NeurIPS 2026 论文列表

A widely held assumption in knowledge distillation is that teacher and student representations must occupy a compatible or explicitly aligned feature space. We propose RPKD (Random Prototype Knowledge Distillation), which discards this assumption by projecting both networks into a shared set of randomly initialized, frozen prototype vectors, requiring no architecture-specific adapters, no class-specific alignment, and minimal architectural assumptions. Two branches handle the transfer: a logit branch aligning global prototype similarity distributions and a feature branch matching spatially-resolved prototype activation maps. Both operate within the same fixed prototype space, which can be interpreted as a random feature embedding that approximately preserves inter-sample similarity structure, keeping RPKD agnostic to the internal dimensions and inductive biases of either network. In low-category settings, decoupling the prototype vocabulary from the task label space yields richer supervision than the label space alone, an advantage absent from logit-based methods, whose supervisory signal collapses as class count shrinks. This advantage is especially relevant in real-world scenarios where the label space is typically constrained. Extensive experiments demonstrate the effectiveness of RPKD, achieving a maximum gain of $\mathbf{+8.26\%}$ over OFA on CIFAR-100, $\mathbf{+12.46\%}$ on ImageNet-100, and $\mathbf{+1.34\%}$ on ImageNet-1K. Source code will be released upon acceptance. Source code will be released upon acceptance.

Large language models (LLMs) trained purely on text ostensibly lack any direct perceptual experience, yet their internal representations are implicitly shaped by multimodal regularities encoded in language. We test the hypothesis that explicit sensory prompting can surface this latent structure, bringing a text‑only LLM into closer representational alignment with specialist vision and audio encoders. When a _sensory prompt_ tells the model to 'see' or 'hear', it cues the model to resolve its next‑token predictions as if they were conditioned on latent visual or auditory evidence that is never actually supplied. Our findings reveal that lightweight prompt engineering can reliably activate modality‑appropriate representations in purely text‑trained LLMs.

This paper studies the convergence of the Optimistic Multiplicative Weights Update algorithm (OMWU) in two-player zero-sum games. Recent works have identified instances on which the last-iterate of OMWU can converge arbitrarily slowly, but understanding when and why this slow convergence occurs has remained open. In this work, we develop a new analysis framework that gives sharp, quantitative explanations for this behavior. Our analysis is based on viewing the algorithm's dual iterates as an *optimistic skew-gradient descent* with respect to an energy function. We prove over the dual iterates that energy is dissipative, and by establishing tight bounds on the magnitude of dissipation, our analysis quantifies the geometric bottlenecks that arise when the corresponding primal iterates are close to the simplex boundary. This further translates into a new linear last-iterate convergence rate in KL divergence on games with a unique and interior Nash equilibrium. Compared to prior work, this new rate contains a much sharper dependence on game-specific constants, and we prove this dependence is optimal. Moreover, these geometric insights further translate into new separations on *uniform* convergence rates for OMWU. On the one hand, we prove *constant lower bounds* on the uniform *best-iterate* convergence rate in KL divergence and Total Variation distance from Nash. On the other hand, we establish for the $2\times 2$ setting a new $\widetilde O(T^{-1/2})$ best-iterate rate in duality gap, improving substantially over prior work. Together, this shows in general that uniform convergence rate guarantees do not transfer across different measures of distance to Nash.

Practitioners using machine learning on noisy tabular data can often find simpler, more interpretable models with the same accuracy as black box models. In some cases, this is because the noise in the data induces a large Rashomon set, that is, a large set of near-optimal models, which then frequently contains simpler models. However, our understanding of this effect from discrete hypothesis classes --- the Rashomon set's size, the diversity of its predictions, and implicit regularization --- leads to a contradiction in continuous hypothesis spaces, and thus does not directly establish whether noise should necessarily induce simpler or more diverse models. We reconcile the seemingly conflicting effects by showing geometrically that noise drives simplicity through separate mechanisms for linear, logistic, and generalized additive models. We introduce the Rashomon reducibility cost to quantify whether a given model simplification is possible within the Rashomon set, and characterize how this cost changes under general data properties such as label noise. For practitioners working with noisy tabular data, our results suggest that simpler, more interpretable models will be included in the Rashomon set, so that black box models will generally not be needed.

