Lower Bounds for the Computational Power of Networks of Spiking Neurons

By Wolfgang Maass. 1996

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Citations in the corpus

Deep learning in neural networks: An overview (2014, neutral): “…Legenstein, & Maass, 2014; Izhikevich et al., 2003; Kasabov, 2014; Kempter, Gerstner, & Van Hemmen, 1999; Kistler, Gerstner, & van Hemmen, 1997; Maass, 1996, 1997; Maex & Orban, 1996; Nessler, Pfeiffer, Buesing, & Maass, 2013; Rezende & Gerstner, 2014; Seung, 2003; Song, Miller, & Abbott,…”
SLAYER: Spike Layer Error Reassignment in Time (2018, background): “On the other hand, biologically inspired spiking neurons have long shown great theoretical potential as efﬁcient computational units [1–3] and recent advances in Spiking Neural Network (SNN) hardware [4–6] have renewed research interest in this area.”
Introduction to spiking neural networks: Information processing, learning and applications. (2011, methodology): “The concept of coding by phases has been studied both in models (Hopfield 1995, Maass 1996, Jensen Lisman 1996) and experimentally (Buzsaki 2006).”
Noise as a Resource for Computation and Learning in Networks of Spiking Neurons (2014, background): “, any Turing machine, can be simulated by a deterministic network of spiking neurons [80]).”
A new supervised learning algorithm for multiple spiking neural networks with application in epilepsy and seizure detection (2009, background): “The second generationneurons developed in the 1960s, 1970s, and 1980s defined the internal state in a similar manner but used a mathematically-defined activation function, often a smooth sigmoid or radial basis function, instead of a fixed threshold value, for output determination (Maass, 1996).”
A review of learning in biologically plausible spiking neural networks (2019, unknown): “Bio-inspired SNNs have brain-like representation ability, and they potentially have higher representation capability than traditional rate-based networks (Maass, 1996; Tavanaei et al., 2019).”
Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations (2002, background): “Methods for controlling the dynamics of recurrent neural networks through adaptive mechanisms are reviewed in Pearlmutter (1995). So far, no one has been able to apply these to the case of networks of spiking neurons.”
Networks of Spiking Neurons: The Third Generation of Neural Network Models (1996, methodology): “In order to simulate the subsequent layers of C with spiking neurons of type B, one can employ the construction from Maass (1996a).”
Error-backpropagation in temporally encoded networks of spiking neurons (2000, methodology): “The theoretical work by Maass [28] already refuted this notion (as also argued in [15]), but the results presented here demonstrate networks of spiking neurons with biologically plausible (relatively long) time constants capable of performing complex non-linear classification tasks.”
Deep Learning in Spiking Neural Networks (2018, background): “This raises a question: How are neural networks in the brain trained if derivative-based optimization is not available? Although spiking networks have theoretically been shown to have Turing-equivalent computing power (Maass, 1996), it remains a challenge to train SNNs, especially deep SNNs using mu”