Convolutional Sparse Coding via the Locally Competitive Algorithm on Loihi 2

Sparse coding provides a principled framework for signal representation by expressing an input as a linear combination of only a small number of basis functions. The Locally Competitive Algorithm (LCA) is particularly attractive in the context of neuromorphic computing because its dynamics, leaky integration, thresholding, and lateral inhibition map naturally to neuromorphic hardware. While prior work has studied non-convolutional LCA on Loihi 2, the convolutional setting is of particular interest because it introduces spatial structure, weight sharing, overlapping receptive fields, and scaling behavior that are more representative of practical sparse inference workloads. In this work, we present a Loihi 2 implementation of convolutional sparse coding via the LCA and evaluate it against a conventional GPU baseline on the same inference problems. The implementation follows a one-layer recurrent LCA formulation and extends it to convolutional feature maps with local inhibitory kernels derived from pairwise filter interactions. To the best of our knowledge, this is the first implementation and benchmark of convolutional LCA on Loihi 2. Our goal is not only to demonstrate feasibility, but also to clarify in which operating regimes convolutional sparse inference becomes attractive on neuromorphic hardware. The resulting study positions convolutional LCA as a useful benchmark for structured sparse inference on emerging neuromorphic systems.

The Resurrection of the ReLU

Modeling sophisticated activation functions within deep learning architectures has evolved into a distinct research direction. Functions such as GELU, SELU, and SiLU offer smooth gradients and improved convergence properties, making them popular choices in state-of-the-art models. Despite this trend, the classical ReLU remains appealing due to its simplicity, inherent sparsity, and other advantageous topological characteristics. However, ReLU units are prone to becoming irreversibly inactive - a phenomenon known as the dying ReLU problem - which limits their overall effectiveness. In this work, we introduce surrogate gradient learning for ReLU (SUGAR) as a novel, plug-and-play regularizer for deep architectures. SUGAR preserves the standard ReLU function during the forward pass but replaces its derivative in the backward pass with a smooth surrogate that avoids zeroing out gradients. We demonstrate that SUGAR, when paired with a well-chosen surrogate function, substantially enhances generalization performance over convolutional network architectures such as VGG-16 and ResNet-18, providing sparser activations while effectively resurrecting dead ReLUs. Moreover, we show that even in modern architectures like Conv2NeXt and Swin Transformer - which typically employ GELU - substituting these with SUGAR yields competitive and even slightly superior performance. These findings challenge the prevailing notion that advanced activation functions are necessary for optimal performance. Instead, they suggest that the conventional ReLU, particularly with appropriate gradient handling, can serve as a strong, versatile revived classic across a broad range of deep learning vision models.

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

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.