{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "import nengo\n", "%load_ext nengo.ipynb\n", "from nengo.dists import Uniform\n", "from nengo.utils.ensemble import tuning_curves\n", "from nengo.utils.ipython import hide_input\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "def aligned(n_neurons, radius=0.9):\n", " intercepts = np.linspace(-radius, radius, n_neurons)\n", " encoders = np.tile([[1], [-1]], (n_neurons // 2, 1))\n", " intercepts *= encoders[:, 0]\n", " return intercepts, encoders\n", "\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "text": [ "" ] }, { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 1, "text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction \n", "The Neural Engineering Framework (NEF) is the set of theoretical methods that are used in Nengo for constructing neural models. The NEF is based on Eliasmith & Anderson's (2003) book from MIT Press. This notebook introduces the three main principles discussed in that book and implemented in Nengo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Principle 1: Representation\n", "\n", "## Encoding\n", "\n", "Neural populations represent time-varying signals through their spiking responses. A signal is a vector of real numbers of arbitrary length. This example is a 1D signal going from -1 to 1 in 1 second." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = nengo.Network(label=\"NEF summary\")\n", "with model:\n", " input = nengo.Node(lambda t: t * 2 - 1)\n", " input_probe = nengo.Probe(input)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(1.0)\n", "\n", "plt.plot(sim.trange(), sim.data[input_probe], lw=2)\n", "plt.title(\"Input signal\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.xlim(0, 1);\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "These signals drive neural populations based on each neuron's *tuning curve* (which is similar to the I-F (current-frequency) curve, if you're familiar with that).\n", "\n", "The tuning curve describes how much a particular neuron will fire as a function of the input signal." ] }, { "cell_type": "code", "collapsed": false, "input": [ "intercepts, encoders = aligned(8) # Makes evenly spaced intercepts\n", "with model:\n", " A = nengo.Ensemble(8, dimensions=1,\n", " intercepts=intercepts,\n", " max_rates=Uniform(80, 100), \n", " encoders=encoders)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", "\n", " eval_points, activities = tuning_curves(A, sim)\n", "plt.plot(eval_points, activities, lw=2)\n", "plt.xlabel(\"Input signal\")\n", "plt.ylabel(\"Firing rate (Hz)\");\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "output_type": "display_data", "png": 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bbkmS8PX1ZciQIXKl0W1MTZ2Wb+Iy+Cgi+coMYBdbc+YO0VcA2Vm0XgXQZYQQ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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can drive these neurons with our input signal and observe their spiking activity over time." ] }, { "cell_type": "code", "collapsed": false, "input": [ "with model:\n", " nengo.Connection(input, A)\n", " A_spikes = nengo.Probe(A.neurons)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(1)\n", "\n", "ax = plt.subplot(1, 1, 1)\n", "rasterplot(sim.trange(), sim.data[A_spikes], ax)\n", "ax.set_xlim(0, 1)\n", "ax.set_ylabel('Neuron')\n", "ax.set_xlabel('Time (s)');\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "output_type": "display_data", "png": 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AxpGtImJanYEDFQAAgPZwDwAAMkUAAECmCAAAyBQBAACZIgAAIFOtB4DtA2w/bPsR26eN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\nADL1/xMtjV7atkw5AAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Decoding\n", "\n", "We can estimate the input signal originally encoded by decoding the pattern of spikes. To do this, we first filter the spike train with a temporal filter that accounts for postsynaptic current (PSC) activity." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = nengo.Network(label=\"NEF summary\")\n", "with model:\n", " input = nengo.Node(lambda t: t * 2 - 1)\n", " input_probe = nengo.Probe(input)\n", " intercepts, encoders = aligned(8) # Makes evenly spaced intercepts\n", " A = nengo.Ensemble(8, dimensions=1,\n", " intercepts=intercepts,\n", " max_rates=Uniform(80, 100), \n", " encoders=encoders)\n", " nengo.Connection(input, A)\n", " A_spikes = nengo.Probe(A.neurons, synapse=0.01)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(1)\n", "\n", "scale = 180\n", "for i in range(A.n_neurons):\n", " plt.plot(sim.trange(), sim.data[A_spikes][:,i] - i*scale)\n", "plt.xlim(0, 1)\n", "plt.ylim(scale * (-A.n_neurons+1), scale)\n", "plt.ylabel(\"Neuron\")\n", "plt.yticks(np.arange(scale/1.8, (-A.n_neurons + 1) * scale, -scale), np.arange(A.n_neurons));\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "output_type": "display_data", "png": 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bBUHH4prb1V8ch03BYbfxzCXDaXN5uOmNdZKEurYj2kiNDefR8wezdm89v/mk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\nKQKfJSUl4mh2RVFXP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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we mulitply those filtered spike trains with decoding weights and sum them together to give an estimate of the input based on the spikes.