Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world applications, a theoretical understanding of their generalization capabilities remains underdeveloped.

Recent blind super-resolution (SR) methods typically consist of two branches, one for degradation prediction and the other for conditional restoration. However, our experiments show that a one-branch network can achieve comparable performance to the two-branch scheme. Then we wonder: how can one-branch networks automatically learn to distinguish degradations? To find the answer, we propose a new diagnostic tool - Filter Attribution method based on Integral Gradient (FAIG). Unlike previous integral gradient methods, our FAIG aims at finding the most discriminative filters instead of input pixels/features for degradation removal in blind SR networks. With the discovered filters, we further develop a simple yet effective method to predict the degradation of an input image. Based on FAIG, we show that, in one-branch blind SR networks, 1) we are able to find a very small number of (1%) discriminative filters for each specific degradation; 2) The weights, locations and connections of the discovered filters are all important to determine the specific network function.

In the adversarial training framework of Carmon et al. (2019); Gowal et al. (2021), people use generated/real unlabeled data with pseudolabels to improve adversarial robustness. We provide statistical insights to explain why the artificially generated data improve adversarial training. In particular, we study how the attack strength and the quality of the unlabeled data affect adversarial robustness in this framework. Our results show that with a high-quality unlabeled data generator, adversarial training can benefit greatly from this framework under large attack strength, while a poor generator can still help to some extent. To make adaptions concerning the quality of generated data, we propose an algorithm that performs online adjustment to the weight between the labeled real data and the generated data, aiming to optimize the adversarial risk. Numerical studies are conducted to verify our theories and show the effectiveness of the proposed algorithm.

By forcing at most N out of M consecutive weights to be non-zero, the recent N:M network sparsity has received increasing attention for its two attractive advantages: 1) Promising performance at a high sparsity.

Neural Ordinary Differential Equations (NODEs) have proven successful in learning dynamical systems in terms of accurately recovering the observed trajectories. While different types of sparsity have been proposed to improve robustness, the generalization properties of NODEs for dynamical systems beyond the observed data are underexplored. We systematically study the influence of weight and feature sparsity on forecasting as well as on identifying the underlying dynamical laws. Besides assessing existing methods, we propose a regularization technique to sparsify "input-output connections" and extract relevant features during training. Moreover, we curate real-world datasets consisting of human motion capture and human hematopoiesis single-cell RNA-seq data to realistically analyze different levels of out-of-distribution (OOD) generalization in forecasting and dynamics identification respectively. Our extensive empirical evaluation on these challenging benchmarks suggests that weight sparsity improves generalization in the presence of noise or irregular sampling. However, it does not prevent learning spurious feature dependencies in the inferred dynamics, rendering them impractical for predictions under interventions, or for inferring the true underlying dynamics. Instead, feature sparsity can indeed help with recovering sparse ground-truth dynamics compared to unregularized NODEs.

Dataset Condensation is a newly emerging technique aiming at learning a tiny dataset that captures the rich information encoded in the original dataset. As the size of datasets contemporary machine learning models rely on becomes increasingly large, condensation methods become a prominent direction for accelerating network training and reducing data storage. Despite numerous methods have been proposed in this rapidly growing field, evaluating and comparing different condensation methods is non-trivial and still remains an open issue. The quality of condensed dataset are often shadowed by many critical contributing factors to the end performance, such as data augmentation and model architectures. The lack of a systematic way to evaluate and compare condensation methods not only hinders our understanding of existing techniques, but also discourages practical usage of the synthesized datasets. This work provides the first large-scale standardized benchmark on Dataset Condensation. It consists of a suite of evaluations to comprehensively reflect the generability and effectiveness of condensation methods through the lens of their generated dataset. Leveraging this benchmark, we conduct a large-scale study of current condensation methods, and report many insightful findings that open up new possibilities for future development. The benchmark library, including evaluators, baseline methods, and generated datasets, is open-sourced1 to facilitate future research and application.