NeurIPS 2025 论文列表

This paper introduces a novel kernel-based formulation of the Equalized Odds (EO) criterion, denoted as $\operatorname{EO}_k$, for fair representation learning (FRL) in supervised settings. The central goal of FRL is to mitigate discrimination regarding a sensitive attribute $S$ while preserving prediction accuracy for the target variable $Y$. Our proposed criterion enables a rigorous and interpretable quantification of three core fairness objectives: independence ($\widehat{Y} \perp S$), separation—also known as equalized odds ($\widehat{Y} \perp S \mid Y$), and calibration ($Y \perp S \mid \widehat{Y}$). Under both unbiased ($Y \perp S$) and biased ($Y \not \perp S$) conditions, we show that $\operatorname{EO}_k$ satisfies both independence and separation in the former, and uniquely preserves predictive accuracy while lower bounding independence and calibration in the latter, thereby offering a unified analytical characterization of the tradeoffs among these fairness criteria. We further define the empirical counterpart, $\widehat{\operatorname{EO}}_k$, a kernel-based statistic that can be computed in quadratic time, with linear-time approximations also available. A concentration inequality for $\widehat{\operatorname{EO}}_k$ is derived, providing performance guarantees and error bounds, which serve as practical certificates of fairness compliance. While our focus is on theoretical development, the results lay essential groundwork for principled and provably fair algorithmic design in future empirical studies.

We study the online multi-class selection problem with group fairness guarantees, where limited resources must be allocated to sequentially arriving agents. Our work addresses two key limitations in the existing literature. First, we introduce a novel lossless rounding scheme that ensures the integral algorithm achieves the same expected performance as any fractional solution. Second, we explicitly address the challenges introduced by agents who belong to multiple classes. To this end, we develop a randomized algorithm based on a relax-and-round framework. The algorithm first computes a fractional solution using a resource reservation approach---referred to as the *set-aside* mechanism---to enforce fairness across classes. The subsequent rounding step preserves these fairness guarantees without degrading performance. Additionally, we propose a learning-augmented variant that incorporates untrusted machine-learned predictions to better balance fairness and efficiency in practical settings.

Despite growing empirical evidence of bias amplification in machine learning, its theoretical foundations remain poorly understood. We develop a formal framework for majority-minority learning tasks, showing how standard training can favor majority groups and produce stereotypical predictors that neglect minority-specific features. Assuming population and variance imbalance, our analysis reveals three key findings: (i) the close proximity between "full-data" and stereotypical predictors, (ii) the dominance of a region where training the entire model tends to merely learn the majority traits, and (iii) a lower bound on the additional training required. Our results are illustrated through experiments in deep learning for tabular and image classification tasks.

Recent works have studied fair resource allocation in social settings, where fairness is judged by the impact of allocation decisions rather than more traditional minimum or maximum thresholds on the allocations themselves. Our work significantly adds to this literature by developing continuous resource allocation strategies that adhere to *equality of impact*, a generalization of equality of opportunity. We derive methods to maximize total welfare across groups subject to minimal violation of equality of impact, in settings where the outcomes of allocations are unknown but have a diminishing marginal effect. While focused on a two-group setting, our study addresses a broader class of welfare dynamics than explored in prior work. Our contributions are threefold. First, we introduce *Equality of Impact (EoI)*, a fairness criterion defined via group-level impact functions. Second, we design an online algorithm for non-noisy settings that leverages the problem’s geometric structure and achieves constant cumulative fairness regret. Third, we extend this approach to noisy environments with a meta-algorithm and empirically demonstrate that our methods find fair allocations and perform competitively relative to representative baselines.

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiDiff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations. Our code is available at https://github.com/rees-c/sgequidiff.

