A network of spiking neurons for computing sparse representations in an energy efficient way
This addresses the need for energy-efficient sparse representation computation in applied mathematics and neuroscience, though it appears incremental as it builds on existing algorithms with comparable performance.
The paper tackles the problem of computing sparse redundant representations in an energy-efficient manner by proposing a hybrid distributed algorithm (HDA) that operates on a network of simple nodes, showing that its numerical performance matches existing algorithms with representation error decaying as 1/t asymptotically and as 1/sqrt(t) under Gaussian white noise.
Computing sparse redundant representations is an important problem both in applied mathematics and neuroscience. In many applications, this problem must be solved in an energy efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating via low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, such operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We show that the numerical performance of HDA is on par with existing algorithms. In the asymptotic regime the representation error of HDA decays with time, t, as 1/t. HDA is stable against time-varying noise, specifically, the representation error decays as 1/sqrt(t) for Gaussian white noise.