title: Optimal sparse approximation with integrate and fire neurons.
abstract: Sparse approximation is a hypothesized coding strategy where a population of sensory neurons (e.g. V1) encodes a stimulus using as few active neurons as possible. We present the Spiking LCA (locally competitive algorithm), a rate encoded Spiking Neural Network (SNN) of integrate and fire neurons that calculate sparse approximations. The Spiking LCA is designed to be equivalent to the nonspiking LCA, an analog dynamical system that converges on a ℓ(1)-norm sparse approximations exponentially. We show that the firing rate of the Spiking LCA converges on the same solution as the analog LCA, with an error inversely proportional to the sampling time. We simulate in NEURON a network of 128 neuron pairs that encode 8 × 8 pixel image patches, demonstrating that the network converges to nearly optimal encodings within 20 ms of biological time. We also show that when using more biophysically realistic parameters in the neurons, the gain function encourages additional ℓ(0)-norm sparsity in the encoding, relative both to ideal neurons and digital solvers.
authors.affiliation: Electronic Systems Laboratory, Georgia Tech Research Institute, 400 10th St NW, Atlanta, Georgia 30318, United States of America.
authors.forename: Samuel
authors.initials: S
authors.lastname: Shapero
authors.forename: Mengchen
authors.initials: M
authors.lastname: Zhu
authors.forename: Jennifer
authors.initials: J
authors.lastname: Hasler
authors.forename: Christopher
authors.initials: C
authors.lastname: Rozell
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D013997:Time Factors