Widely adopted evaluation metrics for sparse-view CT reconstruction, such as Structural Similarity Index Measure and Peak Signal-to-Noise Ratio, prioritize pixel-wise fidelity but often fail to capture the completeness of critical anatomical structures, particularly small or thin regions that are easily missed. To address this limitation, we propose a suite of novel anatomy-aware evaluation metrics designed to assess structural completeness across anatomical structures, including large organs, small organs, intestines, and vessels. Building on these metrics, we introduce CARE, a Completeness-Aware Reconstruction Enhancement framework that incorporates structural penalties during training to encourage anatomical preservation of significant structures. CARE is model-agnostic and can be seamlessly integrated into analytical, implicit, and generative methods. When applied to these methods, CARE substantially improves structural completeness in CT reconstructions, achieving up to **32%** improvement for large organs, **22%** for small organs, **40%** for intestines, and **36%** for vessels.

Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty---due to incomplete knowledge---requires richer representations than those offered by classical probability. Imprecise probability (IP) theory offers such models, capturing ambiguity and partial belief. This has driven growing interest in imprecise probabilistic machine learning (IPML), where inference and decision-making rely on broader uncertainty models---highlighting the need for metrics beyond classical probability. This work introduces the Integral Imprecise Probability Metric (IIPM) framework, a Choquet integral-based generalisation of classical Integral Probability Metric to the setting of capacities---a broad class of IP models encompassing many existing ones, including lower probabilities, probability intervals, belief functions, and more. Theoretically, we establish conditions under which IIPM serves as a valid metric and metrises a form of weak convergence of capacities. Practically, IIPM not only enables comparison across different IP models but also supports the quantification of epistemic uncertainty~(EU) within a single IP model. In particular, by comparing an IP model with its conjugate, IIPM gives rise to a new class of epistemic uncertainty measures---Maximum Mean Imprecision (MMI) ---which satisfy key axiomatic properties proposed in the Uncertainty Quantification literature. We validate MMI through selective classification experiments, demonstrating strong empirical performance against established EU measures, and outperforming them when classical methods struggle to scale to a large number of classes. Our work advances both theory and practice in Imprecise Probabilistic Machine Learning, offering a principled framework for comparing and quantifying epistemic uncertainty under imprecision.

Measuring similarity between training examples is critical for curating high-quality and diverse pretraining datasets for language models. However, similarity is typically computed with a generic off-the-shelf embedding model that has been trained for tasks such as retrieval. Whether these embedding-based similarity metrics are well-suited for pretraining data selection remains largely unexplored. In this paper, we propose a new framework to assess the suitability of a similarity metric specifically for data curation in language model pretraining applications. Our framework's first evaluation criterion captures how well distances reflect generalization in pretraining loss between different training examples. Next, we use each embedding model to guide a standard diversity-based data curation algorithm and measure its utility by pretraining a language model on the selected data and evaluating downstream task performance. Finally, we evaluate the capabilities of embeddings to distinguish between examples from different data sources. With these evaluations, we demonstrate that standard off-the-shelf embedding models are not well-suited for the pretraining data curation setting, underperforming even remarkably simple embeddings that are extracted from models trained on the same pretraining corpus. Our experiments are performed on the Pile, for pretraining a 1.7B parameter language model on 200B tokens. We believe our analysis and evaluation framework serves as a foundation for the future design of embeddings that specifically reason about similarity in pretraining datasets.

Robust unlearning is crucial for safely deploying large language models (LLMs) in environments where data privacy, model safety, and regulatory compliance must be ensured. Yet the task is inherently challenging, partly due to difficulties in reliably measuring whether unlearning has truly occurred. Moreover, fragmentation in current methodologies and inconsistent evaluation metrics hinder comparative analysis and reproducibility. To unify and accelerate research efforts, we introduce OpenUnlearning, a standardized and extensible framework designed explicitly for benchmarking both LLM unlearning methods and metrics. OpenUnlearning integrates 13 state-of-the-art unlearning algorithms and 16 diverse evaluations across 3 leading benchmarks (TOFU, MUSE, and WMDP) and also enables analyses of forgetting behaviors across 450+ publicly released checkpoints. Leveraging OpenUnlearning, we propose a novel meta-evaluation benchmark focused specifically on assessing the faithfulness and robustness of evaluation metrics themselves. We also benchmark diverse unlearning methods and provide a comparative analysis against an extensive evaluation suite. Overall, we establish a clear, community-driven pathway toward rigorous development in LLM unlearning research.

