There has been a line of work characterizing the generalization performance of neural networks using norm-based methods. However, when compared with empirical results, norm-based generalization bounds tend to be overly loose and even become vacuous. This paper seeks to unravel this phenomenon for equivariant tensor networks through the lens of topology, by investigating the relation between operator norms and compactness, as well as the null space of equivariant linear operators. We proved that while the boundedness of the operator norm is a sufficient condition for a class of equivariant tensor networks to be compact, it is not necessary. This observation sheds light on occasions where norm-based methods may lead to an arbitrarily loose generalization bound. Furthermore, we demonstrate that due to the sparsity of equivariant linear operators, their common null space can be significantly larger than that of ordinary linear operators. This might encourage larger operator norms to compensate for the "energy loss" caused by mapping into the null spaces, leading to larger and looser norm-based generalization bounds.

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) andf-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 onf-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.

We study the Out-of-Distribution (OOD) generalization in machine learning and propose a general framework that provides 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. Moreover, 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 recover the best among existing OOD generalization bounds.

In this paper, we investigate the latency minimization resource allocation for a multi-user augmented reality (AR) system based on mobile edge computing (MEC). First, we develop a novel data sharing model for the delay-sensitive AR tasks. Then, by integrating the partial offloading scheme into the task processing, we formulate a weighted-sum latency minimization problem to improve the quality of experience (QoE) for AR devices. Both the optimal task segmentation strategy and the optimal joint resource allocation are derived in closed-form. Finally, numerical results show that the proposed partial task offloading with data sharing scheme can achieve a better delay performance as compared against some benchmark schemes.