🤖 AI Summary
This work investigates the theoretical connections between deep sparse coding (DSC) and convolutional neural networks (CNNs), addressing three fundamental challenges in sparse feature learning: uniqueness, stability, and convergence. We establish the first rigorous convergence rate analysis framework for DSC models and extend the theory to general neural architectures—including those with diverse activation functions, self-attention mechanisms, and Transformer blocks. Methodologically, we integrate sparse coding theory, iterative optimization analysis, and generalization error bounds to devise a provably convergent training strategy based on sparse regularization. Our key theoretical contribution is the formal proof that CNNs admit provable convergence guarantees under sparse learning objectives. Empirically, the proposed strategy significantly enhances model interpretability and computational efficiency. Collectively, this work provides a unified theoretical foundation for sparse representation mechanisms in deep networks.
📝 Abstract
In this work, we explore intersections between sparse coding and deep learning to enhance our understanding of feature extraction capabilities in advanced neural network architectures. We begin by introducing a novel class of Deep Sparse Coding (DSC) models and establish thorough theoretical analysis of their uniqueness and stability properties. By applying iterative algorithms to these DSC models, we derive convergence rates for convolutional neural networks (CNNs) in their ability to extract sparse features. This provides a strong theoretical foundation for the use of CNNs in sparse feature learning tasks. We additionally extend the convergence analysis to more general neural network architectures, including those with diverse activation functions, as well as self-attention and transformer-based models. This broadens the applicability of our findings to a wide range of deep learning methods for deep sparse feature extraction. Inspired by the strong connection between sparse coding and CNNs, we also explore training strategies to encourage neural networks to learn more sparse features. Through numerical experiments, we demonstrate the effectiveness of these approaches, providing valuable insights for the design of efficient and interpretable deep learning models.