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

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.

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