In Transformer attention, distinct weight vectors $\boldsymbol{\alpha} \neq \boldsymbol{\alpha}'$ can produce the same aggregated representation $\mathbf{V}\boldsymbol{\alpha} = \mathbf{V}\boldsymbol{\alpha}'$. When $\operatorname{rank}(\mathbf{V}) \leq n-2$, configurations with entirely different dominant source tokens collide on a set of positive Lebesgue measure, a condition satisfied in over 97% of attention heads in BERT-Base. Such collisions are harmful: the downstream FFN receives identical inputs despite the attention having attended to entirely different source tokens, and must therefore produce identical outputs regardless of which tokens actually dominated, fundamentally limiting any computation that requires sensitivity to attention source, such as multi-hop reasoning, attribution, or knowledge retrieval. No increase in depth, width, or data can compensate, because the routing weights are discarded before the FFN is reached. The routing weights $\{\alpha_{ij}\}$, however, are available within the same forward pass and can be retained as a compact side-channel to restore the missing signal. We call this structural information loss *routing non-identifiability*. In BERT-Base, value-matrix rank deficiency suppresses $k \geq 107$ routing dimensions (over 84% of degrees of freedom) before any FFN computation. To quantify the practical gap, we introduce the Routing Reconstruction Task (RRT): standard Transformers achieve 31.4% source-identification accuracy while oracle routing statistics reach 94.6%, a 63-point gap consistent with an information bottleneck in the FFN input. We then propose the Route-Aware FFN (RA-FFN), a drop-in module that appends four compact routing statistics to each FFN block at under 1.1% additional parameter cost, recovering over 75% of the oracle gain. RA-FFN improves all benchmarks tested: at 110M scale, gains cover multi-hop reasoning, language modelling, and translation, with multi-hop gains $6\times$ larger than single-hop; at 7B scale on Llama-2-7B and Mistral-7B, gains extend further to mathematics (GSM8K) and general reasoning (MMLU, ARC-Challenge, HellaSwag), ordered by routing sensitivity.

Neural network-based virtual microphone estimation (neural-VME) synthesizes microphone signals at unobserved spatial locations from a limited set of real microphone (RM) physical recordings. This enables high-resolution arrays that improve spatial processing for downstream tasks such as speech enhancement. However, existing methods rely on supervised training with ground-truth signals captured at virtual locations, requiring datasets that scale with the number of virtual microphones (VM) and leaving open the question of how to design optimal large-array configurations. We propose \textit{Virtual-Flow}, a flow-matching framework that implicitly generates VM signals conditioned on real recordings, without requiring ground-truth targets. We introduce an unsupervised training strategy based on pseudo-VM targets constructed from time-delayed superpositions of real recordings, and show that it improves magnitude estimation in high-frequency bands, yielding richer spatial cues for beamforming. Experiments demonstrate that the proposed Virtual-Flow, combined with reflow distillation, outperforms existing state-of-the-art neural-VME models on downstream neural beamforming and speech enhancement tasks while requiring lower computational load.

We show that a generative model can discover concepts from data in an unsupervised setting while learning to generate. The Dirichlet Concept Diffusion Model (DCDM) embeds concept discovery into diffusion-based generation. DCDM learns concept centers and infers a Dirichlet distribution over them for each input. The resulting weighted center shapes the forward diffusion mean and reverse denoising process, so components are learned through the same evidence lower bound used to model the data. The method uses no class labels, attribute annotations, captions, pretrained text-to-image priors, or semantic concept supervision. Analysis shows how the formulation preserves concept-level information along diffusion paths and reduces denoising ambiguity, creating pressure for concept centers to capture stable modes. Experiments across diverse image domains show that the learned components form coherent prototypes, support interventions, and reflect recurring visual structure.

