NeurIPS 2025 Papers

Temporal graph link prediction aims to predict future interactions between nodes in a graph based on their historical interactions, which are encoded in node embeddings. We observe that heterogeneity naturally appears in temporal interactions, e.g., a few node pairs can make most interaction events, and interaction events happen at varying intervals. This leads to the problems of ineffective temporal information encoding and forgetting of past interactions for a pair of nodes that interact intermittently for their link prediction. Existing methods, however, do not consider such heterogeneity in their learning process, and thus their learned temporal node embeddings are less effective, especially when predicting the links for infrequently interacting node pairs. To cope with the heterogeneity, we propose a novel framework called TAMI, which contains two effective components, namely log time encoding function (LTE) and link history aggregation (LHA). LTE better encodes the temporal information through transforming interaction intervals into more balanced ones, and LHA prevents the historical interactions for each target node pair from being forgotten. State-of-the-art temporal graph neural networks can be seamlessly and readily integrated into TAMI to improve their effectiveness. Experiment results on 13 classic datasets and three newest temporal graph benchmark (TGB) datasets show that TAMI consistently improves the link prediction performance of the underlying models in both transductive and inductive settings. Our code is available at https://github.com/Alleinx/TAMI_temporal_graph.

Directly generating 3D meshes, the default representation for 3D shapes in the graphics industry, using auto-regressive (AR) models has become popular these days, thanks to their sharpness, compactness in the generated results, and ability to represent various types of surfaces. However, AR mesh generative models typically construct meshes face by face in lexicographic order, which does not effectively capture the underlying geometry in a manner consistent with human perception. Inspired by 2D models that progressively refine images, such as the prevailing next-scale prediction AR models, we propose generating meshes auto-regressively in a progressive coarse-to-fine manner. Specifically, we view mesh simplification algorithms, which gradually merge mesh faces to build simpler meshes, as a natural fine-to-coarse process. Therefore, we generalize meshes to simplicial complexes and develop a transformer-based AR model to approximate the reverse process of simplification in the order of level of detail, constructing meshes initially from a single point and gradually adding geometric details through local remeshing, where the topology is not predefined and is alterable. Our experiments show that this novel progressive mesh generation approach not only provides intuitive control over generation quality and time consumption by early stopping the auto-regressive process but also enables applications such as mesh refinement and editing.

Mixed-Integer Linear Programming (MILP) is a fundamental and powerful framework for modeling complex optimization problems across diverse domains. Recently, learning-based methods have shown great promise in accelerating MILP solvers by predicting high-quality solutions. However, most existing approaches are developed and evaluated in single-domain settings, limiting their ability to generalize to unseen problem distributions. This limitation poses a major obstacle to building scalable and general-purpose learning-augmented solvers. To address this challenge, we introduce RoME, a domain-Robust Mixture-of-Experts (MoE) framework for predicting MILP solutions across domains. RoME dynamically routes problem instances to specialized experts based on learned task embeddings. The model is trained using a two-level distributionally robust optimization strategy: inter-domain to mitigate global shifts across domains, and intra-domain to enhance local robustness by introducing perturbations on task embeddings. We reveal that cross-domain training not only enhances the model's generalization capability to unseen domains but also improves performancewithin each individual domain by encouraging the model to capture more general intrinsic combinatorial patterns. Specifically, a single RoME model trained on three domains achieves an average improvement of $67.7\%$ then evaluated on five diverse domains. We further test the pretrained model on MIPLIB in a zero-shot setting, demonstrating its ability to deliver measurable performance gains on challenging real-world instances where existing learning-based approaches often struggle to generalize.

Predicting protein function from sequence is a central challenge in computational biology. While existing methods rely heavily on structured ontologies or similarity-based techniques, they often lack the flexibility to express structure-free functional descriptions and novel biological functions. In this work, we introduce Prot2Text-V2, a novel multimodal sequence-to-text model that generates free-form natural language descriptions of protein function directly from amino acid sequences. Our method combines a protein language model as a sequence encoder (ESM-3B) and a decoder-only language model (LLaMA-3.1-8B-Instruct) through a lightweight nonlinear modality projector. A key innovation is our Hybrid Sequence-level Contrastive Alignment Learning (H-SCALE), which improves cross-modal learning by matching mean- and std-pooled protein embeddings with text representations via contrastive loss. After the alignment phase, we apply instruction-based fine-tuning using LoRA on the decoder to teach the model how to generate accurate protein function descriptions conditioned on the protein sequence. We train Prot2Text-V2 on about 250K curated entries from SwissProt and evaluate it under low-homology conditions, where test sequences have low similarity with training samples. Prot2Text-V2 consistently outperforms traditional and LLM-based baselines across various metrics.

