NeurIPS 2026 Papers

Equipping VLM agents with world modeling capabilities has shown strong potential for complex reasoning and long-horizon planning, while reducing the dependence of policy learning on costly real-world interactions. Existing methods mainly rely on prospective simulation to predict the consequences of candidate actions. However, this forward-only paradigm focuses on *what will happen next* and provides limited constraints for verifying whether an action is causally consistent with the observed state transition, which can lead to plausible-looking but physically incoherent behaviors. In this paper, we challenge the view of world modeling as only prospective prediction and introduce Retrospective World Modeling, a new agent learning paradigm that enables agents to reason backward by estimating the retrospective attribution distribution $P(\hat{a}_{t}|s_t, s_{t+1})$ for the action that most likely caused a given transition. Based on this capability, we formulate the Self-Consistency Reward (SCR), an intrinsic signal that measures the probabilistic consistency between the policy action and the retrospective explanation. Integrating SCR into reinforcement learning provides dense transition-level feedback and steers agents toward behaviors that are both task-effective and physically grounded. Extensive experiments across diverse agentic tasks show that our method substantially improves policy robustness and generalization over prospective-only world modeling baselines.

Visual foundation models (VFMs) provide strong region-level representations for semantic segmentation, substantially improving high-level semantic understanding. However, accurate boundary recovery remains challenging, especially for fine structures and semantic transitions. A key reason is that conventional pixel-level supervision largely treats pixels independently and lacks explicit modeling of local structure and neighboring-pixel relationships. To address this issue, we propose a Local Structure (LS) regularization framework that constrains the second-order local organization of semantic transition regions. Unlike existing boundary losses that mainly supervise contour location, distance, overlap, or topology, LS models boundary neighborhoods through a structure-tensor representation of semantic probability fields. It decomposes local boundary structure into two complementary cues: Local Structure Magnitude (LSM), which measures the strength of anisotropic class transitions, and Local Structure Orientation (LSO), which describes their dominant geometric orientation. LS is model-agnostic, compatible with different VFM-backbone-decoder combinations, and introduces no extra inference cost. Extensive experiments on four diverse datasets show that LS consistently improves boundary-sensitive performance while also enhancing overall IoU, demonstrating its effectiveness for boundary-structure learning in semantic segmentation.

Model merging has emerged as a promising paradigm for composing large language models directly in weight space, enabling training-free integration of specialized models. However, existing methods rely on parameter-space averaging that systematically induces generation dysregulation---a spectrum of failure modes ranging from structural repetition and termination failure to circular reasoning, and at the extreme, full semantic collapse into incoherent symbols. Even when source models exhibit near-zero dysregulation, existing methods introduce it at $>$97\% (14B/32B scales), collapsing reasoning benchmarks by up to 70 points. We propose Sparse Complementary Fusion with Reverse KL (\textbf{SCF-RKL}), a data-free merging framework that selects complementary parameters via reverse KL divergence on parameter-group proxy distributions. This structure-preserving, sparsity-inducing design maintains proxy-space geometry---theoretically motivated via entropy and subspace bounds---and empirically suppresses generation dysregulation while integrating new capabilities. Extensive experiments on 24 benchmarks across 7B--32B models spanning reasoning, instruction following, safety, and vision demonstrate that SCF-RKL achieves the best overall performance across scales while maintaining near-zero dysregulation ($<$1\%) and strong generalization.

Multimodal alignment under scarce paired supervision aims to align independently pretrained unimodal encoders using limited image--text pairs, offering a practical alternative when large-scale joint pretraining is infeasible. Such scenarios call for lightweight objectives that go beyond local correspondences and capture distributional mismatch between heterogeneous embeddings. Existing methods often derive supervision from limited pairs through contrastive objectives or geometry-preserving regularization, encouraging instance-level correspondence or structural consistency but providing limited direct supervision on global cross-modal mismatch. This motivates a distribution-level objective that complements paired supervision by comparing image and text embedding distributions. In this paper, we propose $\textbf{Spec}$tral Characteristic Distribution $\textbf{Align}$ment ($\textbf{SpecAlign}$), a lightweight spectral alignment framework that reduces cross-modal mismatch by comparing image and text characteristic functions over learnable spectral queries. Since characteristic functions uniquely determine probability distributions, SpecAlign provides a principled signal for capturing multi-scale discrepancies beyond pointwise alignment. To obtain informative and stable queries, SpecAlign employs a Structured Direction--Radius Sampler (SDRS) that decouples direction and radius modeling. Extensive evaluations on transfer, retrieval, robustness, and representation analyses demonstrate consistent gains, validating spectral distribution-level supervision for data-efficient multimodal alignment.