We investigate the problem of sequentially selecting elements of an unknown matroid in an online manner to form an independent set, with the goal of maximizing the minimum probability of acceptance across all elements, a property we define as $f$-fairness. Under adversarial arrival orders, we design an $\alpha(\ln(k)+1)$-fair algorithm, where $\alpha$ is the arboricity of the matroid and $k$ is the rank, a result that is nearly optimal. For laminar matroids, we develop an $(2\alpha-1)$-fair algorithm, which is optimal up to constant factors, achieved through a novel online coloring scheme. In the random arrival order setting, we achieve a $(4+o(1))\alpha$-fair algorithm for graphic matroids, matching the optimal result up to constant factors, relying on a novel technique for learning a degeneracy ordering using a sampled subset of edges. We further generalize our result to $p$-matchoids, obtaining a $\beta(p\ln k+1)$-fair algorithm for the adversarial arrival model, where $\beta$ is the optimal offline fairness. Notably, all our results can be extended to a setting with no prior knowledge of the matroid with only a logarithmic increase in the fairness factor.

What is the shortest path between two data points lying in a high-dimensional space? While the answer is trivial in Euclidean geometry, it becomes significantly more complex when the data lies on a curved manifold—requiring a Riemannian metric to describe the space's local curvature. Estimating such a metric, however, remains a major challenge in high dimensions. In this work, we propose a method for deriving Riemannian metrics directly from pretrained Energy-Based Models (EBMs)—a class of generative models that assign low energy to high-density regions. These metrics define spatially varying distances, enabling the computation of geodesics—shortest paths that follow the data manifold’s intrinsic geometry. We introduce two novel metrics derived from EBMs and show that they produce geodesics that remain closer to the data manifold and exhibit lower curvature distortion, as measured by alignment with ground-truth trajectories. We evaluate our approach on increasingly complex datasets: synthetic datasets with known data density, rotated character images with interpretable geometry, and high-resolution natural images embedded in a pretrained VAE latent space. Our results show that EBM-derived metrics consistently outperform established baselines, especially in high-dimensional settings. Our work is the first to derive Riemannian metrics from EBMs, enabling data-aware geodesics and unlocking scalable, geometry-driven learning for generative modeling and simulation.

With emerging application of Federated Learning (FL) in decision-making scenarios, it is imperative to regulate model fairness to prevent disparities across sensitive groups (e.g., female, male). Current research predominantly focuses on two concepts of group fairness within FL: *Global Fairness* (overall model disparity across all clients) and *Local Fairness* (the disparity within each client). However, the non-decomposable, non-differentiable nature of fairness criteria pose two fundamental, unresolved challenges for fair FL: (i) *Harmonizing global and local fairness, especially in multi-class classification*; (ii) *Enabling a controllable, optimal accuracy-fairness trade-off*. To tackle the aforementioned challenges, we propose a novel controllable federated group-fairness calibration framework, named FedFACT. FedFACT identifies the Bayes-optimal classifiers under both global and local fairness constraints in multi-class case, yielding models with minimal performance decline while guaranteeing fairness. To effectively realize an adjustable, optimal accuracy-fairness balance, we derive specific characterizations of the Bayes-optimal fair classifiers for reformulating fair FL as personalized cost-sensitive learning problem for in-processing, and bi-level optimization for post-processing. Theoretically, we provide convergence and generalization guarantees for FedFACT to approach the near-optimal accuracy under given fairness levels. Extensive experiments on multiple datasets across various data heterogeneity demonstrate that FedFACT consistently outperforms baselines in balancing accuracy and global-local fairness.