Performativity of predictions refers to the phenomenon where prediction-informed decisions influence the very targets they aim to predict—a dynamic commonly observed in policy-making, social sciences, and economics. In this paper, we initiate an end-to-end framework of statistical inference under performativity. Our contributions are twofold. First, we establish a central limit theorem for estimation and inference in the performative setting, enabling standard inferential tasks such as constructing confidence intervals and conducting hypothesis tests in policy-making contexts. Second, we leverage this central limit theorem to study prediction-powered inference (PPI) under performativity. This approach yields more precise estimates and tighter confidence regions for the model parameters (i.e., policies) of interest in performative prediction. We validate the effectiveness of our framework through numerical experiments. To the best of our knowledge, this is the first work to establish a complete statistical inference under performativity, introducing new challenges and inference settings that we believe will provide substantial value to policy-making, statistics, and machine learning.

Understanding how the test risk scales with model complexity is a central question in machine learning. Classical theory is challenged by the learning curves observed for large over-parametrized deep networks. Capacity measures based on parameter count typically fail to account for these empirical observations. To tackle this challenge, we consider norm-based capacity measures and develop our study for random features based estimators, widely used as simplified theoretical models for more complex networks. In this context, we provide a precise characterization of how the estimator’s norm concentrates and how it governs the associated test error. Our results show that the predicted learning curve admits a phase transition from under- to over-parameterization, but no double descent behavior. This confirms that more classical U-shaped behavior is recovered considering appropriate capacity measures based on models norms rather than size. From a technical point of view, we leverage deterministic equivalence as the key tool and further develop new deterministic quantities which are of independent interest.

Graph Neural Networks (GNNs) achieve strong performance in node classification tasks but exhibit substantial performance degradation under label noise. Despite recent advances in noise-robust learning, a principled approach that exploits the node-neighbor interdependencies inherent in graph data for label noise detection remains underexplored. To address this gap, we propose GD$^2$, a noise-aware \underline{G}raph learning framework that detects label noise by leveraging \underline{D}ual-view prediction \underline{D}iscrepancies. The framework contrasts the \textit{ego-view}, constructed from node-specific features, with the \textit{structure-view}, derived through the aggregation of neighboring representations. The resulting discrepancy captures disruptions in semantic coherence between individual node representations and the structural context, enabling effective identification of mislabeled nodes. Building upon this insight, we further introduce a view-specific training strategy that enhances noise detection by amplifying prediction divergence through differentiated view-specific supervision. Extensive experiments on multiple datasets and noise settings demonstrate that \name~achieves superior performance over state-of-the-art baselines.

It has been shown that the chain of thought (CoT) can enhance the power of LLMs to simulate a Turing machine or an algorithm, and in particular its mathematical reasoning ability. The memorization capability of LLMs is an important aspect of their expressive ability, which offers valuable insight into designing models with enhanced generalization potential. Currently, the optimal memorization capacities of transformers have been established for both the general dataset and the dataset that satisfies a specific separability condition. However, the question of whether the CoT can improve the memorization capability of LLMs remains unexamined. To fill this gap, we establish the memorization capability for fixed-precision autoregressive transformers with or without CoT. Precisely, we first give the necessary and sufficient conditions for transformers to memorize a finite language and then provide the upper and lower bounds for the number of parameters of the memorization transformers. Our result indicates that the classes of languages that can be memorized by transformers with or without CoT do not contain each other, and the same number of parameters is needed for transformers with or without CoT to memorize, implying that CoT does not enhance a transformer’s memorization power significantly. We further show that CoT can not help transformers to memory certain infinite languages.

Distribution-free uncertainty estimation for ensemble methods is increasingly desirable due to the widening deployment of multi-modal black-box predictive models. Conformal prediction is one approach that avoids such distributional assumptions. Methods for conformal aggregation have in turn been proposed for ensembled prediction, where the prediction regions of individual models are merged as to retain coverage guarantees while minimizing conservatism. Merging the prediction regions directly, however, sacrifices structures present in the conformal scores that can further reduce conservatism. We, therefore, propose a novel framework that extends the standard scalar formulation of a score function to a multivariate score that produces more efficient prediction regions. We then demonstrate that such a framework can be efficiently leveraged in both classification and predict-then-optimize regression settings downstream and empirically show the advantage over alternate conformal aggregation methods.

We study the problem of preconditioning in the setting of sequential prediction. From the theoretical lens of linear dynamical systems, we show that applying a convolution to the input sequence translates to applying a polynomial to the unknown transition matrix in the hidden space. With this insight, we develop a novel preconditioning method that convolves the input sequence with the coefficients of the Chebyshev or Legendre polynomials. We formally prove that this improves the regret of a wide family of prediction methods. We proceed to apply this preconditioning technique to the method of spectral filtering. This gives the first sublinear regret bound that is also hidden-dimension free (up to logarithmic factors) even when the hidden transition matrix is asymmetric. From rigorous experiments on synthetic data we show that our simple preconditioning method generalizes to both 1) settings where the data is \emph{not} from a linear dynamical system and 2) a broad range of learning algorithms, including recurrent neural networks.