Graph Neural Networks (GNNs) perform computations on graphs by routing the signal between graph regions using a graph shift operator or a message passing scheme. Often, the propagation of the signal leads to a loss of information, where the signal tends to diffuse across the graph instead of being deliberately routed between regions of interest. Two notions that depict this phenomenon are oversmoothing and oversquashing. In this paper, we propose an alternative approach for modeling signal propagation, inspired by quantum mechanics, using the notion of observables. Specifically, we model the place in the graph where the signal lies, how much the signal is concentrated there, and how much of the signal is propagated towards a location of interest when applying a GNN. Using these new concepts, we prove that standard spectral GNNs have poor signal propagation capabilities. We then propose a new type of spectral GNN, termed Schrödinger GNN, which we show has a superior capacity to route the signal across the graph.

Automatic Prompt Optimization (APO) aims to improve the capabilities of Large Language Models (LLMs), yet existing methods remain limited by their result-oriented nature. Training-free approaches often converge to suboptimal prompts, while training-based methods suffer from reward sparsity and optimization instability. More importantly, both paradigms focus on obtaining the final prompt rather than learning the prompt optimization process itself. To address this dilemma, we propose \textbf{ProPO}, a trajectory-driven \textbf{Pro}cess learning framework for \textbf{P}rompt \textbf{O}ptimization guided by multi-dimensional composite rewards. Specifically, ProPO introduces a historical trajectory reflection mechanism for high-quality exploration. Concurrently, we adopt adaptive rubric rewards to provide fine-grained supervision and alleviate reward sparsity. More importantly, we design a novel Process Logic Reward that supervises the consistency of the reflection process. Extensive experiments demonstrate that ProPO, integrated with GRPO, establishes a new SOTA performance. Notably, ProPO achieves a remarkable \textbf{70.00\%} accuracy on the highly complex AIME-2026 task and an absolute gain of \textbf{+25.25\%} over the zero-shot baseline on Subjectivity Classification (Subj). Furthermore, empirical analyses reveal that our multi-dimensional reward mechanism provides finer-grained and denser signals, allowing the model to learn the prompt optimization process, and ultimately enabling it to generate significantly higher-quality prompts.

Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory — supervision that is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors — concise, step-level evidence snippets extracted from the web — as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher–student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5\% overhead per step from a single additional forward pass.

This paper considers a practical few-shot anomaly detection (FSAD) setting, termed **discriminative FSAD**, where a limited number of both normal and anomalous examples are available as references during inference. Existing FSAD methods rely on normal-only references through normality matching, ignoring the discriminative clues in anomalous references, while directly fitting both references can overfit to the seen anomalies. We introduce **IDEAL**, an intrinsic deviation learning framework that leverages both reference types to learn intrinsic deviation patterns characterizing generalizable abnormality as deviations from normality. IDEAL decomposes the learning process into two novel components: 1) a Normal Variation Eraser to suppress nuisance normal variations that may lead to noisy deviations from normality, thereby highlighting anomaly-relevant deviation representations; 2) an Intrinsic Deviation Encoder to decompose these denoised deviation representations into intrinsic deviation vectors capturing the most discriminative orthogonal deviation directions. At inference, IDEAL scores query-to-normal deviations preserved after projection onto the learned intrinsic deviation vectors, enabling generalization for both seen and unseen anomalies. Extensive experiments on eight real-world datasets show that IDEAL generalizes effectively to unseen anomalies and consistently outperforms existing state-of-the-art FSAD methods.

