Semi-Unified Sparse Dictionary Learning with Learnable Top-K LISTA and FISTA Encoders

TL;DR

This work tackles the interpretability-versus-efficiency gap in sparse dictionary learning by introducing a semi-unified framework that jointly optimizes a differentiable sparse encoder and a discriminative dictionary. It integrates strict Top-$K$ LISTA and its convex LISTAConv variant into the LC-KSVD2 objective, enabling co-evolution of the sparse codes $G$ with the dictionary $D$, label-consistency matrix $A$, and classifier $W$ under both unsupervised and supervised regimes. A PALM-style convergence analysis is provided for the convex variant, ensuring theoretical stability, while a two-stage training strategy with warm-up and ramped supervision prevents representation collapse. Empirically, the approach achieves strong accuracy on CIFAR-10/100 and TinyImageNet with low memory usage (<$4$ GB) and fast convergence, offering an interpretable, computationally efficient alternative to transformer-based pipelines. The method demonstrates that LC-KSVD2 combined with Learnable Top-$K$ LISTA or LISTAConv can yield competitive performance while maintaining transparency and stability in modern deep architectures.

Abstract

We present a semi-unified sparse dictionary learning framework that bridges the gap between classical sparse models and modern deep architectures. Specifically, the method integrates strict Top-$K$ LISTA and its convex FISTA-based variant (LISTAConv) into the discriminative LC-KSVD2 model, enabling co-evolution between the sparse encoder and the dictionary under supervised or unsupervised regimes. This unified design retains the interpretability of traditional sparse coding while benefiting from efficient, differentiable training. We further establish a PALM-style convergence analysis for the convex variant, ensuring theoretical stability under block alternation. Experimentally, our method achieves 95.6\% on CIFAR-10, 86.3\% on CIFAR-100, and 88.5\% on TinyImageNet with faster convergence and lower memory cost ($<$4GB GPU). The results confirm that the proposed LC-KSVD2 + LISTA/LISTAConv pipeline offers an interpretable and computationally efficient alternative for modern deep architectures.

Figures (1)

• Figure 1: PCA visualization of cat vs. dog samples using frozen ResNet-50 features. The two classes remain highly entangled, and sparse refinement alone cannot yield stable separation.