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notebooks: add a bunch of bistability experiments
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‎notebooks/bistable/bistable-integrator.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%load_ext autoreload\n",
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"%autoreload 2\n",
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"\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"from pim.models.network2 import RecurrentNetwork, Layer, InputLayer, Connection, WeightedConnection\n",
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"from pim.models.new.stone import tb1_output, tn1_output, tn2_output, cpu4_output, cpu1_output, motor_output, CentralComplex"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def linear_neuron(gain, gain_noise, noise):\n",
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" gain = np.random.normal(gain, gain_noise)\n",
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" def f(x):\n",
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" return gain * x + np.random.normal(0, noise)\n",
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" return f\n",
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"\n",
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"def bistable_neuron(Idown, Iup, gain, gain_noise, noise):\n",
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" gain = np.random.normal(gain, gain_noise)\n",
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" state = 0\n",
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" def f(x):\n",
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" nonlocal state\n",
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" if x >= Iup:\n",
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" state = 1\n",
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" elif x <= Idown:\n",
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" state = 0 \n",
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" return state * gain * x + np.random.normal(0, noise)\n",
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" return f"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"class BistableLayer(Layer):\n",
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" def __init__(self, name, N, dI, mI, gain, gain_noise, noise):\n",
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" super().__init__(name)\n",
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" self.N = N\n",
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" self.mI = mI\n",
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" self.gain = np.random.normal(gain, gain_noise)\n",
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" self.noise = noise\n",
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" self.neurons = [bistable_neuron(I_up-dI, I_up, 1.0, 0.0, noise) for I_up in np.linspace((mI-dI)/N, mI, N)]\n",
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" \n",
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" def update(self, x):\n",
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" activity = np.array([neuron(x) for neuron in self.neurons])\n",
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" num_active = np.sum(activity > 0.5)\n",
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" return num_active / self.N * self.mI * self.gain + np.random.normal(0.0, self.noise)\n",
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"\n",
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"class LinearLayer(Layer):\n",
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" def __init__(self, name, gain, gain_noise, noise):\n",
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" super().__init__(name)\n",
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" self.neuron = linear_neuron(gain, gain_noise, noise)\n",
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" \n",
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" def update(self, x):\n",
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" return self.neuron(x)\n",
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" \n",
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"def step(network, input_layer, memory, i):\n",
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" input_layer.set(i)\n",
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" network.step()\n",
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" return memory.output\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"T = np.linspace(0, 20, 100)\n",
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"I = np.zeros(T.size)\n",
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"I[(0.2 < T) & (T < 0.3)] = 1.0\n",
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"I[(2.5 < T) & (T < 3.5)] = 1.0\n",
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"I[(7.5 < T) & (T < 8)] = -1.0\n",
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"I[(12 < T) & (T < 15)] = (T[(12 < T) & (T < 15)]-12)*0.05\n",
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"\n",
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"plt.figure()\n",
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"plt.plot(T, I)\n",
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"plt.plot(T, np.cumsum(I))\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"network = RecurrentNetwork()\n",
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"\n",
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"input_layer = network.add_layer(InputLayer(\"in\"))\n",
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"memory = network.add_layer(BistableLayer(\"mem\", 40, 0.1, 10, 1.00, 0.00, 0.05))\n",
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"#memory = network.add_layer(LinearLayer(\"mem\", 1.0, 0.00, 0.05))\n",
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"\n",
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"network.add_connection(WeightedConnection(\"in\", \"mem\", 1.00))\n",
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"network.add_connection(WeightedConnection(\"mem\", \"mem\", 1.03))\n",
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"\n",
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"output = np.array([step(network, input_layer, memory, i) for i in I])\n",
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"\n",
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"plt.figure()\n",
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"plt.plot(T, I, label=\"input\")\n",
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"plt.plot(T, np.cumsum(I), label=\"true integral\")\n",
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"plt.plot(T, output, label=\"memory\")\n",
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"plt.legend()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "pim",
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"language": "python",
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"name": "pim"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}

‎notebooks/bistable/bistable.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "4c160e3b-e582-41bb-837f-8243f7810d98",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import plotly.express as px\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "45ac964e-91fb-4992-9b34-90b12a47527c",
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"metadata": {},
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"outputs": [],
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"source": [
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"class BistableNeuron:\n",
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" def __init__(self, Idown, Iup, noise = 0.05):\n",
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" self.Iup = Iup\n",
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" self.Idown = Idown\n",
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" self.state = 0\n",
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" self.noise = noise\n",
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" \n",
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" def update(self, I):\n",
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" if I > self.Iup:\n",
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" self.state = 1\n",
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" elif I < self.Idown:\n",
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" self.state = 0\n",
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" return self.state * 1.0 * I + np.random.normal(0, self.noise)\n",
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" \n",
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"def simulate(neuron, T, I):\n",
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" return np.array(\n",
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" [neuron.update(i) for i in I]\n",
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" )"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d3c24b72-230f-4657-8493-57ac479bccc9",
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"metadata": {},
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"outputs": [],
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"source": [
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"neuron = BistableNeuron(0.4, 0.6)\n",
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"\n",
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"T = np.linspace(0, 2, 100)\n",
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"\n",
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"def I(t):\n",
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" I = t.copy()\n",
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" I[t > 1] = (2 - t)[t > 1]\n",
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" return I\n",
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"\n",
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"plt.figure()\n",
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"plt.plot(T, I(T), label=\"input\")\n",
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"plt.plot(T, np.ones(T.size) * neuron.Idown, label=\"I_down\")\n",
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"plt.plot(T, np.ones(T.size) * neuron.Iup, label=\"I_up\")\n",
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"\n",
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"#plt.figure()\n",
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"y = simulate(neuron, T, I(T))\n",
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"plt.plot(T, y, label=\"output\")\n",
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"plt.xlabel(\"time\")\n",
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"plt.ylabel(\"activity\")\n",
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"\n",
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"plt.legend()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "79a3eee1-6bc4-4928-b621-6c3fc20fc2a7",
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"metadata": {},
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"outputs": [],
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"source": [
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"N = 40\n",
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"dI = 0.05\n",
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"neurons = [BistableNeuron(I, I+dI, noise=0.01) for n in range(0, N) for I in (np.random.uniform(0-dI, 1-dI),)]\n",
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"\n",
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"plt.figure()\n",
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"n = np.zeros(T.size)\n",
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"for neuron in neurons:\n",
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" y = simulate(neuron, T, I(T))\n",
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" n += y > I(T) / 2 + 0.05\n",
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" plt.plot(T, y)\n",
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" \n",
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"plt.figure()\n",
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"plt.plot(T, I(T))\n",
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"plt.plot(T, n / N)\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "pim",
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"language": "python",
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"name": "pim"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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