Sharpness‐aware minimization (SAM) has emerged as a highly effective technique for improving model generalization, but its underlying principles are not fully understood. We investigated the phenomenon known as m-sharpness, where the performance of SAM improves monotonically as the micro-batch size for computing perturbations decreases. In practice, the empirical m-sharpness effect underpins the deployment of SAM in distributed training, yet a rigorous theoretical account has remained lacking. To provide a theoretical explanation for m-sharpness, we leverage an extended Stochastic Differential Equation (SDE) framework and analyze the structure of stochastic gradient noise (SGN) to characterize the dynamics of various SAM variants, including n-SAM and m-SAM. Our findings reveal that the stochastic noise introduced during SAM perturbations inherently induces a variance-based sharpness regularization effect. Motivated by our theoretical insights, we introduce Reweighted SAM (RW-SAM), which employs sharpness-weighted sampling to mimic the generalization benefits of m-SAM while remaining parallelizable. Comprehensive experiments validate the effectiveness of our theoretical analysis and proposed method.

Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction based on the statistical notion of relative likelihood: The target of prediction is the set of all (conditional) probability distributions produced by the collection of plausible models, namely those models whose relative likelihood exceeds a specified threshold. This threshold has an intuitive interpretation and allows for controlling the trade-off between correctness and precision of credal predictions. We tackle the problem of approximating credal sets defined in this way by means of suitably modified ensemble learning techniques. To validate our approach, we illustrate its effectiveness by experiments on benchmark datasets demonstrating superior uncertainty representation without compromising predictive performance. We also compare our method against several state-of-the-art baselines in credal prediction.

When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning creates a feedback loop that shapes both the model and the population of its users. In this work, we introduce evolutionary prediction games, a framework grounded in evolutionary game theory which models such feedback loops as natural-selection processes among groups of users. Our theoretical analysis reveals a gap between idealized and real-world learning settings: In idealized settings with unlimited data and computational power, repeated learning creates competition and promotes competitive exclusion across a broad class of behavioral dynamics. However, under realistic constraints such as finite data, limited compute, or risk of overfitting, we show that stable coexistence and mutualistic symbiosis between groups becomes possible. We analyze these possibilities in terms of their stability and feasibility, present mechanisms that can sustain their existence, and empirically demonstrate our findings.

Vertical Federated Learning (VFL) enables participants to collaboratively train models on aligned samples while keeping their heterogeneous features private and distributed. Despite their utility, VFL models remain vulnerable to adversarial attacks during inference. Adversarial Training (AT), which generates adversarial examples at each training iteration, stands as the most effective defense for improving model robustness. However, applying AT in VFL settings (VFAL) faces significant computational efficiency challenges, as the distributed training framework necessitates iterative propagations across participants. To this end, we propose **_DecVFAL_** framework, which substantially accelerates **_VFAL_** training through a dual-level ***Dec***oupling mechanism applied during adversarial sample generation. Specifically, we first decouple the bottom modules of clients (directly responsible for adversarial updates) from the remaining networks, enabling efficient _lazy sequential propagations_ that reduce communication frequency through delayed gradients. We further introduce _decoupled parallel backpropagation_ to accelerate delayed gradient computation by eliminating idle waiting through parallel processing across modules. Additionally, we are the first to establish convergence analysis for VFAL, rigorously characterizing how our decoupling mechanism interacts with existing VFL dynamics, and prove that _DecVFAL_ achieves an $\mathcal{O}(1/\sqrt{K})$ convergence rate matching that of standard VFLs. Experimental results show that _DecVFAL_ ensures competitive robustness while significantly achieving about $3\sim10\times$ speed up.

In this paper, we unify more than 10 existing one-step diffusion distillation approaches, such as Diff-Instruct, DMD, SIM, SiD, $f$-distill, etc, inside a theory-driven framework which we name the \textbf{\emph{Uni-Instruct}}. Uni-Instruct is motivated by our proposed diffusion expansion theory of the $f$-divergence family. Then we introduce key theories that overcome the intractability issue of the original expanded $f$-divergence, resulting in an equivalent yet tractable loss that effectively trains one-step diffusion models by minimizing the expanded $f$-divergence family. The novel unification introduced by Uni-Instruct not only offers new theoretical contributions that help understand existing approaches from a high-level perspective but also leads to state-of-the-art one-step diffusion generation performances. On the CIFAR10 generation benchmark, Uni-Instruct achieves record-breaking Frechet Inception Distance (FID) values of \textbf{\emph{1.46}} for unconditional generation and \textbf{\emph{1.38}} for conditional generation. On the ImageNet-$64\times 64$ generation benchmark, Uni-Instruct achieves a new SoTA one-step diffusion FID value of \textbf{\emph{1.06}}, which outperforms its 79-step teacher diffusion with a significant improvement margin of 1.29 (1.06 vs 2.35). We also apply Uni-Instruct on broader tasks like text-to-3D generation. For text-to-3D generation, Uni-Instruct gives decent results, which slightly outperforms previous methods, such as SDS and VSD, in terms of both generation quality and diversity. Both the solid theoretical and empirical contributions of Uni-Instruct will potentially help future studies on one-step diffusion distillation and knowledge transferring of diffusion models.

