A Framework for Analyzing, Designing, and Visualizing Spiking Neural Networks Part I: Linear Response Surfaces

Koohestan-Mahalian, Fatemeh; Cotter, N.E.; Zamani, Princess Tara; Rubart, Audrey M.

doi:10.1109/access.2020.3047993

Cited by 1 publication

(8 citation statements)

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“…As shown in [19], for firing time t = 0, the term c(0 -t i ) = -c(t i ) appears in the solution of (1). Thus, -c(t i ) now matches the slope of the sign of the synaptic response.…”

Section: Linear Spike Response Model Reviewmentioning

confidence: 99%

“…A challenging problem in the LSRM, and in general in spiking neuron models, is to derive a transfer function that maps input-spike times to exact output spike times rather than averaging or blurring timing information. In our previous paper [19], the linearity feature of LSRM made the calculation of such mappings possible. We briefly recap the derivation here.…”

Section: Linear Spike Response Model Reviewmentioning

confidence: 99%

“…Finally, we solve (1) in a piecewise fashion. If the state of each synapse is known, i.e., idle, rising, or falling, (1) reduces to the equation of a hyperplane, as detailed in [19]. The need to specify the state of each synapse leads to the definition of what we have termed a "c-function" (equaling the negative of the PSP slope), i.e., -1, +1, and 0 when an LPSP rises, falls, or is idle, as shown in Fig.…”

Section: Linear Spike Response Model Reviewmentioning

confidence: 99%

“…In part I of this paper [19], we review various spiking neuron modeling approaches that have been progressing towards more simplified descriptions of the relationship between the input and output firing times of a spiking neuron. A very simple model we use in Part I, is a version of the Spike Response Model (SRM) described by Gerstner [20] that models PSPs with isosceles triangles.…”

Section: Introductionmentioning

confidence: 99%

“…We introduced a complete geometrical transfer function that captures the mapping between input and output firing times of this linearized spiking neuron. We call the mappings "Linear Response Surfaces" (LRSs), and our linearized neuron model in [19] the "Linear SRM" (LSRM).…”

Section: Introductionmentioning

confidence: 99%

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A Framework for Analyzing, Designing, and Visualizing Spiking Neural Networks—Part II: Nonlinear Response Surfaces

et al. 2020

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In this second part of a two-part study, we extend to nonlinear synaptic responses a new framework, called Response Surfaces (RSs), for analyzing, designing, and visualizing spiking neurons and networks. An RS is the transfer function between input and output firing times of a spiking neuron and shows all the patterns of input spike times that fire a neuron at a given time. Here in Part II, we present four mathematically tractable functions to model more realistic post-synaptic-potential waveforms, and we build on the linear RS framework of Part I to create a nonlinear RS framework. We then discuss the qualitative differences between the linear and nonlinear RSs frameworks and revisit problems of Part I using the nonlinear RSs framework: graphing the transfer function of a nonlinear spiking neuron, designing an efficient spiking-XOR gate, analyzing phase-tracking in recurrent SNNs, and developing transfer functions for calculating the output firing times of a spiking neuron given a set of input firing times. For the nonlinear RS framework, we show that the output firing time of a nonlinear spiking neuron is equivalent to the center-ofmass of input spike times (acting as positions) and weights (acting as masses) plus a fixed delay plus a secondorder correction. The second-order centroid correction is one of the main differences between the linear and nonlinear RS frameworks. For recurrent networks, the nonlinear RS framework also shows a more stable behavior compared to linear SNNs, owing to the smooth shapes of nonlinear post-synaptic-potential waveforms.

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“…As shown in [19], for firing time t = 0, the term c(0 -t i ) = -c(t i ) appears in the solution of (1). Thus, -c(t i ) now matches the slope of the sign of the synaptic response.…”

Section: Linear Spike Response Model Reviewmentioning

confidence: 99%

Section: Linear Spike Response Model Reviewmentioning

confidence: 99%

Section: Linear Spike Response Model Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations