NeurIPS 2025 Papers

Deep neural networks trained with gradient descent exhibit varying rates of learning for different patterns. However, the complexity of fitting models to data makes direct elucidation of the dynamics of learned patterns challenging. To circumvent this, many works have opted to characterize phases of learning through summary statistics known as order parameters. In this work, we propose a unifying framework for constructing order parameters based on the Neural Tangent Kernel (NTK), in which the relationship with the data set is more transparent. In particular, we derive a local approximation of the NTK for a class of deep regression models (SIRENs) trained to reconstruct natural images. In so doing, we analytically connect three seemingly distinct phase transitions: the emergence of wave patterns in residuals (a novel observation), loss rate collapse, and NTK alignment. Our results provide a dynamical perspective on the observed biases of SIRENs, and deep image regression models more generally.

The remarkable success of the autoregressive paradigm has made significant advancement in Multimodal Large Language Models (MLLMs), with powerful models like Show-o, Transfusion and Emu3 made notable strides in unified image understanding and generation. For the first time, we uncover a common phenomenon: the understanding capability of MLLMs is usually stronger than their generative capability, with a significant gap between them. Building on this insight, we propose HermesFlow, a simple and general framework designed to seamlessly bridge the gap between understanding and generation in MLLMs. Specifically, we take the homologous data as input to curate homologous preference data of both understanding and generation. Through Pair-DPO and self-play iterative optimization, HermesFlow effectively aligns multimodal understanding and generation using homologous preference data. Extensive experiments demonstrate the significant superiority of our approach over prior methods, particularly in narrowing the gap between multimodal understanding and generation. These findings highlight the potential of HermesFlow as a general alignment framework for next-generation multimodal foundation models.

Diffusion models operating in discrete state spaces have emerged as powerful approaches, demonstrating remarkable efficacy across diverse domains, including reasoning tasks and molecular design. Despite their promising applications, the theoretical foundations of these models remain substantially underdeveloped, with the existing literature predominantly focusing on continuous-state diffusion models. A critical gap persists in the theoretical understanding of discrete diffusion modeling: the absence of a rigorous framework for quantifying estimation error with finite data. Consequently, the fundamental question of how precisely one can reconstruct the true underlying distribution from a limited training set remains unresolved. In this work, we analyze the estimation error induced by a score estimation of the discrete diffusion models. One of the main difficulties in the analysis stems from the fact that the cardinality of the state space can be exponentially large with respect to its dimension, which results in an intractable error bound by a naive approach. To overcome this difficulty, we make use of a property that the state space can be smoothly embedded in a continuous Euclidean space that enables us to derive a cardinality independent bound, which is more practical in real applications. In particular, we consider a setting where the state space is structured as a hypercube graph, and another where the induced graph Laplacian can be asymptotically well approximated by the ordinary Laplacian defined on the continuous space, and then derive state space size independent bounds.

Understanding the conformational landscape of proteins is essential for elucidating protein function and facilitating drug design. However, existing protein conformation benchmarks fail to capture the full energy landscape, limiting their ability to evaluate the diversity and physical plausibility of AI-generated structures. We introduce ProteinConformers, a large-scale benchmark dataset comprising over 381,000 physically realistic conformations for 87 CASP targets. These were derived from more than 40,000 structural decoys via extensive all-atom molecular dynamics simulations totaling over 6 million CPU hours. Using this dataset, we propose novel metrics to evaluate conformational diversity and plausibility, and systematically benchmark six protein conformation generative models. Our results highlight that leveraging large-scale protein sequence data can enhance a model’s ability to explore conformational space, potentially reducing reliance on MD-derived data. Additionally, we find that PDB and MD datasets influence model performance differently, current models perform well on inter-atomic distance prediction but struggle with inter-residue orientation generation. Overall, our dataset, evaluation metrics, and benchmarking results provide the first comprehensive foundation for assessing generative models in protein conformational modeling. Dataset and instructions are available at https://huggingface.co/ datasets/Jim990908/ProteinConformers/tree/main. Codes are stored at https://github.com/auroua/ProteinConformers. An interactive website locates at https://zhanggroup.org/ProteinConformers.

