dorsal/arxiv
View SchemaTemporal correlation based learning in neuron models
| Authors | Juergen Jost |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0511012 |
| URL | https://arxiv.org/abs/q-bio/0511012 |
Abstract
We study a learning rule based upon the temporal correlation (weighted by a learning kernel) between incoming spikes and the internal state of the postsynaptic neuron, building upon previous studies of spike timing dependent synaptic plasticity (\cite{KGvHW,KGvH1,vH}). Our learning rule for the synaptic weight $w_{ij}$ is $$ \dot w_{ij}(t)= \epsilon \int_{-\infty}^\infty \frac{1}{T_l} \int_{t-T_l}^t \sum_\mu \delta(\tau+s-t_{j,\mu}) u(\tau) d\tau\ \Gamma(s)ds $$ where the $t_{j,\mu}$ are the arrival times of spikes from the presynaptic neuron $j$ and the function $u(t)$ describes the state of the postsynaptic neuron $i$. Thus, the spike-triggered average contained in the inner integral is weighted by a kernel $\Gamma(s)$, the learning window, positive for negative, negative for positive values of the time diffence $s$ between post- and presynaptic activity. An antisymmetry assumption for the learning window enables us to derive analytical expressions for a general class of neuron models and to study the changes in input-output relationships following from synaptic weight changes. This is a genuinely non-linear effect (\cite{SMA}).
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"abstract": "We study a learning rule based upon the temporal correlation (weighted by a\nlearning kernel) between incoming spikes and the internal state of the\npostsynaptic neuron, building upon previous studies of spike timing dependent\nsynaptic plasticity (\\cite{KGvHW,KGvH1,vH}). Our learning rule for the synaptic\nweight $w_{ij}$ is $$ \\dot w_{ij}(t)= \\epsilon \\int_{-\\infty}^\\infty\n\\frac{1}{T_l} \\int_{t-T_l}^t \\sum_\\mu \\delta(\\tau+s-t_{j,\\mu}) u(\\tau) d\\tau\\\n\\Gamma(s)ds $$ where the $t_{j,\\mu}$ are the arrival times of spikes from the\npresynaptic neuron $j$ and the function $u(t)$ describes the state of the\npostsynaptic neuron $i$. Thus, the spike-triggered average contained in the\ninner integral is weighted by a kernel $\\Gamma(s)$, the learning window,\npositive for negative, negative for positive values of the time diffence $s$\nbetween post- and presynaptic activity. An antisymmetry assumption for the\nlearning window enables us to derive analytical expressions for a general class\nof neuron models and to study the changes in input-output relationships\nfollowing from synaptic weight changes. This is a genuinely non-linear effect\n(\\cite{SMA}).",
"arxiv_id": "q-bio/0511012",
"authors": [
"Juergen Jost"
],
"categories": [
"q-bio.NC"
],
"title": "Temporal correlation based learning in neuron models",
"url": "https://arxiv.org/abs/q-bio/0511012"
},
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