IntroductionBasic Neuron ModelsModeling LIF NeuronsTuning CurvesConnecting with Synapses and Post-Synaptic Potentials (PSPs)Information Transfer and DecodersTranslating Data to SpikesAdaptive LIF NeuronsModel Scaling (Optional)Research Replication: Unsupervised Learning of Digit Recognition Using STDP (Part 1)Research Replication: Unsupervised Learning of Digit Recognition Using STDP (Part 2)
Learning through Spike-Timing Dependent Plasticity (STDP)
function getDW(t_pre, t_post) {
if(t_pre <= t_post) {
return a_plus*Math.exp((t_pre - t_post)/tau_plus);
} else {
return -a_minus*Math.exp(-(t_pre - t_post)/tau_minus);
}
}
class STDPWeights {
constructor(numPre, numPost, tau_plus = 0.02, tau_minus = 0.02, a_plus = 0.01, a_minus = 0.011, g_min = 0, g_max = 1) {
this.numPre = numPre;
this.numPost = numPost;
this.tau_plus = tau_plus;
this.tau_minus = tau_minus;
this.x = times(numPre, 0); // An array with numPre zeros
this.y = times(numPost, 0); // An array with numPost zeros
this.a_plus = a_plus;
this.a_minus = a_minus;
this.g_min = g_min;
this.g_max = g_max;
this.w = times2d(numPre, numPost, 0); // A 2-D array; numPre x numPost zeros (normally would be random)
}
updateWeights(preOutputs, postOutputs) {
const preSpikeIndices = getIndicesGreaterThan0(preOutputs); // Indices of pre-synaptic spiking neurons
const postSpikeIndices = getIndicesGreaterThan0(postOutputs); // Indices of poast-synaptic spiking neurons
// Increment x for spiking pre-synaptic neurons
preSpikeIndices.forEach((ps_idx) => {
this.x[ps_idx] += this.a_plus;
});
// Increment y for spiking poast-synaptic neurons
postSpikeIndices.forEach((ps_idx) => {
this.y[ps_idx] -= this.a_minus;
});
const alpha_g = this.g_max - this.g_min; // Scaling factor for weight updates
// Loop over the *index* of every pre-synaptic neuron that spiked
preSpikeIndices.forEach((ps_idx) => {
// And for every post-synaptic neuron connected to this pre-synaptic neuron, update
// the connection weight by the `y` value for that post-synaptic neuron
for(let i = 0; i<this.numPost; i++) {
this.w[ps_idx][i] += alpha_g * this.y[i];
// Make sure it is between this.g_min and this.g_max
if(this.w[ps_idx][i] < this.g_min) { this.w[ps_idx][i] = this.g_min; } // if less than g_min, set to g_min
if(this.w[ps_idx][i] > this.g_max) { this.w[ps_idx][i] = this.g_max; } // if greater than g_max, set to g_max
}
});
// Loop over the *index* of every post-synaptic neuron that spiked
postSpikeIndices.forEach((ps_idx) => {
// And for every pre-synaptic neuron connected to this post-synaptic neuron, update
// the connection weight by the `x` value for that pre-synaptic neuron
for(let i = 0; i<this.numPre; i++) {
this.w[i][ps_idx] += alpha_g * this.x[i];
// Make sure it is between this.g_min and this.g_max
if(this.w[i][ps_idx] < this.g_min) { this.w[i][ps_idx] = this.g_min; } // if less than g_min, set to g_min
if(this.w[i][ps_idx] > this.g_max) { this.w[i][ps_idx] = this.g_max; } // if greater than g_max, set to g_max
}
});
}
step(t_step) {
// Loop through each value of this.x and decay
for(let i = 0; i<this.x.length; i++) {
this.x[i] = this.x[i] * (1 - t_step/this.tau_plus);
}
// Loop through each value of this.y and decay
for(let i = 0; i<this.y.length; i++) {
this.y[i] = this.y[i] * (1 - t_step/this.tau_minus);
}
}
}
getDWView(
// Pre-synaptic spikes
[
"x x x x x x",
" x x xxx x ",
],
// Post-synaptic spikes
[
" xx x x ",
" x x x ",
])
function times(n, funcVal) {
const result = [];
const func = (typeof funcVal === 'function') ? funcVal : (() => funcVal);
for(let i = 0; i<n; i++) {
result.push(func(i));
}
return result;
}
function times2d(n1, n2, funcVal) {
const result = [];
const func = (typeof funcVal === 'function') ? funcVal : (() => funcVal);
for(let i = 0; i<n1; i++) {
const row = [];
for(let j = 0; j<n2; j++) {
row.push(func(i, j));
}
result.push(row);
}
return result;
}
function getIndicesGreaterThan0(arr) {
return arr.map((_, index) => index).filter((index) => arr[index] > 0);
}
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