We propose two simple, principled and practical algorithms that enjoy provable scaling laws for the test-time compute of large language models (LLMs). The first one is a two-stage knockout-style algorithm: given an input problem, it first generates multiple candidate solutions, and then aggregate them via a knockout tournament for the final output. Assuming that the LLM can generate a correct solution with non-zero probability and do better than a random guess in comparing a pair of correct and incorrect solutions, we prove theoretically that the failure probability of this algorithm decays to zero exponentially or by a power law (depending on the specific way of scaling) as its test-time compute grows. The second one is a two-stage league-style algorithm, where each candidate is evaluated by its average win rate against multiple opponents, rather than eliminated upon loss to a single opponent. Under analogous but more robust assumptions, we prove that its failure probability also decays to zero exponentially with more test-time compute. Both algorithms require a black-box LLM and nothing else (e.g., no verifier or reward model) for a minimalistic implementation, which makes them appealing for practical applications and easy to adapt for different tasks. Through extensive experiments with diverse models and datasets, we validate the proposed theories and demonstrate the outstanding scaling properties of both algorithms.

In this paper, we investigate the universal approximation property of deep, narrow multilayer perceptrons (MLPs) for $C^1$ functions under the Sobolev norm, specifically the $W^{1, \infty}$ norm. Although the optimal width of deep, narrow MLPs for approximating continuous functions has been extensively studied, significantly less is known about the corresponding optimal width for $C^1$ functions. We demonstrate that \textit{the optimal width} can be determined in a wide range of cases within the $C^1$ setting. Our approach consists of two main steps. First, leveraging control theory, we show that any diffeomorphism can be approximated by deep, narrow MLPs. Second, using the Borsuk-Ulam theorem and various results from differential geometry, we prove that the optimal width for approximating arbitrary $C^1$ functions via diffeomorphisms is $\min(n + m, \max(2n + 1, m))$ in certain cases, including $(n,m) = (8,8)$ and $(16,8)$, where $n$ and $m$ denote the input and output dimensions, respectively. Our results apply to a broad class of activation functions.

Many real-world decision-making problems face the off-dynamics challenge: the agent learns a policy in a source domain and deploys it in a target domain with different state transitions. The distributionally robust Markov decision process (DRMDP) addresses this challenge by finding a robust policy that performs well under the worst-case environment within a pre-specified uncertainty set of transition dynamics. Its effectiveness heavily hinges on the proper design of these uncertainty sets, based on prior knowledge of the dynamics. In this work, we propose a novel linear mixture DRMDP framework, where the nominal dynamics is assumed to be a linear mixture model. In contrast with existing uncertainty sets directly defined as a ball centered around the nominal kernel, linear mixture DRMDPs define the uncertainty sets based on a ball around the mixture weighting parameter. We show that this new framework provides a more refined representation of uncertainties compared to conventional models based on $(s,a)$-rectangularity and $d$-rectangularity, when prior knowledge about the mixture model is present. We propose a meta algorithm for robust policy learning in linear mixture DRMDPs with general $f$-divergence defined uncertainty sets, and analyze its sample complexities under three divergence metrics instantiations: total variation, Kullback-Leibler, and $\chi^2$ divergences. These results establish the statistical learnability of linear mixture DRMDPs, laying the theoretical foundation for future research on this new setting.

Direct preference optimization (DPO) methods have shown strong potential in aligning text-to-image diffusion models with human preferences by training on paired comparisons. These methods improve training stability by avoiding the REINFORCE algorithm but still struggle with challenges such as accurately estimating image probabilities due to the non-linear nature of the sigmoid function and the limited diversity of offline datasets. In this paper, we introduce Diffusion Denoising Ranking Optimization (Diffusion-DRO), a new preference learning framework grounded in inverse reinforcement learning. Diffusion-DRO removes the dependency on a reward model by casting preference learning as a ranking problem, thereby simplifying the training objective into a denoising formulation and overcoming the non-linear estimation issues found in prior methods. Moreover, Diffusion-DRO uniquely integrates offline expert demonstrations with online policy-generated negative samples, enabling it to effectively capture human preferences while addressing the limitations of offline data. Comprehensive experiments show that Diffusion-DRO delivers improved generation quality across a range of challenging and unseen prompts, outperforming state-of-the-art baselines in both both quantitative metrics and user studies. Our source code and pre-trained models are available at https://github.com/basiclab/DiffusionDRO.

