Sparse and silent coding in neural circuits

TL;DR

This paper introduces a new neural algorithm for sparse coding that combines $l_0$-norm and $l_1$-norm methods, enabling efficient, biologically plausible representations of natural stimuli without requiring prior knowledge of feature sparsity.

Contribution

The authors develop a novel algorithm integrating $l_0$-norm spike-based probabilistic optimization with $l_1$-norm ideas, facilitating neural implementation and adaptable sparsity levels.

Findings

Algorithm enables neural plausibility without predefined sparsity.

Significantly broadens the domain of optimal solutions for $l_1$-norm based methods.

Effective in representing natural stimuli with varying feature counts.

Abstract

Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an important role in neural information processing. However, due to the computational complexity of the task, only approximate solutions provide the required efficiency (in terms of time). As new results show, under particular conditions there exist efficient solutions by minimizing the magnitude of the coefficients (`$l_1$-norm') instead of minimizing the size of the active subset of features (`$l_0$-norm'). Straightforward neural implementation of these solutions is not likely, as they require \emph{a priori} knowledge of the number of active features. Furthermore, these methods utilize iterative re-evaluation of the reconstruction error, which in turn implies that final sparse forms (featuring `population sparseness') can only be reached through the formation of a series of non-sparse representations, which is in contrast with the overall sparse functioning of the neural systems (`lifetime sparseness'). In this article we present a novel algorithm which integrates our previous `$l_0$-norm' model on spike based probabilistic optimization for sparse coding with ideas coming from novel `$l_1$-norm' solutions. The resulting algorithm allows neurally plausible implementation and does not require an exactly defined sparseness level thus it is suitable for representing natural stimuli with a varying number of features. We also demonstrate that the combined method significantly extends the domain where optimal solutions can be found by `$l_1$-norm' based algorithms.