dorsal/arxiv
View SchemaRandom Walks for Spike-Timing Dependent Plasticity
| Authors | Alan Williams, Todd K. Leen, Patrick D. Roberts |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0312038 |
| URL | https://arxiv.org/abs/q-bio/0312038 |
| DOI | 10.1103/PhysRevE.70.021916 |
Abstract
Random walk methods are used to calculate the moments of negative image equilibrium distributions in synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of sensory electric fields. Of particular behavioral importance to the fish is the variance of the equilibrium postsynaptic potential in the presence of noise, which is determined by the variance of the equilibrium weight distribution. Recurrence relations are derived for the moments of the equilibrium weight distribution, for arbitrary postsynaptic potential functions and arbitrary learning rules. For the case of homogeneous network parameters, explicit closed form solutions are developed for the covariances of the synaptic weight and postsynaptic potential distributions.
{
"annotation_id": "3c997b02-2dec-4c51-b2fd-2f7d1e15d0f2",
"date_created": "2026-03-02T18:01:30.960000Z",
"date_modified": "2026-03-02T18:01:30.960000Z",
"file_hash": "1123e222ffb94b97c72106fe43d0d1b7337993da3374d40895108ce14ac86b85",
"private": false,
"record": {
"abstract": "Random walk methods are used to calculate the moments of negative image\nequilibrium distributions in synaptic weight dynamics governed by spike-timing\ndependent plasticity (STDP). The neural architecture of the model is based on\nthe electrosensory lateral line lobe (ELL) of mormyrid electric fish, which\nforms a negative image of the reafferent signal from the fish\u0027s own electric\ndischarge to optimize detection of sensory electric fields. Of particular\nbehavioral importance to the fish is the variance of the equilibrium\npostsynaptic potential in the presence of noise, which is determined by the\nvariance of the equilibrium weight distribution. Recurrence relations are\nderived for the moments of the equilibrium weight distribution, for arbitrary\npostsynaptic potential functions and arbitrary learning rules. For the case of\nhomogeneous network parameters, explicit closed form solutions are developed\nfor the covariances of the synaptic weight and postsynaptic potential\ndistributions.",
"arxiv_id": "q-bio/0312038",
"authors": [
"Alan Williams",
"Todd K. Leen",
"Patrick D. Roberts"
],
"categories": [
"q-bio.NC"
],
"doi": "10.1103/PhysRevE.70.021916",
"title": "Random Walks for Spike-Timing Dependent Plasticity",
"url": "https://arxiv.org/abs/q-bio/0312038"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "08943442-55d7-49df-a732-2747b854da00",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}