Understanding the generalization of deep neural networks is one of the most important tasks in deep learning. Although much progress has been made, theoretical error bounds still often behave disparately from empirical observations. In this work, we develop margin-based generalization bounds, where the margins are normalized with optimal transport costs between independent random subsets sampled from the training distribution. In particular, the optimal transport cost can be interpreted as a generalization of variance which captures the structural properties of the learned feature space. Our bounds robustly predict the generalization error, given training data and network parameters, on large scale datasets. Theoretically, we demonstrate that the concentration and separation of features play crucial roles in generalization, supporting empirical results in the literature.

Features extracted from deep layers of classification networks are widely used as image descriptors. Here, we exploit an unexplored property of these features: their internal dissimilarity. While small image patches are known to have similar statistics across image scales, it turns out that the internal distribution of deep features varies distinctively between scales. We show how this deep self dissimilarity (DSD) property can be used as a powerful visual fingerprint. Particularly, we illustrate that full-reference and no-reference image quality measures derived from DSD are highly correlated with human preference. In addition, incorporating DSD as a loss function in training of image restoration networks, leads to results that are at least as photo-realistic as those obtained by GAN based methods, while not requiring adversarial training.

Federated learning (FL) is a distributed learning framework that leverages commonalities between distributed client datasets to train a global model. Under heterogeneous clients, however, FL can fail to produce stable training results. Personalized federated learning (PFL) seeks to address this by learning individual models tailored to each client. One approach is to decompose model training into shared representation learning and personalized classifier training. Nonetheless, previous works struggle to navigate the bias-variance trade-off in classifier learning, relying solely on limited local datasets or introducing costly techniques to improve generalization.In this work, we frame representation learning as a generative modeling task, where representations are trained with a classifier based on the global feature distribution. We then propose an algorithm, pFedFDA, that efficiently generates personalized models by adapting global generative classifiers to their local feature distributions. Through extensive computer vision benchmarks, we demonstrate that our method can adjust to complex distribution shifts with significant improvements over current state-of-the-art in data-scarce settings.

Disease grading is a crucial task in medical image analysis. Due to the continuous progression of diseases, i.e., the variability within the same level and the similarity between adjacent stages, accurate grading is highly challenging.Furthermore, in real-world scenarios, models trained on limited source domain datasets should also be capable of handling data from unseen target domains.Due to the cross-domain variants, the feature distribution between source and unseen target domains can be dramatically different, leading to a substantial decrease in model performance.To address these challenges in cross-domain disease grading, we propose a Severity-aware Recurrent Modeling (Samba) method in this paper.As the core objective of most staging tasks is to identify the most severe lesions, which may only occupy a small portion of the image, we propose to encode image patches in a sequential and recurrent manner.Specifically, a state space model is tailored to store and transport the severity information by hidden states.Moreover, to mitigate the impact of cross-domain variants, an Expectation-Maximization (EM) based state recalibration mechanism is designed to map the patch embeddings into a more compact space.We model the feature distributions of different lesions through the Gaussian Mixture Model (GMM) and reconstruct the intermediate features based on learnable severity bases.Extensive experiments show the proposed Samba outperforms the VMamba baseline by an average accuracy of 23.5\%, 5.6\% and 4.1\% on the cross-domain grading of fatigue fracture, breast cancer and diabetic retinopathy, respectively. Source code is available at \url{https://github.com/BiQiWHU/Samba}.

Model editing is a growing area of research that is particularly valuable in contexts where modifying key model components, like neurons or filters, can significantly impact the model's performance. The key challenge lies in identifying important components useful to the model's predictions. We apply model editing to address two active areas of research, Structured Pruning, and Selective Class Forgetting. In this work, we adopt a distributional approach to the problem of identifying important components, leveraging the recently proposed discriminative filters hypothesis, which states that well-trained (convolutional) models possess discriminative filters that are essential to prediction. To do so, we define discriminative ability in terms of the Bayes error rate associated with the feature distributions, which is equivalent to computing the Total Variation (TV) distance between the distributions. However, computing the TV distance is intractable, motivating us to derive novel witness function-based lower bounds on the TV distance that require no assumptions on the underlying distributions; using this bound generalizes prior work such as Murti et al. [39] that relied on unrealistic Gaussianity assumptions on the feature distributions. With these bounds, we are able to discover critical subnetworks responsible for classwise predictions, and derive DISCEDIT-SP and DISCEDIT-U, algorithms for structured pruning requiring no access to the training data and loss function, and selective forgetting respectively. We apply DISCEDIT-U to selective class forgetting on models trained on CIFAR10 and CIFAR100, and we show that on average, we can reduce accuracy on a single class by over 80% with a minimal reduction in test accuracy on the remaining classes. Similarly, on Structured pruning problems, we obtain 40.8% sparsity on ResNet50 on Imagenet, with only a 2.6% drop in accuracy with minimal fine-tuning.

Deep neural networks, trained with large amount of labeled data, can fail to generalize well when tested with examples from a target domain whose distribution differs from the training data distribution, referred as the source domain. It can be expensive or even infeasible to obtain required amount of labeled data in all possible domains. Unsupervised domain adaptation sets out to address this problem, aiming to learn a good predictive model for the target domain using labeled examples from the source domain but only unlabeled examples from the target domain. Domain alignment approaches this problem by matching the source and target feature distributions, and has been used as a key component in many state-of-the-art domain adaptation methods. However, matching the marginal feature distributions does not guarantee that the corresponding class conditional distributions will be aligned across the two domains. We propose co-regularized domain alignment for unsupervised domain adaptation, which constructs multiple diverse feature spaces and aligns source and target distributions in each of them individually, while encouraging that alignments agree with each other with regard to the class predictions on the unlabeled target examples. The proposed method is generic and can be used to improve any domain adaptation method which uses domain alignment. We instantiate it in the context of a recent state-of-the-art method and observe that it provides significant performance improvements on several domain adaptation benchmarks.