{ "cells": [ { "cell_type": "markdown", "id": "ec5fa894", "metadata": {}, "source": [ "# Tutorial 3 · An E/I balanced network\n", "\n", "**What you'll learn.** How to assemble the canonical conductance-based\n", "excitatory/inhibitory (COBA) network end to end, run it for a second of\n", "biological time, and plot the population spike raster that reveals\n", "asynchronous-irregular activity.\n", "\n", "**Who it's for.** Readers comfortable with {doc}`02-synapse-and-projection`.\n", "(Audience: simulation.)\n", "\n", "This is the Vogels–Abbott (2005) balanced network as described in Brette et al.\n", "(2007): 4000 leaky integrate-and-fire neurons (3200 excitatory, 800 inhibitory),\n", "sparsely connected, with conductance-based exponential synapses. Excitation and\n", "inhibition roughly cancel, so neurons fire irregularly at low rates rather than\n", "locking together." ] }, { "cell_type": "code", "execution_count": 1, "id": "3f9acf48", "metadata": { "execution": { "iopub.execute_input": "2026-06-17T09:09:57.207299Z", "iopub.status.busy": "2026-06-17T09:09:57.207100Z", "iopub.status.idle": "2026-06-17T09:10:01.253094Z", "shell.execute_reply": "2026-06-17T09:10:01.251973Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n" ] } ], "source": [ "import brainpy\n", "import brainstate\n", "import braintools\n", "import brainunit as u\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "ce46af48", "metadata": {}, "source": [ "## Build the network\n", "\n", "A single shared population `N` holds all 4000 neurons. Two projections feed back\n", "onto it: an excitatory one (reversal potential 0 mV, fast 5 ms synapses) and an\n", "inhibitory one (reversal potential −80 mV, slower 10 ms synapses). Each\n", "projection uses one `AlignPostProj` — the postsynaptic-aligned state means the\n", "whole network's synaptic memory is just `O(N)`." ] }, { "cell_type": "code", "execution_count": 2, "id": "6b5180e2", "metadata": { "execution": { "iopub.execute_input": "2026-06-17T09:10:01.256123Z", "iopub.status.busy": "2026-06-17T09:10:01.255619Z", "iopub.status.idle": "2026-06-17T09:10:01.261265Z", "shell.execute_reply": "2026-06-17T09:10:01.260710Z" } }, "outputs": [], "source": [ "class EINet(brainstate.nn.Module):\n", " def __init__(self):\n", " super().__init__()\n", " self.n_exc = 3200\n", " self.n_inh = 800\n", " self.num = self.n_exc + self.n_inh\n", " self.N = brainpy.state.LIFRef(\n", " self.num,\n", " V_rest=-60. * u.mV, V_th=-50. * u.mV, V_reset=-60. * u.mV,\n", " tau=20. * u.ms, tau_ref=5. * u.ms,\n", " V_initializer=braintools.init.Normal(-55., 2., unit=u.mV),\n", " )\n", " self.E = brainpy.state.AlignPostProj(\n", " comm=brainstate.nn.EventFixedProb(\n", " self.n_exc, self.num, conn_num=0.02, conn_weight=0.6 * u.mS),\n", " syn=brainpy.state.Expon.desc(self.num, tau=5. * u.ms),\n", " out=brainpy.state.COBA.desc(E=0. * u.mV),\n", " post=self.N,\n", " )\n", " self.I = brainpy.state.AlignPostProj(\n", " comm=brainstate.nn.EventFixedProb(\n", " self.n_inh, self.num, conn_num=0.02, conn_weight=6.7 * u.mS),\n", " syn=brainpy.state.Expon.desc(self.num, tau=10. * u.ms),\n", " out=brainpy.state.COBA.desc(E=-80. * u.mV),\n", " post=self.N,\n", " )\n", "\n", " def update(self, t, inp):\n", " with brainstate.environ.context(t=t):\n", " spk = self.N.get_spike() != 0.\n", " self.E(spk[:self.n_exc]) # excitatory neurons -> all\n", " self.I(spk[self.n_exc:]) # inhibitory neurons -> all\n", " self.N(inp)\n", " return self.N.get_spike()" ] }, { "cell_type": "markdown", "id": "46c9aab7", "metadata": {}, "source": [ "## Simulate one second\n", "\n", "We use `dt = 0.1 ms` and run for 1000 ms, injecting a constant background\n", "current. `for_loop` compiles the whole 10000-step rollout once and returns the\n", "stacked spike matrix; the optional progress bar reports compilation/run\n", "progress." ] }, { "cell_type": "code", "execution_count": 3, "id": "84b59b64", "metadata": { "execution": { "iopub.execute_input": "2026-06-17T09:10:01.262889Z", "iopub.status.busy": "2026-06-17T09:10:01.262532Z", "iopub.status.idle": "2026-06-17T09:10:07.107901Z", "shell.execute_reply": "2026-06-17T09:10:07.107210Z" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8d38267ffe8e4fb5886fd029b8d01c8a", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/10000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_idx, n_idx = u.math.where(spikes)\n", "plt.figure(figsize=(8, 5))\n", "plt.scatter(times[t_idx].to_decimal(u.ms), n_idx, s=1, color='k')\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('Neuron index')\n", "plt.title('COBA E/I network — asynchronous irregular firing')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7deefafd", "metadata": {}, "source": [ "## See also\n", "\n", "- {doc}`04-train-an-snn` — switch from simulating a fixed network to *training*\n", " one.\n", "- {doc}`../howto/sim-coba-cuba-synapses` — the current-based (CUBA) counterpart\n", " of this network.\n", "- {doc}`../howto/sim-reproduce-a-paper` — reproduce a published oscillation\n", " result.\n", "- {doc}`/examples/brainpy-gallery` — more complete simulation scripts." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.11" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "07dbdba0b39446c7b6a7381ae4e15282": { "model_module": "@jupyter-widgets/controls", "model_module_version": "2.0.0", 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