens. Training-free, RegimeVGGT achieves a $6.7\times$ speedup over VGGT* at matched reconstruction quality. Code: \url{https://anonymous.4open.science/status/RegimeVGGT-9477}

Neural Operators (NOs) are powerful architectures for learning mappings between function spaces. While most advances focus on refining kernel parameterizations over the $d$-dimensional physical domain, the evolution of lifted embeddings remains underexplored, which often drives models toward computationally expensive embedding-scaling designs to improve approximation. In this paper, we introduce an auxiliary function dimension that models embedding evolution in operator form, thereby reformulating the NO pipeline in $d+1$ dimensions. We instantiate this framework via Fourier-based operators acting jointly on the physical and auxiliary domains, yielding a basis-diversified auxiliary evolution module as an alternative to brute-force embedding scaling. Across more than ten increasingly challenging benchmarks, ranging from the 1D heat equation to the highly nonlinear 3D Rayleigh–Taylor instability, our model consistently achieves the lowest relative $L_2$ error among the evaluated baselines. Crucially, this advantage is empirically supported by (1) controlled budget-aware comparisons against scaled and ablated baselines; (2) robustness under mixed-resolution training and super-resolution inference; and (3) zero-shot generalization to unseen temporal regimes. In addition, we present a broader set of design choices for lifting and recovery operators, demonstrating their impact on our model’s predictive performance.

Existing LLM-based policy optimizers see only scalar rewards: that a policy scored 0.45, but not whether the agent got stuck in a loop, fell into a hole on the third step, or performed well on 19 out of 20 rollouts and failed catastrophically on one. We propose Reflective Prompted Policy Optimization (R2PO), a two-stage LLM framework for policy search over compact policy classes that augments scalar reward feedback with trajectory-level behavioral evidence. A Search-LLM acts as a global policy optimizer and proposes candidate policy parameters; the environment executes them; a Critic-LLM then inspects the resulting rollouts and proposes targeted parameter revisions grounded in observed states, actions, and rewards. Across ten environments, ablations show R2PO's gains arise from a design that explicitly separates global search from behavior-grounded revision and uses selection to filter high-variance edits. We further identify a dominant failure mode, salience bias. When presented with multiple rollouts, the Critic-LLM fixates on improving a single failure even when most trajectories succeed. In a three-trajectory variant, where the Critic-LLM is shown the best, worst, and median rollout from each evaluation, this behavior explains 76.6\% of regressions on CartPole. R2PO mitigates this by reasoning over aggregate rollout statistics, median-trajectory selection, and a revision rule. Using a relatively small open-weight 20B-parameter model, R2PO achieves the highest mean best reward across all ten environments, while reaching near-optimal performance substantially earlier in training (e.g., near-maximum CartPole reward within $\sim$500 episodes), and training far more stably than both deep RL and prior LLM-based methods. Together, these results show that treating trajectories as first-class in-context evidence, rather than background artifacts reduced to scalar returns, fundamentally changes how even comparatively small LLMs can search over policy spaces, enabling them to learn faster, diagnose more precisely, and reliably improve external controllers rather than tune them by trial and error.

Recent advances in generative modeling have enabled the efficient computation of Schrödinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods inspired by flow matching. However, these have not covered SBs with reflecting dynamics, a useful model choice with built-in guarantees that generated samples stay in the data domain. Existing alternatives for reflected SBs instead rely on more complex training based on forward--backward SDE theory, requiring expensive higher-order derivatives and sampling entire paths during training. In this article, we introduce a partially simulation-free framework that allows reflected SBs to be trained similarly to flow matching, using a new sampling method and regression target. We demonstrate our results by coupling pairs of well-known high-dimensional image datasets. Using reflected dynamics incurs negligible additional wall-clock time during both training and inference while maintaining or slightly improving generative performance.