We propose a unified framework for adaptive routing in multitask, multimodal prediction settings where data heterogeneity and task interactions vary across samples. We introduce a routing-based architecture that dynamically selects modality processing pathways and task-sharing strategies on a per-sample basis. Our model defines multiple modality paths, including raw and fused representations of text and numeric features, and learns to route each input through the most informative modality-task expert combination. Task-specific predictions are produced by shared or independent heads depending on the routing decision, and the entire system is trained end-to-end. We evaluate the model on both synthetic data and real-world psychotherapy notes, predicting depression and anxiety outcomes. Our experiments show that our method consistently outperforms fixed multitask or single-task baselines, and that the learned routing policy provides interpretable insights into modality relevance and task structure. This addresses critical challenges in personalized healthcare by providing per-subject adaptive information processing that accounts for data and task correlation heterogeneity.

Selective classifiers improve model reliability by abstaining on inputs the model deems uncertain. However, few practical approaches achieve the gold-standard performance of a perfect-ordering oracle that accepts examples exactly in order of correctness. Our work formalizes this shortfall as the selective-classification gap and present the first finite-sample decomposition of this gap to five distinct sources of looseness: Bayes noise, approximation error, ranking error, statistical noise, and implementation- or shift-induced slack. Our analysis reveals that monotone post-hoc calibration—often believed to strengthen selective classifiers—has limited impact on closing this gap, since it rarely alters the model’s underlying score ranking. Bridging the gap therefore requires scoring mechanisms that can effectively reorder predictions rather than merely rescale them. We validate our decomposition on synthetic two-moons data and on real-world vision and language benchmarks, isolating each error component through controlled experiments. Our results show that (i) Bayes noise and limited model capacity can account for substantial gaps, (ii) only non-monotone or feature-aware calibrators consistently reduce the ranking term, and (iii) distribution shift introduces a separate slack that demands distributionally robust training. Together, our decomposition yields a quantitative error budget as well as actionable design guidelines that practitioners can use to build selective classifiers which approximate ideal oracle behavior more closely.

Metal-Organic Frameworks (MOFs) have attracted considerable attention due to their unique properties including high surface area and tunable porosity, and promising applications in catalysis, gas storage, and drug delivery. Structure prediction for MOFs is a challenging task, as these frameworks are intrinsically periodic and hierarchically organized, where the entire structure is assembled from building blocks like metal nodes and organic linkers. To address this, we introduce MOF-BFN, a novel generative model for MOF structure prediction based on Bayesian Flow Networks (BFNs). Given the local geometry of building blocks, MOF-BFN jointly predicts the lattice parameters, as well as the positions and orientations of all building blocks within the unit cell. In particular, the positions are modelled in the fractional coordinate system to naturally incorporate the periodicity. Meanwhile, the orientations are modeled as unit quaternions sampled from learned Bingham distributions via the proposed Bingham BFN, enabling effective orientation generation on the 4D unit hypersphere. Experimental results demonstrate that MOF-BFN achieves state-of-the-art performance across multiple tasks, including structure prediction, geometric property evaluation, and de novo generation, offering a promising tool for designing complex MOF materials.

Prediction-Powered Inference (PPI) is a recently proposed statistical inference technique for parameter estimation that leverages pseudo-labels on both labeled and unlabeled data to construct an unbiased, low-variance estimator. In this work, we extend its core idea to semi-supervised learning (SSL) for model training, introducing a novel unbiased gradient estimator. This extension addresses a key challenge in SSL: while unlabeled data can improve model performance, its benefit heavily depends on the quality of pseudo-labels. Inaccurate pseudo-labels can introduce bias, leading to suboptimal models. To balance the contributions of labeled and pseudo-labeled data, we utilize an interpolation parameter and tune it on the fly, alongside the model parameters, using a one-dimensional online learning algorithm. We verify the practical advantage of our approach through experiments on both synthetic and real datasets, demonstrating improved performance over classic SSL baselines and PPI methods that tune the interpolation parameter offline.