Heterogeneous federated learning enables collaborative training across clients under dual heterogeneity of models and data, posing challenges for effective knowledge transfer. Federated mutual learning employs proxy models to bridge cross-model knowledge exchange; however, existing methods remain limited to direct alignment between the outputs of private and proxy models, ignoring the deep discrepancies in representation and decision spaces between them. Such cognitive biases cause knowledge to be transferred only at shallow levels and trigger performance bottlenecks. To address this, this paper proposes FedKWAZ to identify and exploit Knowledge Weak-Aware Zones (KWAZ)—spatial zones of deep knowledge misalignment between private and proxy models, further refined into Semantic Weak-Aware Zones and Decision Weak-Aware Zones, which characterize cognitive misalignments in representation and decision spaces as focal targets for enhanced bidirectional distillation. FedKWAZ designs a Hierarchical Adaptive Patch Mixing (HAPM) mechanism to generate multiple mixed samples and employs a Knowledge Discrepancy Perceptron (KDP) to select the samples exhibiting the largest representation and decision discrepancies, thereby mining critical KWAZ. These modules are integrated into a two-stage mutual learning framework, achieving global class-level representation-decision consistency alignment and local KWAZ-guided refinement, structurally bridging cognitive biases across heterogeneous mutual learning models. Experimental results on multiple datasets and model configurations demonstrate the superior performance of FedKWAZ.

We study the problem of differentially private continual counting in the unbounded setting where the input size $n$ is not known in advance. Current state-of-the-art algorithms based on optimal instantiations of the matrix mechanism cannot be directly applied here because their privacy guarantees only hold when key parameters are tuned to $n$. Using the common `doubling trick' avoids knowledge of $n$ but leads to suboptimal and non-smooth error. We solve this problem by introducing novel matrix factorizations based on logarithmic perturbations of the function $\frac{1}{\sqrt{1-z}}$ studied in prior works, which may be of independent interest. The resulting algorithm has smooth error, and for any $\alpha > 0$ and $t\leq n$ it is able to privately estimate the sum of the first $t$ data points with $O(\log^{2+2\alpha}(t))$ variance. It requires $O(t)$ space and amortized $O(\log t)$ time per round, compared to $O(\log(n)\log(t))$ variance, $O(n)$ space and $O(n \log n)$ pre-processing time for the nearly-optimal bounded-input algorithm of Henzinger et al. Empirically, we find that our algorithm's performance is also comparable to theirs in absolute terms: our variance is less than $1.5\times$ theirs for $t$ as large as $2^{24}$.

Top-$k$ decoding is a widely used method for sampling from LLMs: at each token, only the largest $k$ next-token-probabilities are kept, and the next token is sampled after re-normalizing them to sum to unity. Top-$k$ and other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-$k$ decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-$k$ decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We introduce *Bregman decoders* obtained by minimizing a separable Bregman divergence (for both the *primal* and *dual* cases) with a sparsity-inducing $\ell_0$-regularization; in particular, these decoders are *adaptive* in the sense that the sparsity parameter $k$ is chosen depending on the underlying token distribution. Despite the combinatorial nature of the sparse Bregman objective, we show how to optimize it efficiently for a large class of divergences. We prove that (i) the optimal decoding strategies are greedy, and further that (ii) the objective is discretely convex in $k$, such that the optimal $k$ can be identified in logarithmic time. We note that standard top-$k$ decoding arises as a special case for the KL divergence, and construct new decoding strategies with substantially different behaviors (e.g., non-linearly up-weighting larger probabilities after re-normalization).

