With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more. Since all of these values require exponential time to compute exactly, research has focused on efficient approximation methods using two techniques: Monte Carlo sampling and linear regression formulations. In this work, we present a new way of combining both of these techniques. Our approach is more flexible than prior algorithms, allowing for linear regression to be replaced with any function family whose probabilistic values can be computed efficiently. This allows us to harness the accuracy of tree-based models like XGBoost, while still producing unbiased estimates. From experiments across eight datasets, we find that our methods give state-of-the-art performance for estimating probabilistic values. For Shapley values, the error of our methods can be 6.5 lower than Permutation SHAP (the most popular Monte Carlo method), 3.8 lower than Kernel SHAP (the most popular linear regression method), and 2.6 lower than Leverage SHAP (the prior stateof-the-art Shapley value estimator). For more general probabilistic values, we can obtain error 215 lower than the best estimator from prior work.

We provide novel information-theoretic generalization bounds for stochastic gradient Langevin dynamics (SGLD) under the assumptions of smoothness and dissipativity, which are widely used in sampling and non-convex optimization studies. Our bounds are time-independent and decay to zero as the sample size increases, regardless of the number of iterations and whether the step size is fixed. Unlike previous studies, we derive the generalization error bounds by focusing on the time evolution of the Kullback-Leibler divergence, which is related to the stability of datasets and is the upper bound of the mutual information between output parameters and an input dataset. Additionally, we establish the first information-theoretic generalization bound when the training and test loss are the same by showing that a loss function of SGLD is sub-exponential. This bound is also time-independent and removes the problematic step size dependence in existing work, leading to an improved excess risk bound by combining our analysis with the existing non-convex optimization error bounds.

Understanding the dynamics of optimization in deep learning is increasingly important as models scale. While stochastic gradient descent (SGD) and its variants reliably find solutions that generalize well, the mechanisms driving this generalization remain unclear. Notably, these algorithms often prefer flatter or simpler minima--particularly in overparameterized settings. Prior work has linked flatness to generalization, and methods like Sharpness-Aware Minimization (SAM) explicitly encourage flatness, but a unified theory connecting data structure, optimization dynamics, and the nature of learned solutions is still lacking. In this work, we develop a linear stability framework that analyzes the behavior of SGD, random perturbations, and SAM--particularly in two-layer ReLU networks. Central to our analysis is a coherence measure that quantifies how gradient curvature aligns across data points, revealing why certain minima are stable and favored during training.

Iterative imputation is a prevalent method for missing data imputation, where each feature is imputed iteratively by treating it as a target variable estimated from all other features. However, iterative imputation method suffers from two principal limitations: it imposes a single parametric model form to impute all features, neglecting the potential for optimal models to vary among features, which risks model misspecification; and it assumes every feature contains missing values, overlooking the potential presence of non-missing features, termed as oracle features, which are informative for imputation. To address these limitations, we propose kernel point imputation (KPI), a bi-level optimization framework for iterative missing data imputation. At the inner level, KPI adaptively learns the optimal model form for each feature within a reproducing kernel Hilbert space, addressing limitation . At the outer level, KPI utilizes oracle features as supervisory signals to iteratively refine the imputations, addressing limitation . Experiments demonstrate that KPI outperforms competitive imputation methods. Code is available at https://github.com/FMLYD/kpi.git.

Federated clustering (FC) aims to discover global cluster structures across decentralized clients without sharing raw data, making privacy preservation a fundamental requirement. There are two critical challenges: (1) privacy leakage during collaboration, and (2) robustness degradation due to aggregation of proxy information from non-independent and identically distributed (Non-IID) local data, leading to inaccurate or inconsistent global clustering. Existing solutions typically rely on model-specific local proxies, which are sensitive to data heterogeneity and inherit inductive biases from their centralized counterparts, thus limiting robustness and generality. We propose Omni Federated Clustering (OmniFC), a unified and modelagnostic framework. Leveraging Lagrange coded computing, our method enables clients to share only encoded data, allowing exact reconstruction of the global distance matrix--a fundamental representation of sample relationships--without leaking private information, even under client collusion. This construction is naturally resilient to Non-IID data distributions. This approach decouples FC from model-specific proxies, providing a unified extension mechanism applicable to diverse centralized clustering methods. Theoretical analysis confirms both reconstruction fidelity and privacy guarantees, while comprehensive experiments demonstrate OmniFC's superior robustness, effectiveness, and generality across various benchmarks compared to state-of-the-art methods.