Hybrid models and neural differential equations (NDEs) are becoming increasingly important for modelling physical systems; however, they often encounter stability and accuracy issues during long-term integration. Training on unrolled trajectories is known to limit these divergences but quickly becomes too computationally expensive due to the need to compute gradients over an iterative process, making this method impractical for large-scale physical systems (e.g. weather and climate forecasting). Two popular paradigms for improving the stability of learned dynamics are to train on interpolated or noisy samples or to regularize the Jacobian of the learned representation. In this work, we demonstrate that these paradigms can be understood under a common lens and that they both correspond to an approximation of the gradients obtained in an unrolled learning strategy. Building on this understanding, we derive a principled and complete approach to regularize training and demonstrate its impact on the stability of learned dynamical systems.

Canonical Correlation Analysis (CCA) is a fundamental method for multiview shared space learning. However, its strict reliance on paired data poses a significant limitation, as such data is often difficult to obtain or entirely unavailable. In this paper, we present Unpaired CCA (UCCA), a novel method that learns linear projections to maximize the correlation of the true underlying pairing without access to any paired samples during training. We first establish theoretical results connecting the Quadratic Assignment Problem (QAP) to CCA. Leveraging these theoretical insights, we derive a practical method to maximize correlation exclusively from unpaired data. To the best of our knowledge, UCCA is the first approach to learn maximally correlated projections in a strictly unpaired setting. We validate UCCA on real-world multi-modal datasets, demonstrating that it significantly outperforms recent unpaired alignment baselines in recovering the underlying true correlation. This work fills a critical gap between traditional statistical multiview learning and the growing field of unpaired data learning.

Vision-language perception has achieved impressive progress in aligning natural language with visual observations, yet grounding high-level semantics into part-level physical interaction remains challenging. To address this gap, we propose UniRAP, a unified model for inferring part-level physical affordances and mapping language instructions to actionable geometric representations. UniRAP formulates this problem as a conditional multimodal generation task, integrating visual inputs, textual instructions, and optional prompts into a shared spatiotemporal representation space through a unified interface token mechanism. To predict executable contact geometry, we introduce a Unified Affordance Decoder (UAD), which jointly performs object detection, part-level affordance segmentation, and 4-DoF interaction pose estimation by leveraging intermediate segmentation features. In addition, we propose a curriculum-based transfer training strategy that progressively adapts the model from general visual parsing to interaction-aware perception, improving data efficiency under limited textual annotations. Experiments show that UniRAP achieves state-of-the-art performance on referring expression segmentation, affordance grounding, and interaction pose estimation, while maintaining strong spatiotemporal consistency in dynamic video scenarios. These results demonstrate the effectiveness of UniRAP as a unified perception framework for language-guided physical manipulation. All data and code will be made publicly available.

The proliferation of multimodal data has underscored the imperative for efficiency in cross-modal retrieval. By mapping data into a unified Hamming space, Cross-modal hashing (CMH) significantly enhances both storage and computational efficiency, thereby establishing itself as a preferred favored paradigm for retrieval tasks. However most methods assume complete data, which rarely holds in practice. In incomplete settings, missing modalities (e.g., text or image) break semantic correspondence and make unsupervised hashing unreliable. Therefore, we propose Unsupervised Generative Completion and Graph-attention Refinement for Incomplete Cross-modal Hashing (UGGRH) method. Specifically, UGGRH leverages pretrained generative models for modality completion and employs a discriminator-guided similarity refinement module to fuse intra-modal relations with paired image-text matching signals, thereby constructing a robust cross-modal similarity matrix that yields a noise-tolerant similarity target for training. After that, it learns discriminative binary codes via hash-aware graph attention and cross-modal fusion, to refine modality embeddings and produce unified hash codes. Experiments on MIRFlickr25K, NUS-WIDE, and MS COCO datasets demonstrate that UGGRH consistently achieves superior performance under high missing rates and modality imbalance, showing significant improvements in retrieval accuracy and robustness across challenging incomplete scenarios.