Multi-modal Large Language Models (LLM) have advanced conversational abilities but struggle with providing live, interactive step-by-step guidance, a key capability for future AI assistants. Effective guidance requires not only delivering instructions but also detecting their successful execution, as well as identifying and alerting users to mistakes, all of which has to happen in real-time. This requires models that are not turn-based, but that can react asynchronously to a video stream, as well as video data showing users performing tasks including mistakes and their corrections. To this end, we introduce Qualcomm Interactive Cooking, a new benchmark and dataset built upon CaptainCook4D, which contains user mistakes during task execution. Our dataset and benchmark features densely annotated, timed instructions and feedback messages, specifically including mistake alerts precisely timestamped to their visual occurrence in the video. We evaluate state-of-the-art multi-modal LLMs on the Qualcomm Interactive Cooking benchmark and introduce LiveMamba, a streaming multi-modal LLM designed for interactive instructional guidance. This work provides the first dedicated benchmark and a strong baseline for developing and evaluating on live, situated coaching.

Imaging inverse problems aim to recover high-dimensional signals from undersampled, noisy measurements, a fundamentally ill-posed task with infinite solutions in the null-space of the sensing operator. To resolve this ambiguity, prior information is typically incorporated through handcrafted regularizers or learned models that constrain the solution space. However, these priors typically ignore the task-specific structure of that null-space. In this work, we propose Non-Linear Projections of the Null-Space (NPN), a novel class of regularization that, instead of enforcing structural constraints in the image domain, promotes solutions that lie in a low-dimensional projection of the sensing matrix's null-space with a neural network. Our approach has two key advantages: (1) Interpretability: by focusing on the structure of the null-space, we design sensing-matrix-specific priors that capture information orthogonal to the signal components that are fundamentally blind to the sensing process. (2) Flexibility: NPN is adaptable to various inverse problems, compatible with existing reconstruction frameworks, and complementary to conventional image-domain priors. We provide theoretical guarantees on convergence and reconstruction accuracy when used within plug-and-play methods. Empirical results across diverse sensing matrices demonstrate that NPN priors consistently enhance reconstruction fidelity in various imaging inverse problems, such as compressive sensing, deblurring, super-resolution, computed tomography, and magnetic resonance imaging, with plug-and-play methods, unrolling networks, deep image prior, and diffusion models.

Recent advancements in large multimodal models (LMMs) have significantly enhanced performance across diverse tasks, with ongoing efforts to further integrate additional modalities such as video and audio. However, most existing LMMs remain vulnerable to hallucinations, the discrepancy between the factual multimodal input and the generated textual output, which has limited their applicability in various real-world scenarios. This paper presents the first systematic investigation of hallucinations in LMMs involving the three most common modalities: language, visual, and audio. Our study reveals two key contributors to hallucinations: overreliance on unimodal priors and spurious inter-modality correlations. To address these challenges, we introduce the benchmark The Curse of Multi-Modalities (CMM), which comprehensively evaluates hallucinations in LMMs, providing a detailed analysis of their underlying issues. Our findings highlight key vulnerabilities, including imbalances in modality integration and biases from training data, underscoring the need for balanced cross-modal learning and enhanced hallucination mitigation strategies. Based on our observations and findings, we suggest potential research directions that could enhance the reliability of LMMs.

Conventional federated learning (FL) assumes a closed world with a fixed total number of clients. In contrast, new clients continuously join the FL process in real-world scenarios, introducing new knowledge. This raises two critical demands: detecting new knowledge, i.e., knowledge discovery, and integrating it into the global model, i.e., knowledge adaptation. Existing research focuses on coarse-grained knowledge discovery, and often sacrifices source domain performance and adaptation efficiency. To this end, we propose a fine-grained federated domain adaptation approach in open set (Gains). Gains splits the model into an encoder and a classifier, empirically revealing features extracted by the encoder are sensitive to domain shifts while classifier parameters are sensitive to class increments. Based on this, we develop fine-grained knowledge discovery and contribution-driven aggregation techniques to identify and incorporate new knowledge. Additionally, an anti-forgetting mechanism is designed to preserve source domain performance, ensuring balanced adaptation. Experimental results on multi-domain datasets across three typical data-shift scenarios demonstrate that Gains significantly outperforms other baselines in performance for both source-domain and target-domain clients. Code is available at: https://github.com/Zhong-Zhengyi/Gains.

Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory. It is known that physical phenomena based on these theories have an energy conservation law or a dissipation law. Therefore, in the simulations of such physical phenomena, numerical methods that preserve the energy-conservation or dissipation laws are desirable. However, because various energy-behavior-preserving numerical methods have been proposed, it is difficult to discover the best one. In this study, we propose a method for learning highly accurate energy-behavior-preserving integrators from data. Numerical results show that our approach certainly learns energy-behavior-preserving numerical methods that are more accurate than existing numerical methods for various differential equations, including chaotic Hamiltonian systems, dissipative systems, and a nonlinear partial differential equation. We also provide universal approximation theorems for the proposed approach.

The Unaligned Multi-view Clustering (UMC) aims to learn a discriminative cluster structure from unaligned multi-view data, where the features of samples are not completely aligned across multiple views. Most existing methods usually prioritize employing various alignment strategies to align sample representations across views and then conduct cross-view fusion on aligned representations for subsequent clustering. However, ***due to the heterogeneity of representations across different views, these alignment strategies often fail to achieve ideal view-alignment results, inevitably leading to unreliable alignment-based fusion.*** To address this issue, we propose an alignment-free consistency fusion framework named AF-UMC, which bypasses the traditional view-alignment operation and directly extracts consistent representations from each view to perform global cross-view consistency fusion. Specifically, we first construct a cross-view consistent basis space by a cross-view reconstruction loss and a designed Structural Clarity Regularization (SCR), where autoencoders extract consistent representations from each view through projecting view-specific data to the constructed basis space. Afterwards, these extracted representations are globally pulled together for further cross-view fusion according to a designed Instance Global Contrastive Fusion (IGCF). Compared with previous methods, AF-UMC directly extracts consistent representations from each view for global fusion instead of alignment for fusion, which significantly mitigates the degraded fusion performance caused by undesired view-alignment results while greatly reducing algorithm complexity and enhancing its efficiency. Extensive experiments on various datasets demonstrate that our AF-UMC exhibits superior performance against other state-of-the-art methods.

Heterogeneous Federated Learning (HtFL) enables collaborative learning across clients with diverse model architectures and non-IID data distributions, which are prevalent in real-world edge computing applications. Existing HtFL approaches typically employ proxy datasets to facilitate knowledge sharing or implement coarse-grained model-level knowledge transfer. However, such approaches not only elevate risks of user privacy leakage but also lead to the loss of fine-grained model-specific knowledge, ultimately creating barriers to effective knowledge sharing. To address these challenges, we propose FedFree, a novel data-free and model-free HtFL framework featuring two key innovations. First, FedFree introduces a reverse layer-wise knowledge transfer mechanism that aggregates heterogeneous client models into a global model solely using Gaussian-based pseudo data, eliminating reliance on proxy datasets. Second, it leverages Knowledge Gain Entropy (KGE) to guide targeted layer-wise knowledge alignment, ensuring that each client receives the most relevant global updates tailored to its specific architecture. We provide rigorous theoretical convergence guarantees for FedFree and conduct extensive experiments on CIFAR-10 and CIFAR-100. Results demonstrate that FedFree achieves substantial performance gains, with relative accuracy improving up to 46.3% over state-of-the-art baselines. The framework consistently excels under highly heterogeneous model/data distributions and in large scale settings.

Foundational world models must be both interactive and preserve spatialtemporal coherence to enable effective future planning with different action choices. However, present models for long video generation have limited inherent world modeling capabilities due to two main challenges: compounding errors and insufficient memory mechanisms. We enhance image-to-video models with interactive capabilities through additional action conditioning and autoregressive framework, and reveal that compounding error is inherently irreducible in autoregressive video generation, while insufficient memory mechanism leads to incoherence of world models. We propose video retrieval augmented generation (VRAG) with explicit global state conditioning, which significantly reduces long-term compounding errors and increases spatialtemporal consistency of video world models. In contrast, naive autoregressive generation with extended context windows and retrieval-augmented generation prove less effective for video generation, primarily due to the limited in-context learning capabilities of current video models. Our work illuminates the fundamental challenges in video world models and establishes a comprehensive benchmark for improving video generation models with internal world modeling capabilities.