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We study the Out-of-Distribution (OOD) generalization in machine learning and propose a general framework that establishes information-theoretic generalization bounds. Our framework interpolates freely between Integral Probability Metric (IPM) and $f$-divergence, which naturally recovers some known results (including Wasserstein- and KL-bounds), as well as yields new generalization bounds. Additionally, we show that our framework admits an optimal transport interpretation. When evaluated in two concrete examples, the proposed bounds either strictly improve upon existing bounds in some cases or match the best existing OOD generalization bounds. Moreover, by focusing on $f$-divergence and combining it with the Conditional Mutual Information (CMI) methods, we derive a family of CMI-based generalization bounds, which include the state-of-the-art ICIMI bound as a special instance. Finally, leveraging these findings, we analyze the generalization of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm, showing that our derived generalization bounds outperform existing information-theoretic generalization bounds in certain scenarios.

Dataset distillation offers an efficient way to reduce memory and computational costs by optimizing a smaller dataset with performance comparable to the full-scale original. However, for large datasets and complex deep networks (e.g., ImageNet-1K with ResNet-101), the extensive optimization space limits performance, reducing its practicality. Recent approaches employ pre-trained diffusion models to generate informative images directly, avoiding pixel-level optimization and achieving notable results. However, these methods often face challenges due to distribution shifts between pre-trained models and target datasets, along with the need for multiple distillation steps across varying settings. To address these issues, we propose a novel framework orthogonal to existing diffusion-based distillation methods, leveraging diffusion models for selection rather than generation. Our method starts by predicting noise generated by the diffusion model based on input images and text prompts (with or without label text), then calculates the corresponding loss for each pair. With the loss differences, we identify distinctive regions of the original images. Additionally, we perform intra-class clustering and ranking on selected patches to maintain diversity constraints. This streamlined framework enables a single-step distillation process, and extensive experiments demonstrate that our approach outperforms state-of-the-art methods across various metrics.

This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the precision and the observations, we show that the sample complexity scales poly-logarithmically with the size of the precision matrix and its Cholesky factor. The key challenge in these estimation tasks is the polynomial growth of the condition number of the target matrices with their size. For precision estimation, our theory hinges on an intuitive local regression technique on the lattice graph which exploits the approximate sparsity implied by the screening effect. For Cholesky factor estimation, we leverage a block-Cholesky decomposition recently used to establish complexity bounds for sparse Cholesky factorization.

In the field of machine unlearning, certified unlearning has been extensively studied in convex machine learning models due to its high efficiency and strong theoretical guarantees. However, its application to deep neural networks (DNNs), known for their highly nonconvex nature, still poses challenges. To bridge the gap between certified unlearning and DNNs, we propose several simple techniques to extend certified unlearning methods to nonconvex objectives. To reduce the time complexity, we develop an efficient computation method by inverse Hessian approximation without compromising certification guarantees. In addition, we extend our discussion of certification to nonconvergence training and sequential unlearning, considering that real-world users can send unlearning requests at different time points. Extensive experiments on three real-world datasets demonstrate the efficacy of our method and the advantages of certified unlearning in DNNs.

In safe offline reinforcement learning (RL), the objective is to develop a policy that maximizes cumulative rewards while strictly adhering to safety constraints, utilizing only offline data. Traditional methods often face difficulties in balancing these constraints, leading to either diminished performance or increased safety risks. We address these issues with a novel approach that begins by learning a conservatively safe policy through the use of Conditional Variational Autoencoders, which model the latent safety constraints. Subsequently, we frame this as a Constrained Reward-Return Maximization problem, wherein the policy aims to optimize rewards while complying with the inferred latent safety constraints. This is achieved by training an encoder with a reward-Advantage Weighted Regression objective within the latent constraint space. Our methodology is supported by theoretical analysis, including bounds on policy performance and sample complexity. Extensive empirical evaluation on benchmark datasets, including challenging autonomous driving scenarios, demonstrates that our approach not only maintains safety compliance but also excels in cumulative reward optimization, surpassing existing methods. Additional visualizations provide further insights into the effectiveness and underlying mechanisms of our approach.

A provenance analysis for a query evaluation or a model checking computation extracts information on how its result depends on the atomic facts of the model or database. Traditional work on data provenance was, to a large extent, restricted to positive query languages or the negation-free fragment of first-order logic and showed how provenance abstractions can be usefully described as elements of commutative semirings -- most generally as multivariate polynomials with positive integer coefficients. We describe and evaluate here a provenance approach for dealing with negation, based on quotient semirings of polynomials with dual indeterminates. This not only provides a semiring provenance analysis for full first-order logic (and other logics and query languages with negation) but also permits a reverse provenance analysis, i.e., finding models that satisfy various properties under given provenance tracking assumptions. We describe the potential for applications to explaining missing query answers or failures of integrity constraints, and to using these explanations for computing repairs. This approach also is the basis of a systematic study of semiring semantics in a broad logical context.

We present a new method for obtaining norm bounds for random matrices, where each entry is a low-degree polynomial in an underlying set of independent real-valued random variables. Such matrices arise in a variety of settings in the analysis of spectral and optimization algorithms, which require understanding the spectrum of a random matrix depending on data obtained as independent samples. Using ideas of decoupling and linearization from analysis, we show a simple way of expressing norm bounds for such matrices, in terms of matrices of lower-degree polynomials corresponding to derivatives. Iterating this method gives a simple bound with an elementary proof, which can recover many bounds previously required more involved techniques.

Image-level weakly supervised semantic segmentation (WSSS) is a fundamental yet challenging computer vision task facilitating scene understanding and automatic driving. Most existing methods resort to classification-based Class Activation Maps (CAMs) to play as the initial pseudo labels, which tend to focus on the discriminative image regions and lack customized characteristics for the segmentation task. To alleviate this issue, we propose a novel activation modulation and recalibration (AMR) scheme, which leverages a spotlight branch and a compensation branch to obtain weighted CAMs that can provide recalibration supervision and task-specific concepts. Specifically, an attention modulation module (AMM) is employed to rearrange the distribution of feature importance from the channel-spatial sequential perspective, which helps to explicitly model channel-wise interdependencies and spatial encodings to adaptively modulate segmentation-oriented activation responses. Furthermore, we introduce a cross pseudo supervision for dual branches, which can be regarded as a semantic similar regularization to mutually refine two branches. Extensive experiments show that AMR establishes a new state-of-the-art performance on the PASCAL VOC 2012 dataset, surpassing not only current methods trained with the image-level of supervision but also some methods relying on stronger supervision, such as saliency label. Experiments also reveal that our scheme is plug-and-play and can be incorporated with other approaches to boost their performance.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.