Continual learning aims to acquire tasks sequentially without catastrophic forgetting, yet standard strategies face a core tradeoff: regularization-based methods (e.g., EWC) can overconstrain updates when task optima are weakly overlapping, while replay-based methods can retain performance but drift due to imperfect replay. We study a hybrid perspective: \emph{trust region continual learning} that combines generative replay with a Fisher-metric trust region constraint. We show that, under local approximations, the resulting update admits a MAML-style interpretation with a single implicit inner step: replay supplies an old-task gradient signal (query-like), while the Fisher-weighted penalty provides an efficient offline curvature shaping (support-like). This yields an emergent meta-learning property in continual learning: the model becomes an initialization that rapidly \emph{re-converges} to prior task optima after each task transition, without explicitly optimizing a bilevel objective. Empirically, on task-incremental diffusion image generation and continual diffusion-policy control, trust region continual learning achieves the best final performance and retention, and consistently recovers early-task performance faster than EWC, replay, and continual meta-learning baselines.

Algorithms with predictions, or learning-augmented algorithms, has proved to be an extremely useful paradigm for combining machine learning with traditional algorithms. One of the textbook settings for this is searching a sorted array. Without a prediction classical binary search takes $O(\log n)$ queries, while with a prediction we can use "doubling binary search" to find the target key using $O(\log \eta)$ queries, where $\eta$ is the error of the prediction measured as the absolute value of the difference between the true location and the predicted location. Since an array is just a path graph, in this paper we ask whether similar bounds can be achieved for search on even slightly more general graphs: trees. We show first that the high-level answer is "no": there is no search algorithm that uses $O(\log \eta)$ queries, where now $\eta$ is the graph distance between the predicted location and the true location. However, as our main result, we show that such bounds can be achieved on trees which are "path-like" in that they have low pathwidth. In particular, we prove that there is a search algorithm which uses at most $O(k \log \eta)$ queries, where $k$ is the pathwidth of the tree. We also prove a lower bound showing that our algorithm has existentially optimal query complexity. Finally, we show experimentally, on real-life inputs, that our algorithm has query complexity which is notably better than the simple non-prediction based algorithm.

Halpernian actual causation, the formal study of which events in a specific situation caused a specific outcome in acyclic structural causal models, underpins legal responsibility, moral blame, and the assessment of causal harm. Despite the rich logical framework, no prior sound and complete enumeration procedure is known for finding *all* actual causes in a given setting, blocking downstream tasks such as responsibility attribution, blame assessment, and causal-harm grading that aggregate over the full cause set. We close this gap by introducing *witness targets*: sets of joint configurations containing every counterfactual witness. In combination with an *ancestor intervention grammar* we derive a finite directed acyclic *witness map*. We prove that for every actual cause there exists a contingency set such that the joint intervention set appears as a node of this map, and present an algorithm for *Tracing Actual Causes (TrAC)* that is sound and complete for enumerating all actual causes of any target event. We compare TrAC empirically with existing single-cause baselines on random Boolean structural causal models, demonstrating practical feasibility for graphs of up to 15 nodes.

A key strength of diffusion models lies in their flexibility, since their outputs can be controlled at sampling time through guidance. However, beyond simple cases such as conditional sampling, the target distribution is often left implicit, defined only through a sampling rule or a heuristic energy function. To address this, we propose Jeffrey guidance, a principled framework that extends diffusion-model control to applications beyond what standard guidance can express. It leverages Jeffrey’s rule of conditioning to update marginal distributions towards a prescribed target, preserving the conditional structure and minimally perturbing the joint distribution. We first demonstrate Jeffrey guidance by targeting a prescribed embedding distribution. With Inception embeddings as the target, this leads to substantial reductions in FID on both CIFAR-10 and FFHQ. We further apply Jeffrey guidance to fairness on CelebA-HQ, updating an unconditional diffusion model to enforce independence between attributes.

