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First passage time memory lifetimes for simple, multistate synapses: beyond the eigenvector requirement

First passage time memory lifetimes for simple, multistate synapses: beyond the eigenvector requirement
First passage time memory lifetimes for simple, multistate synapses: beyond the eigenvector requirement
Memory models based on synapses with discrete and bounded strengths store new memories by forgetting old ones. Memory lifetimes in such memory systems may be defined in a variety of ways. A mean first passage time (MFPT) definition overcomes much of the arbitrariness and many of the problems associated with the more usual signal-to-noise ratio (SNR) definition. We have previously computed MFPT lifetimes for simple, binary-strength synapses that lack internal, plasticity-related states. In simulation we have also seen that for multistate synapses, optimality conditions based on SNR lifetimes are absent with MFPT lifetimes, suggesting that such conditions may be artifactual. Here we extend our earlier work by computing the entire first passage time (FPT) distribution for simple, multistate synapses, from which all statistics, including the MFPT lifetime, may be extracted. For this, we develop a Fokker-Planck equation using the jump moments for perceptron activation. Two models are considered that satisfy a particular eigenvector condition that this approach requires. In these models, MFPT lifetimes do not exhibit optimality conditions, while in one but not the other, SNR lifetimes do exhibit optimality. Thus, not only are such optimality conditions artifacts of the SNR approach, but they are also strongly model dependent. By examining the variance in the FPT distribution, we may identify regions in which memory storage is subject to high variability, although MFPT lifetimes are nevertheless robustly positive. In such regions, SNR lifetimes are typically (defined to be) zero. FPT-defined memory lifetimes therefore provide an analytically superior approach and also have the virtue of being directly related to a neuron's firing properties.
8-67
Elliott, Terry
b4262f0d-c295-4ea4-b5d8-3931470952f9
Elliott, Terry
b4262f0d-c295-4ea4-b5d8-3931470952f9

Elliott, Terry (2019) First passage time memory lifetimes for simple, multistate synapses: beyond the eigenvector requirement. Neural Computation, 31 (1), 8-67. (doi:10.1162/neco_a_01147).

Record type: Article

Abstract

Memory models based on synapses with discrete and bounded strengths store new memories by forgetting old ones. Memory lifetimes in such memory systems may be defined in a variety of ways. A mean first passage time (MFPT) definition overcomes much of the arbitrariness and many of the problems associated with the more usual signal-to-noise ratio (SNR) definition. We have previously computed MFPT lifetimes for simple, binary-strength synapses that lack internal, plasticity-related states. In simulation we have also seen that for multistate synapses, optimality conditions based on SNR lifetimes are absent with MFPT lifetimes, suggesting that such conditions may be artifactual. Here we extend our earlier work by computing the entire first passage time (FPT) distribution for simple, multistate synapses, from which all statistics, including the MFPT lifetime, may be extracted. For this, we develop a Fokker-Planck equation using the jump moments for perceptron activation. Two models are considered that satisfy a particular eigenvector condition that this approach requires. In these models, MFPT lifetimes do not exhibit optimality conditions, while in one but not the other, SNR lifetimes do exhibit optimality. Thus, not only are such optimality conditions artifacts of the SNR approach, but they are also strongly model dependent. By examining the variance in the FPT distribution, we may identify regions in which memory storage is subject to high variability, although MFPT lifetimes are nevertheless robustly positive. In such regions, SNR lifetimes are typically (defined to be) zero. FPT-defined memory lifetimes therefore provide an analytically superior approach and also have the virtue of being directly related to a neuron's firing properties.

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mfpt-2d - Accepted Manuscript
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Accepted/In Press date: 29 August 2018
e-pub ahead of print date: 2 January 2019

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Local EPrints ID: 423213
URI: https://eprints.soton.ac.uk/id/eprint/423213
PURE UUID: 1b9ab937-650a-497d-9777-7aec0e3b5c9f

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Date deposited: 19 Sep 2018 16:30
Last modified: 13 Mar 2019 18:06

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Author: Terry Elliott

University divisions

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