Graph foundation models have emerged as a promising paradigm for generalizing across diverse structural tasks. Current approaches serialize graphs into node token sequences and apply autoregressive or masked prediction, yet this node sequential modeling disrupts the relation-centric nature of graphs and violates permutation equivariance. We propose **relational diffusion**, a framework that reconceptualizes graph modeling through edge co-occurrence modeling. By treating edges as fundamental modeling units and learning their joint distribution via discrete diffusion processes, our approach naturally respects the relational semantics of graphs while maintaining permutation equivariance. We introduce topological edge tokenization to enrich edge representations with multi-hop structural context, and relational prompt completion to unify node classification, link prediction, and graph classification as sequence completion problems over edge representations. Through extensive experiments, we demonstrate that relational diffusion achieves strong performance while providing a principled foundation aligned with the relational nature of graphs.

In multimodal classification, late-fusion approaches classify concatenated modality-specific features extracted by unimodal neural networks. When modality imbalance is pronounced, various regularization techniques have been proposed to balance the learning process and overcome the inferior performance of late-fusion networks. In contrast, this work demonstrates that multimodal data can be effectively classified without any explicit modality fusion, using deep ensembles of unimodal networks. We systematically compare deep ensembles to late-fusion networks at equal parameter count and show that ensembles consistently outperform state-of-the-art late-fusion methods designed to address modality imbalance. This advantage also holds over intermediate-fusion techniques we evaluated and over hybrid methods that combine unimodal and multimodal predictions. We propose and empirically validate a method for selecting the number of models per modality in an ensemble, avoiding computationally expensive exhaustive search. Under extreme modality imbalance and small ensemble sizes, the heuristic indicates that ensembles of unimodal models trained solely on the stronger modality are preferable; as the ensemble scales up, incorporating models from the weaker modality becomes beneficial. Both predictions align with our empirical findings. To systematically explore the challenges of optimizing multimodal models, we propose a synthetic multimodal framework that allows control over both the number of modalities and their predictive strength; our findings are consistent across synthetic and real-world datasets. Finally, by fitting scaling laws to bimodal datasets, we estimate the asymptotic performance of ensembles.

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become computationally challenging in more general settings with non-canonical, non-smooth, or nonlinear link functions, where the resulting optimization landscape may be ill-conditioned, non-convex, or non-differentiable. In this paper, we study an alternative estimation framework based on variational inequalities (VIs), which formulates GLM estimation through an operator-based equilibrium condition rather than likelihood minimization. We analyze the VI estimator from a statistical perspective and establish finite-sample error bounds and asymptotic normality under mild regularity conditions, together with convergence guarantees for fixed-point and stochastic approximation algorithms. The framework accommodates a broad class of link functions, including non-canonical and non-monotone cases satisfying a strong Minty-type condition, and extends naturally to generalized additive models via basis expansion. Numerical experiments demonstrate that the VI approach achieves competitive finite-sample accuracy and improved numerical stability relative to MLE, particularly in GLMs and GAMs with non-canonical or non-smooth link functions.

Deep neural networks continue to grow in parameter count, driving up training and inference cost on GPUs. Sparse neural networks and Dynamic Sparse Training (DST) promise to reduce these costs, but most implementations rely on binary masks over dense tensors and recover little of the theoretical compute, memory, or energy savings. We propose SNACK, a truly sparse GPU layer that stores and computes only non-zero connections. SNACK exposes a simple PyTorch API for restructuring connections and backpropagating gradients entirely in the sparse paradigm, and uses a custom COO-format SpMM CUDA kernel with a batch-to-Streaming-Multiprocessor mapping tuned for the small-batch, high-sparsity regime typical of large-model training and single-stream inference. At the kernel level, SNACK is up to $7\times$ faster than the masked dense baseline (Dense+Mask) and competitive with cuSPARSE, Sputnik, and FlashSparse at 95\% sparsity. At 90\% sparsity, a single SNACK layer accelerates training by $8\times$ and $3.7\times$, and inference by $4\times$ and $2\times$, over Dense+Mask and fully dense layers, respectively, while using 25\% less memory than dense and substantially less energy. End-to-end, SNACK reduces GPT-2 peak training memory by up to 40\% and graph-style inference latency by $4.8\times$ over Dense+Mask at 99\% sparsity.

Neural denoisers trained with pointwise distortion losses such as MSE often suppress the temporal regularities that downstream tasks depend on---a failure that becomes acute under non-Gaussian, impulsive, or non-stationary disturbances. We propose a training framework that lifts a family of classical complexity descriptors---permutation entropy, sample entropy, Lempel-Ziv complexity, and Higuchi fractal dimension---into end-to-end differentiable objectives via calibrated soft surrogates with straight-through gradients. Three complementary mechanisms emerge from this lifting: (i) early fusion injects local structural priors as auxiliary inputs, (ii) a complexity-consistency regularizer matches the multi-scale complexity of denoiser outputs to clean references, and (iii) a curriculum sampler prioritizes examples whose noise-induced complexity inflation is largest. We prove that additive noise strictly inflates ordinal uncertainty for bounded piecewise-smooth signals, and that, under bounded surrogate calibration, complexity consistency yields a strictly larger expected decision margin than MSE-only training. On OFDM/QAM communication signals under AWGN, $1/f$ colored, and $\alpha$-stable impulsive noise, our framework reduces post-detection bit error rate by 29--47% over Transformer (PatchTST, iTransformer), GNN, and CNN baselines, with statistically significant gains across five seeds and 95% bootstrap confidence intervals. The improvements transfer to over-the-air conditions on the public RadioML 2018.01A benchmark (single-carrier QAM portion) and a new 50-session in-house SDR testbed, yielding 22--26% relative BER reduction without fine-tuning. The framework is architecture-agnostic and adds $\leq 3.5\%$ FLOPs over the underlying backbone.

It remains unclear whether quantum machine learning (QML) truly holds an advantage when tackling practical and meaningful tasks. In exploring this question, the importance of classical data encoding, often overlooked, becomes increasingly evident. Amplitude encoding, which can embed $2^n$ classical data into $n$ qubits, is widely used due to its apparent efficiency. However, its potential limitations for QML have yet to be fully explored. In this paper, we establish a theoretical result for the limitations caused by quantum encoding and point out the existence of a concentration phenomenon in amplitude encoding. Compared to prior work, our theoretical result operates under more general conditions and leads to a stronger conclusion. This concentration phenomenon causes the classification predictions to remain close to random guessing, regardless of the training process. Our findings shed new light on a long-standing puzzle in the field of QML: why some QML models perform well on simple datasets like MNIST but fail to generalize to more complex practical tasks. By highlighting the pivotal role of encoding design in QML, our work clearly indicates that future research needs to focus more on the design of classical data encoding to advance the effectiveness of QML.

Plug-and-Play (PnP) methods have become standard tools for solving imaging inverse problems by replacing the intractable maximum a posteriori (MAP) denoiser with the MMSE one. While this mismatch has been widely treated as unavoidable, recent works have sought to close this gap by targeting the MAP with diffusion-model scores. We show this is problematic in practice: learned scores do not match the true ones, so MAP-targeting iterations converge to cartoon-like images rather than realistic ones, and better results are obtained by stopping short of convergence. We turn this observation into a design principle and introduce $\texttt{ProxiMAP}$, an iterative MAP approximation whose noise schedule keeps the iterate's residual noise matched to the denoiser's training noise. This keeps the denoiser in-distribution where its score is reliable, and yields implicit early stopping that avoids the failure mode above. $\texttt{ProxiMAP}$ is a modular drop-in replacement for MMSE denoisers in standard PnP algorithms and consistently sharpens reconstructions across deblurring, inpainting, super-resolution, and phase retrieval. Building on the same principle, we propose a hybrid variant that applies $\texttt{ProxiMAP}$ only in the late iterations of PnP, where the denoiser is most reliable—matching or exceeding the full-replacement variant at a fraction of the cost.