Recently, Muon has gained substantial attention as an appealing alternative to Adam, with many works highlighting its advantages through spectral normalization and improved conditioning. Yet this positive theoretical narrative contrasts with its empirical performance in large language model (LLM) training, where Muon’s gains over Adam/AdamW are often mixed, schedule-sensitive, and not uniformly superior. To address this gap, we develop a trajectory-level theory characterizing both the strengths and limitations of Muon. We introduce a mixed-spiked matrix sensing model whose sensing operator decomposes into signal, spike, and bulk components, capturing a mixture of anisotropic structure and long-tail information reminiscent of LLM training. On top of it, we adopted a river-valley perspective in which we view the landscape as composed of a river direction flowing to the desired solution and hill directions encoding nuisance or task-irrelevant information. In the momentum-free setting, we show that Muon moves faster along the information-bearing river direction during early optimization, but can converge much more slowly near the river bottom than gradient descent. We then extend the river-valley perspective to general nonconvex objectives with momentum by studying points on the spectral river. There, while Muon converges faster early on, its orthogonalized update removes residual scale information, making it prone to overshooting and oscillation near the target solution. Together, these results suggest that our characterizations extend beyond spiked matrix sensing and motivate switching to GD-like refinement optimizers in the final phase, rather than relying only on a fixed learning-rate schedule for Muon. We also provide preliminary evidence supporting this two-stage approach in language model training experiments.

Causal representation learning (CRL) offers the promise of uncovering the underlying causal model by which observed data was generated, but the practical applicability of existing methods remains limited by the strong assumptions required for identifiability and by challenges in applying them to real-world settings. Most current approaches are applicable only to relatively restrictive model classes, such as linear or polynomial models, which limits their flexibility and robustness in practice. One promising approach to this problem seeks to address these issues by leveraging changes in causal influences among latent variables. In this vein we propose a more general and relaxed framework than typically applied, formulated by imposing constraints on the function classes applied. Within this framework, we establish partial identifiability results under weaker conditions, including scenarios where only a subset of causal influences change. We then extend our analysis to a broader class of latent post-nonlinear models. Building on these theoretical insights, we develop a flexible method for learning latent causal representations. We demonstrate the effectiveness of our approach on synthetic and semi-synthetic datasets, and further showcase its applicability in a case study on human motion analysis, a complex real-world domain that also highlights the potential to broaden the practical reach of identifiable CRL models.

Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade during cross-architecture transfer or in the presence of feature noise. We introduce TopoPrune, a framework which resolves this challenge by leveraging topology to capture the stable, intrinsic structure of data. TopoPrune operates at two scales, (1) utilizing a *topology-aware manifold approximation* to establish a global low-dimensional embedding of the dataset. Subsequently, (2) it employs *differentiable persistent homology* to perform a local topological optimization on the manifold embeddings, ranking samples by their structural complexity. We demonstrate that our *unified dual-scale topological approach* ensures high accuracy and precision, particularly at significant dataset pruning rates (e.g., 90%). Furthermore, through the inherent stability properties of topology, TopoPrune is (a) exceptionally robust to noise perturbations of latent feature embeddings and (b) demonstrates superior transferability across diverse network architectures. This study demonstrates a promising avenue towards stable and principled topology-based frameworks for robust data-efficient learning.

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is thanks to its high versatility, as clusters are detected from the persistent components in the sublevel sets of any user-defined function (gene expression, pixel values, etc), and efficiency, as topological clustering enjoys robustness guarantees. However, ToMATo is also limited in several ways. First, a graph on the data points needs to be provided as a hyper-parameter of the method (whose fine-tuning is left to the user). Second, ToMATo is known to be very sensitive to outlier values in the function range. Finally, and most importantly, ToMATo can only handle one function at a time, whereas it is critical to use several functions in various applications. In this article, we introduce ToMAToMP: the first topological clustering method able to handle several functions at the same time with theoretical guarantees. More specifically, we leverage a recent tool from multi-parameter persistent homology, called MMA decomposition, to design our clustering algorithm, and prove that it enjoys robustness properties. As corollaries, we show that it can be used to make ToMATo independent of graph tuning, and robust to outliers. Finally, we provide a set of numerical experiments showcasing the efficiency and quality of the clusterings produced by ToMAToMP, by showing strong improvement over non-topological and topological baselines for various datasets.