Recent years have witnessed growing interest in applying Large Reasoning Models (LRMs) to Machine Translation (MT). While most approaches adopt a "pre-thinking" paradigm and benefit from explicit reasoning trajectories, they suffer from substantial inference cost and latency. To address these limitations, we propose ReflectMT, a two-stage reflection internalization framework for machine translation that employs a "post-thinking" paradigm. Our approach develops the model's "translate–reflect–refine" capability through reinforcement learning. In the first stage, we cultivate the model's capacity for high-quality reflection and refinement, thereby enhancing its semantic comprehension and task-specific knowledge. In the second stage, we train the model to internalize the knowledge acquired during reflection. As a result, during inference, ReflectMT operates in a direct translation mode, producing high-quality translations on the first attempt without any explicit reasoning steps. Experimental results on benchmarks such as WMT24 demonstrate that our model’s first-pass translations during inference outperform multi-step reasoning LRMs (e.g., DeepSeek-R1) in both automatic metrics and GPT-based evaluation, achieving a 2.16-point improvement in GPT-based translation quality evaluation while reducing token consumption by 94.33%.

We introduce ReflectDrive-2, a masked discrete diffusion planner with a separate action expert for autonomous driving that represents plans as discrete trajectory tokens and generates them through parallel masked decoding. This discrete token space enables in-place trajectory revision: AutoEdit rewrites selected tokens using the same model, without requiring an auxiliary refinement network. To train this capability, we use a two-stage procedure. First, we construct structure-aware perturbations of expert trajectories along longitudinal progress and lateral heading directions and supervise the model to recover the original expert trajectory. We then fine-tune the full decision--draft--reflect rollout with reinforcement learning (RL), assigning terminal driving reward to the final post-edit trajectory and propagating policy-gradient credit through full-rollout transitions. Full-rollout RL proves crucial for coupling drafting and editing: under supervised training alone, inference-time AutoEdit improves PDMS by at most $0.3$, whereas RL increases its gain to $1.9$. We also co-design an efficient reflective decoding stack for the decision--draft--reflect pipeline, combining shared-prefix KV reuse, Alternating Step Decode, and fused on-device unmasking. On NAVSIM, ReflectDrive-2 achieves $91.0$ PDMS with camera-only input and $94.8$ PDMS in a best-of-6 oracle setting, while running at $31.8$ ms average latency on NVIDIA Thor.

Compositional diffusion planning generates long-horizon trajectories by stitching together overlapping short-horizon segments through score composition. However, when local plan distributions are multimodal, existing compositional methods suffer from mode-averaging, where averaging incompatible local modes leads to plans that are neither locally feasible nor globally coherent. We propose *Refining Compositional Diffusion* (RCD), a training-free guidance method that steers compositional sampling toward high-density, globally coherent plans. RCD leverages the *self-reconstruction error* of a pretrained diffusion model as a proxy for the log-density of composed plans, combined with an *overlap consistency* term that enforces consistency at segment boundaries. We show that the combined guidance concentrates sampling on high-density plans that mitigate mode-averaging. Experiments on challenging long-horizon tasks from OGBench, including locomotion, object manipulation, and pixel-based observations, demonstrate that RCD consistently outperforms existing methods. Project website at [https://refining-compositional-diffusion.github.io/](https://refining-compositional-diffusion.github.io/).

Prediction aggregation aims to combine information from multiple predictors into a more informative one. We study this question in the setting of calibrated predictors, where each prediction must equal the conditional expectation of the quantity being predicted given the predictor's signal. Given several calibrated input predictors and the feature distribution, but not the underlying Bayes probabilities, we ask when one can construct refined calibrated predictors that preserve the information in the original predictors and cannot be further refined using the available information. We formulate calibrated predictors as signaling schemes and define refinement through feature-independent garblings: a predictor refines another if its signal can simulate the other's signal. Constructibility is characterized through observable linear information: each signal corresponds to a vector over the feature space, and a new signal is constructible exactly when its vector lies in the linear span of the input signal vectors. Under this formulation, we establish a sharp algorithmic picture. For deterministic output predictors, bilateral refinement admits a polynomial-time algorithm based on a bipartite graph between the two input signal partitions, while refinement with an arbitrary number of input predictors is $\mathsf{NP}$-hard. In contrast, when randomized output predictors are allowed, we give a polynomial-time algorithm for any number of input predictors by decomposing constructible signal vectors into extreme rays of the associated polyhedral cone.

