Chenwei Yu | Searcharxiv

arXiv2025

Variations of topological theory and ergodic theory via gap function in non-uniform specification

In our previous work [43], we studied qualitative differences between specification and nonuniform specification. In this paper, we investigate quantitative variations governed by the gap function. We first obtain lower bounds for the Bowen topological entropy of irregular sets in terms of the lower linear growth of gap function. In contrast, we prove that every non-empty over-saturated set has full packing topological entropy under non-uniform specification. We also establish a quantitative lower bound for the Bowen topological entropy of transitive points under non-uniform specification, and a lower bound for the exponential growth of periodic orbits under its periodic version. Besides, we construct symbolic systems with a given gap growth which contain an arbitrary subshift. These systems show that the bounds concerning irregular sets and periodic orbits are optimal. They also show that positive linear gap growth may destroy full Bowen entropy of transitive points, the conditional variational principle, the intermediate entropy and pressure properties, and the genericity of continuous functions whose unique maximizing measure has zero entropy.

math.DS↗

arXiv2025

A mini-batch training strategy for deep subspace clustering networks

Mini-batch training is a cornerstone of modern deep learning, offering computational efficiency and scalability for training complex architectures. However, existing deep subspace clustering (DSC) methods, which typically combine an autoencoder with a self-expressive layer, rely on full-batch processing. The bottleneck arises from the self-expressive module, which requires representations of the entire dataset to construct a self-representation coefficient matrix. In this work, we introduce a mini-batch training strategy for DSC by integrating a memory bank that preserves global feature representations. Our approach enables scalable training of deep architectures for subspace clustering with high-resolution images, overcoming previous limitations. Additionally, to efficiently fine-tune large-scale pre-trained encoders for subspace clustering, we propose a decoder-free framework that leverages contrastive learning instead of autoencoding for representation learning. This design not only eliminates the computational overhead of decoder training but also provides competitive performance. Extensive experiments demonstrate that our approach not only achieves performance comparable to full-batch methods, but outperforms other state-of-the-art subspace clustering methods on the COIL100 and ORL datasets by fine-tuning deep networks.

cs.CV↗