2023/05/09 by Bernhard Moser, Moser, Bernhard A., Michael Lunglmayr +1 · 1 citation
Computer Science · Engineering · Neuroscience · #41A65 #82C32 #92B99 #Advanced Memory and Neural Computing #C.1.3 #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Metric Geometry (math.MG) #Neural Networks and Reservoir Computing #Neural and Evolutionary Computing (cs.NE) #Neural dynamics and brain function #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2305.05772
openalex publication_date 2023/05/09 · openalex created_date 2023/05/12 · openalex updated_date 2026/07/28
In order to ease the analysis of error propagation in neuromorphic computing and to get a better understanding of spiking neural networks (SNN), we address the problem of mathematical analysis of SNNs as endomorphisms that map spike trains to spike trains. A central question is the adequate structure for a space of spike trains and its implication for the design of error measurements of SNNs including time delay, threshold deviations, and the design of the reinitialization mode of the leaky-integrate-and-fire (LIF) neuron model. First we identify the underlying topology by analyzing the closure of all sub-threshold signals of a LIF model. For zero leakage this approach yields the Alexiewicz topology, which we adopt to LIF neurons with arbitrary positive leakage. As a result LIF can be understood as spike train quantization in the corresponding norm. This way we obtain various error bounds and inequalities such as a quasi isometry relation between incoming and outgoing spike trains. Another result is a Lipschitz-style global upper bound for the error propagation and a related resonance-type phenomenon.