Image tokenization aims to compress visual signals into latent codes that remain effective for reconstruction and generation. Driven by the multi-scale nature of images, organizing latent along a coarse-to-fine refinement process emerges as a promising direction for visual tokenization. Existing scale-wise tokenizers often introduce this structure through token ordering or latent prefixes, but each target scale is typically decoded directly from its prefix, making different prefixes behave like separate reconstruction codes. This can lead to redundant encoding of global structure across scales and limits the effectiveness of compact token budgets. We propose RefineTok, a scale-wise continuous tokenizer that makes decoding itself progressive. RefineTok carries a visual state across scales and uses each latent prefix to refine the previous state into the next scale, turning scale-wise latents into incremental refinement signals rather than independent reconstruction codes. This design yields a compact and structured latent interface for both reconstruction and downstream generation. Together with prefix-level training, a coarse-centric scale trajectory, and a semantic anchor, RefineTok achieves strong reconstruction fidelity among scale-wise tokenizers and competitive class-conditional generation on ImageNet-1K under compact latent budgets. Meanwhile, it preserves a progressive scale-wise interface that single-scale tokenizers do not provide.

Monocular 3D object detection spans two regimes: closed-set detectors operating within a fixed category vocabulary, and open-vocabulary detectors that localize arbitrary categories by leveraging depth foundation models for 3D geometry. We find that current depth foundation models, despite their strong zero-shot generalization, lack the object-level precision 3D detection demands: substituting a state-of-the-art depth foundation model for a strong detector's predicted depth degrades accuracy, even falling below the detector's own prediction. Rather than pushing detectors or depth models to be more accurate end-to-end, we treat object-level depth refinement as a stand-alone task and present RefineAny3D, a vision-language model that corrects depth without ever predicting a numerical value. Our key insight is that depth error has a direct visual signature in image space: when projected onto the image, a correctly placed box tightly encloses the object, while a too-far box projects too small and a too-close box projects too large. Depth refinement thus reduces to a visual alignment problem rather than a metric regression problem, which we instantiate by extending the VLM's vocabulary with action tokens that replace numerical depth output with categorical decisions, and by supervising the model on a large-scale chain-of-thought dataset that grounds each decision in explicit visual evidence. Applied as a single post-hoc step, RefineAny3D delivers consistent gains across closed-set detectors, open-vocabulary detectors, and 3D auto-labeling tools, and generalizes to novel categories, scenes, and cameras without retraining.

Camouflaged Object Segmentation (COS) aims to identify objects visually hidden in their surrounding environments. Existing COS benchmarks mainly focus on image-level or video-level visual perception, while real-world camouflaged scenes are often accompanied by audio signals and user intentions, where sound semantics and textual expressions provide critical information for localizing hidden targets. To extend the boundary of COS, we introduce a new task, termed Referring and Reasoning Audio-Visual Camouflaged Object Segmentation (R2-AVCOS), which aims to segment camouflaged targets in audio-visual scenes according to textual expressions with referring or reasoning intentions. This task emphasizes understanding audio content and incorporates complex reasoning and world knowledge into expressions. To support this task, we construct R2-AVCOSBench, the first audio-visual benchmark with pixel-level annotations for camouflaged objects specified by referring expressions or inferred through reasoning. It contains 2,654 audio-visual camouflaged videos, 21,232 annotated frames, and 32,329 expressions, including 17,543 referring and 14,786 reasoning expressions. Furthermore, we propose Camouflaged Instructed Segmentation Assistant (CISA), a baseline model built upon a Multimodal Large Language Model (MLLM). CISA understands complex textual and audio-visual cues and performs referring- and reasoning-based camouflaged object segmentation. Extensive experiments show that CISA achieves strong referring and reasoning segmentation ability in audio-visual camouflaged scenes and obtains competitive results on related tasks.

Empirical Risk Minimization treats training samples uniformly, which can degrade performance in noisy or heterogeneous settings. We introduce a reference-guided objective that uses per-sample error comparisons with a fixed reference model to reweight gradient contributions without relying on prediction imitation, while preserving gradient direction and ensuring bounded scaling. Theoretical analysis shows that the formulation induces adaptive weighting with controlled amplification. Experiments on image classification with synthetic label noise and on time-series forecasting demonstrate broad improvements across architectures, particularly in moderate-to-high noise and heterogeneous regimes. Results further indicate that the method is most effective when the error-ranking alignment between the baseline model and the reference model is low, suggesting that gains arise primarily from the diversity of the reference error ranking relative to the learner, rather than the reference's absolute performance.