WARP-LCA: Efficient Convolutional Sparse Coding with Locally Competitive Algorithm

TL;DR

WARP-LCA introduces a predictive warm-start mechanism for the Locally Competitive Algorithm in convolutional sparse coding by incorporating a fully convolutional predictor (WARP-CNN) that initializes the LCA state $u_i$. This warm start dramatically accelerates convergence, enabling faster attainment of sparser, more robust representations that improve reconstruction and denoising in image pipelines, while maintaining compatibility with various thresholding regimes. Through extensive experiments on CIFAR-10, STL-10, and Tiny ImageNet, WARP-LCA shows faster convergence, lower final $\ell_0$ sparsity, and improved PSNR/SSIM compared with standard LCA, and demonstrates robustness to noise and scalability to larger images. The work broadens biologically inspired sparse coding by coupling predictive priors with iterative LCA refinement, achieving practical gains in efficiency and performance, and suggesting avenues for deeper hierarchical sparse coding and adaptive hyperparameter optimization.

Abstract

The locally competitive algorithm (LCA) can solve sparse coding problems across a wide range of use cases. Recently, convolution-based LCA approaches have been shown to be highly effective for enhancing robustness for image recognition tasks in vision pipelines. To additionally maximize representational sparsity, LCA with hard-thresholding can be applied. While this combination often yields very good solutions satisfying an $\ell_0$ sparsity criterion, it comes with significant drawbacks for practical application: (i) LCA is very inefficient, typically requiring hundreds of optimization cycles for convergence; (ii) the use of hard-thresholding results in a non-convex loss function, which might lead to suboptimal minima. To address these issues, we propose the Locally Competitive Algorithm with State Warm-up via Predictive Priming (WARP-LCA), which leverages a predictor network to provide a suitable initial guess of the LCA state based on the current input. Our approach significantly improves both convergence speed and the quality of solutions, while maintaining and even enhancing the overall strengths of LCA. We demonstrate that WARP-LCA converges faster by orders of magnitude and reaches better minima compared to conventional LCA. Moreover, the learned representations are more sparse and exhibit superior properties in terms of reconstruction and denoising quality as well as robustness when applied in deep recognition pipelines. Furthermore, we apply WARP-LCA to image denoising tasks, showcasing its robustness and practical effectiveness. Our findings confirm that the naive use of LCA with hard-thresholding results in suboptimal minima, whereas initializing LCA with a predictive guess results in better outcomes. This research advances the field of biologically inspired deep learning by providing a novel approach to convolutional sparse coding.

Figures (13)

• Figure 1: Illustration of the WARP-LCA Method. The WARP-LCA method integrates a fully convolutional neural network (CNN) to predict LCA states. These predicted states serve as a warm start for the LCA module. After several LCA iterations, the refined sparse activations are optionally processed through a transpose convolution block to reconstruct the image.
• Figure 2: Illustration of the WARP-LCA Method. The WARP-LCA method integrates a fully convolutional neural network (CNN) to predict LCA states. These predicted states serve as a warm start for the LCA module. After several LCA iterations, the refined sparse activations are optionally processed through a transpose convolution block to reconstruct the image. For a detailed description see \ref{['tab:branchnet']}.
• Figure 3: Comparative Speed-Up of WARP-LCA Relative to LCA. The top panels show the maximum PSNR obtained after 1,000 iterations by LCA (red) and WARP-LCA (blue) for CIFAR-10, STL-10, and Tiny ImageNet, illustrating that the PSNR values for both methods typically decrease as the sparsity parameter (i.e., $\lambda$) increases. The bottom panels present the iteration count at which WARP-LCA equals LCA’s PSNR benchmark, alongside the speed-up factor (ratio of LCA’s total iteration count to WARP-LCA’s required count). The speed-up factor generally increases with larger $\lambda$, exhibiting a dataset-dependent minimum within the $\lambda \in [0.15, 0.35]$ interval, thereby highlighting WARP-LCA’s accelerated convergence to equivalent reconstruction quality.
• Figure 4: Encoding Performance Comparison between WARP-LCA and LCA at $\lambda = 0.15$. The figure displays the performance metrics for WARP-LCA and LCA. The columns represent different metrics: Mean Squared Error (MSE) in log-scale, $\ell_0$-Norm, Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity Index (SSIM). For each plot, WARP-LCA and LCA Mean and Standard Deviation of the Metrics are shown for comparison.
• Figure 5: Side-by-Side Comparison of WARP-CNN Reconstructions. Comparison of WARP-CNN outputs and WARP-CNN with one LCA iteration across CIFAR-10, STL-10, and Tiny ImageNet datasets.