Embracing causality in fault reasoning
Artificial Intelligence
Analog versus digital: extrapolating from electronics to neurobiology
Neural Computation
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Convex Optimization
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Sparse coding via thresholding and local competition in neural circuits
Neural Computation
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
Online Learning for Matrix Factorization and Sparse Coding
The Journal of Machine Learning Research
Dual Averaging Methods for Regularized Stochastic Learning and Online Optimization
The Journal of Machine Learning Research
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Computing sparse redundant representations is an important problem in both 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 by 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, the 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/ for gaussian white noise.