Few-shot knowledge graph relational learning seeks to perform reasoning over relations given only a limited number of training examples. While existing approaches largely adopt a meta-learning framework for enabling fast adaptation to new relations, they suffer from two key pitfalls. First, they learn relation metaknowledge in isolation, failing to capture common relational patterns shared across tasks. Second, they struggle to effectively incorporate local, task-specific contexts crucial for rapid adaptation. To address these limitations, we propose MoEMeta, a novel meta-learning framework that disentangles globally shared knowledge from task-specific contexts to enable both effective model generalization and rapid adaptation. MoEMeta introduces two key innovations: (i) a mixture-of-experts (MoE) model that learns globally shared relational prototypes to enhance generalization, and (ii) a task-tailored adaptation mechanism that captures local contexts for fast task-specific adaptation.

The rapid advancement of generative AI enables highly realistic synthetic videos, posing significant challenges for content authentication and raising urgent concerns about misuse.

We study the dynamics of stochastic gradient descent (SGD) for a class of sequence models termed Sequence Single-Index (SSI) models, where the target depends on a single direction in input space applied to a sequence of tokens. This setting generalizes classical single-index models to the sequential domain, encompassing simplified one-layer attention architectures. We derive a closed-form expression for the population loss in terms of a pair of sufficient statistics capturing semantic and positional alignment, and characterize the induced high-dimensional SGD dynamics for these coordinates. Our analysis reveals two distinct training phases: escape from uninformative initialization and alignment with the target subspace, and demonstrates how the sequence length and positional encoding influence convergence speed and learning trajectories. These results provide a rigorous and interpretable foundation for understanding how sequential structure in data can be beneficial for learning with attention-based models. Stochastic Gradient Descent (SGD) is the core optimization tool driving modern machine learning. Recent years have seen substantial progress in understanding its dynamics, particularly in two-layer networks [Saad and Solla, 1995, Mei et al., 2018, Chizat and Bach, 2018, Rotskoff and VandenEijnden, 2022, Sirignano and Spiliopoulos, 2020, Arnaboldi et al., 2023a]. While global convergence is qualitatively well-understood when the network is wide enough, quantitative results are scarcer. A particularly fruitful body of recent theoretical work addressing this gap has focused on deriving precise convergence rates for particular model classes on synthetic data, such as high-dimensional Gaussian single and multi-index models [Ben Arous et al., 2021, Abbe et al., 2022, 2023].

The quality of foundation models depends heavily on their training data. Consequently, great efforts have been put into dataset curation. Yet most approaches rely on manual tuning of coarse-grained mixtures of large buckets of data, or filtering by hand-crafted heuristics. An approach that is ultimately more scalable (let alone more satisfying) is to learn which data is actually valuable for training. This type of meta-learning could allow more sophisticated, fine-grained, and effective curation. Our proposed DataRater is an instance of this idea. It estimates the value of training on any particular data point. This is done by meta-learning using'meta-gradients', with the objective of improving training efficiency on held out data. In extensive experiments across a range of model scales and datasets, we find that using our DataRater to filter data is highly effective, resulting in significantly improved compute efficiency.

In this paper, we consider the general stochastic non-convex optimization problem when the sampling process follows a Markov chain. This problem exhibits its significance in capturing many real-world applications, ranging from asynchronous distributed learning to reinforcement learning. In particular, we consider the worst case where one has no prior knowledge and control of the Markov chain, meaning multiple trajectories cannot be simulated but only a single trajectory is available for algorithm design. We first provide algorithm-independent lower bounds with Ω(ϵ 3) (and Ω(ϵ 4)) samples, when objectives are (mean-squared) smooth, for any first-order methods accessing bounded variance gradient oracles to achieve ϵ-approximate critical solutions of original problems. Then, we propose MarkovChain SPIDER (MaC-SPIDER), which leverages variance-reduced techniques, to achieve a O(ϵ 3) upper bound for mean-squared smooth objective functions. To the best of our knowledge, MaC-SPIDER is the first to achieve O(ϵ 3)complexity when sampling from a single Markovian trajectory. And our proposed lower bound concludes its (near) optimality.