Spiking reservoir computing combines the training efficiency of fixed random recurrent networks with the energy efficiency of event-driven inference, where computation is triggered by sparse spikes rather than executed densely at every timestep. However, existing spiking reservoirs almost exclusively rely on Leaky Integrate-and-Fire (LIF) neurons, whose low-pass dynamics limit their ability to distinguish information encoded at different temporal frequencies. We introduce HRF-Res, a liquid state machine in which LIF neurons are replaced by a heterogeneous population of Harmonic Resonate-and-Fire (HRF) neurons. These neurons exhibit intrinsic oscillatory dynamics and selectively respond to input frequencies, enabling the reservoir to capture frequency-specific temporal patterns. The result is more discriminative representations and higher classification accuracy than LIF-based reservoirs, achieved without sacrificing the energy efficiency of spiking computation, with 9–14× lower energy consumption than an equivalent non-spiking oscillatory reservoir. Evaluated on eight benchmarks spanning time series, sequential images, audio spike trains, and neuromorphic vision, HRF-Res achieves competitive or state-of-the-art performance among spiking reservoir methods. These results demonstrate that introducing frequency-selective dynamics into spiking reservoirs improves representational quality and classification performance while preserving their inherent energy efficiency.

Owing to enhanced capabilities to capture a broad range of higher-order interactions, simplicial neural networks (SNNs) have emerged as a new powerful methodology for graph learning. However, prevailing SNNs are often limited in efficient exploration of heterogeneous graphs, thereby restricting the SNN utility on downstream tasks. To address this challenge, we introduce the concept of L\'{e}vy flights over simplices, offering a new efficient alternative to learning higher-order graph (sub)structures under heterogeneous scenarios. Specifically, we develop a new Fractional Hodge Laplacian Simplicial Neural Network (FHL-SNN), a novel approach leveraging fractional powers of the Hodge-Laplacian and allowing for a more efficient exploration of the underlying higher-order graph organization in conjunction with the link prediction. We establish a theoretical connection between a fractional diffusion process and graph exploration over simplices. In particular, we prove that the L\'{e}vy flight over simplices yields a lower mixing time than that of its non-fractional counterpart. Our extensive experiments on both directed and undirected link prediction tasks illuminate the power of non-local search of graph space via fractional dynamics, yielding relative gains of up to 9\%. Finally, we show that the idea of L\'{e}vy flights over simplices is versatile and that the integration of fractional dynamics to existing SNNs has the potential to further boost the model performance.

Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides the representational plasticity required for high-entropy knowledge injection, Low-Rank Adaptation (LoRA) can match or surpass FFT performance because many tasks only require updates in a low-rank space and benefit from LoRA's additional regularization. Through empirical evaluation across diverse tasks (SQL, Medical QA, and Counterfactual Knowledge) and varying language models (Gemma-3-1B, Qwen2.5-1.5B, and Qwen2.5-3B), we verify both trends and demonstrate that relying solely on either static architecture is structurally limited. To address this challenge, we propose a Mixture of LoRA and Full (MoLF) Fine-Tuning, a unified framework that enables continuous navigation between both training regimes. MoLF dynamically routes updates between FFT and LoRA at the optimizer level to ensure that exact gradient signals are available to both experts throughout training, yielding stable training dynamics. For memory-constrained environments, we also introduce MoLF-Efficient, which freezes base weights and only routes updates among a pair of LoRA experts of potentially varying rank. Our evaluations show that MoLF either improves on or stays within $1.5$% of the better of FFT and LoRA across all settings, while MoLF-Efficient outperforms prior adaptive LoRA approaches by up to $20$% on Fact and $9$% on Med and SQL.

We introduce a new algorithm to sample from a probability density $\pi \propto e^{-V}$ with $V(x): \mathbb{R}^d \rightarrow \mathbb{R}$ a strongly multi-modal potential. Such distributions are challenging to sample from using standard gradient based methods, as exploration typically relies on inefficient diffusions. Inspired by connections between Schrodinger operators, Langevin diffusions and Morse theory, we develop a particle based method that exploits fast relaxation to transition pathways of the so-called Witten PDE on 1-forms (vector fields). Once pathways joining modes are sufficiently well explored, the method relaxes to inexpensive Langevin dynamics for sampling within approximately convex basins. Numerical experiments demonstrate superior performance over cheap gradient based sampling methods and competitive performance at lower cost compared to a state of the art method, parallel tempering.