\n", "\n", "The decoding weights are determined by minimizing the squared difference between the decoded estimate and the actual input signal." ] }, { "cell_type": "code", "collapsed": false, "input": [ "with model:\n", " A_probe = nengo.Probe(A, synapse=0.01) # 10ms PSC filter" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(1)\n", "\n", "plt.plot(sim.trange(), sim.data[input_probe], label=\"Input signal\")\n", "plt.plot(sim.trange(), sim.data[A_probe], label=\"Decoded estimate\")\n", "plt.legend(loc=\"best\")\n", "plt.xlim(0, 1);\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 11, "text": [ "" ] }, { "output_type": "display_data", "png": 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vhBBLhRAp9WOFENOFEJuEEAvsf+e2x3sNDPZM+BBCkPN24YyWTa3KPRSUBhNC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\nsixFaR5Q6yGXpIYQc0ixpLu8pjSEUDg1skg383j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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The accuracy of the decoded estimate increases as the number of neurons increases." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = nengo.Network(label=\"NEF summary\")\n", "with model:\n", " input = nengo.Node(lambda t: t * 2 - 1)\n", " input_probe = nengo.Probe(input)\n", " A = nengo.Ensemble(30, dimensions=1, max_rates=Uniform(80, 100))\n", " nengo.Connection(input, A)\n", " A_spikes = nengo.Probe(A.neurons)\n", " A_probe = nengo.Probe(A, synapse=0.01)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(1)\n", "\n", "plt.figure(figsize=(15, 3.5))\n", "\n", "plt.subplot(1, 3, 1)\n", "eval_points, activities = tuning_curves(A, sim)\n", "plt.plot(eval_points, activities, lw=2)\n", "plt.xlabel(\"Input signal\")\n", "plt.ylabel(\"Firing rate (Hz)\")\n", "\n", "ax = plt.subplot(1, 3, 2)\n", "rasterplot(sim.trange(), sim.data[A_spikes], ax)\n", "plt.xlim(0, 1)\n", "plt.xlabel(\"Time (s)\")\n", "plt.ylabel(\"Neuron\")\n", "\n", "plt.subplot(1, 3, 3)\n", "plt.plot(sim.trange(), sim.data[input_probe], label=\"Input signal\")\n", "plt.plot(sim.trange(), sim.data[A_probe], label=\"Decoded esimate\")\n", "plt.legend(loc=\"best\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.xlim(0, 1);\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "output_type": "display_data", "png": 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5c+YgSRJjxozh008/rT5Dd/z4cUpLSxk1ahTLli2jrMz0XSwvLw8XFxfc3NzY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\nW5hGzjXXkv/ppwAE3n477VavwmvQIPKeeZDTkyZ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vYrNVtGhtKSVpaV8Rv3M8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2AAAg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\nNuya4d+jjQ0br8frdZCTcwbZ2aeEGlgr4ZNblPbx9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yI8726wUffkWjpX1iKMOlLOGEHq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\nMAzDMAzDWIa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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Any smooth signal can be encoded and decoded." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from nengo.processes import WhiteSignal\n", "\n", "model = nengo.Network(label=\"NEF summary\")\n", "with model:\n", " input = nengo.Node(WhiteSignal(1, high=5), size_out=1)\n", " input_probe = nengo.Probe(input)\n", " A = nengo.Ensemble(30, dimensions=1, max_rates=Uniform(80, 100))\n", " nengo.Connection(input, A)\n", " A_spikes = nengo.Probe(A.neurons)\n", " A_probe = nengo.Probe(A, synapse=0.01)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(1)\n", "\n", "plt.figure(figsize=(10, 3.5))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(sim.trange(), sim.data[input_probe], label=\"Input signal\")\n", "plt.plot(sim.trange(), sim.data[A_probe], label=\"Decoded esimate\")\n", "plt.legend(loc=\"best\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.xlim(0, 1)\n", "\n", "ax = plt.subplot(1, 2, 2)\n", "rasterplot(sim.trange(), sim.data[A_spikes], ax)\n", "plt.xlim(0, 1)\n", "plt.xlabel(\"Time (s)\")\n", "plt.ylabel(\"Neuron\");\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 15, "text": [ "" ] }, { "output_type": "display_data", "png": 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1/3hgVD/qduS0XpnRuiQCLV31jiGZxhoLZIxZiM2NwlCamBkbU+36G5OczitW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\nv/12UlNTSUtL49ZbawcKd9xxBwD5+fkefZWVlYwfP57s7Gx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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Principle 2: Transformation\n", "\n", "Encoding and decoding allow us to encode signals over time, and decode transformations of those signals.\n", "\n", "In fact, we can decode arbitrary transformations of the input signal, not just the signal itself (as in the previous example).\n", "\n", "Let's decode the square of our white noise input." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = nengo.Network(label=\"NEF summary\")\n", "with model:\n", " input = nengo.Node(WhiteSignal(1, high=5), size_out=1)\n", " input_probe = nengo.Probe(input,)\n", " A = nengo.Ensemble(30, dimensions=1, max_rates=Uniform(80, 100))\n", " Asquare = nengo.Node(size_in=1)\n", " nengo.Connection(input, A)\n", " nengo.Connection(A, Asquare, function=np.square)\n", " A_spikes = nengo.Probe(A.neurons)\n", " Asquare_probe = nengo.Probe(Asquare, synapse=0.01)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(1)\n", "\n", "plt.figure(figsize=(10, 3.5))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(sim.trange(), sim.data[input_probe], label=\"Input signal\")\n", "plt.plot(sim.trange(), sim.data[Asquare_probe], label=\"Decoded esimate\")\n", "plt.plot(sim.trange(), np.square(sim.data[input_probe]), label=\"Input signal squared\")\n", "plt.legend(loc=\"best\", fontsize='medium')\n", "plt.xlabel(\"Time (s)\")\n", "plt.xlim(0, 1)\n", "\n", "ax = plt.subplot(1, 2, 2)\n", "rasterplot(sim.trange(), sim.data[A_spikes])\n", "plt.xlim(0, 1)\n", "plt.xlabel(\"Time (s)\")\n", "plt.ylabel(\"Neuron\");\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 17, "text": [ "" ] }, { "output_type": "display_data", "png": 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ExERaW1sBCA0NNZeXUnLVVVeRn59Pfn4+hw8f5uWXX/bouS0pqW3hWHmjeT0a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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the spike trains are exactly the same. The only difference is how we're interpreting those spikes. We told Nengo to compute a new set of decoders that estimate the function $x^2$.\n", "\n", "In general, the transformation principle determines how we can decode spike trains to compute linear and nonlinear transformations of signals encoded in a population of neurons. We can then project those transformed signals into another population, and repeat the process. Essentially, this provides a means of computing the neural connection weights to compute an arbitrary function between populations.\n", "\n", "Suppose we are representing a sine wave." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = nengo.Network(label=\"NEF summary\")\n", "with model:\n", " input = nengo.Node(lambda t: np.sin(np.pi * t))\n", " A = nengo.Ensemble(30, dimensions=1, max_rates=Uniform(80, 100))\n", " nengo.Connection(input, A)\n", " A_spikes = nengo.Probe(A.neurons)\n", " A_probe = nengo.Probe(A, synapse=0.01)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(2)\n", "\n", "plt.figure(figsize=(10, 3.5))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(sim.trange(), sim.data[A_probe])\n", "plt.title(\"A\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.xlim(0, 2)\n", "\n", "ax = plt.subplot(1, 2, 2)\n", "rasterplot(sim.trange(), sim.data[A_spikes], ax)\n", "plt.xlim(0, 2)\n", "plt.title(\"A\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.ylabel(\"Neuron\");\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 19, "text": [ "" ] }, { "output_type": "display_data", "png": 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yl7idzknf1HHql5fxcYr7kQ269btVKIeYN1nHzG5v0nYtypPiIpLyIgDJDGXa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\ngCEADs1xkwghBQQdM0IIsUAptQ3AFMQfXbYREX1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"text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear transformations of that signal involve solving for the usual decoders, and scaling those decoding weights. Let us flip this sine wave upside down as it is transmitted between two populations (i.e. population A and population -A)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "with model:\n", " minusA = nengo.Ensemble(30, dimensions=1, max_rates=Uniform(80, 100))\n", " nengo.Connection(A, minusA, function=lambda x: -x)\n", " minusA_spikes = nengo.Probe(minusA.neurons)\n", " minusA_probe = nengo.Probe(minusA, synapse=0.01)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(2)\n", "\n", "plt.figure(figsize=(10, 5))\n", "plt.subplot(2, 2, 1)\n", "plt.plot(sim.trange(), sim.data[A_probe])\n", "plt.title(\"A\")\n", "plt.xticks(())\n", "plt.xlim(0, 2)\n", "\n", "plt.subplot(2,2,3)\n", "plt.plot(sim.trange(), sim.data[minusA_probe])\n", "plt.title(\"-A\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.xlim(0, 2)\n", "\n", "ax = plt.subplot(2,2,2)\n", "rasterplot(sim.trange(), sim.data[A_spikes], ax)\n", "plt.xlim(0, 2)\n", "plt.title(\"A\")\n", "plt.xticks(())\n", "plt.ylabel(\"Neuron\")\n", "\n", "ax = plt.subplot(2,2,4)\n", "rasterplot(sim.trange(), sim.data[minusA_spikes], ax)\n", "plt.xlim(0, 2)\n", "plt.title(\"-A\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.ylabel(\"Neuron\");\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 21, "text": [ "" ] }, { "output_type": "display_data", "png": 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AGwBn1Co9cLoUt8xd52aPiQrDe5OHIDkmEsfPV3gbOxMAHBOzECHgOHyhZUTD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\nsQBBBrHGmE12uAb4AGsLeuS88MOBjO7Ziv62S4aT7MOxC/OOd7MghZ2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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nonlinear transformations involve solving for a new set of decoding weights. Let us add a third population connected to the second one and use it to compute $(-A)^2$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "with model:\n", " A_squared = nengo.Ensemble(30, dimensions=1, max_rates=Uniform(80, 100))\n", " nengo.Connection(minusA, A_squared, function=lambda x: x ** 2)\n", " A_squared_spikes = nengo.Probe(A_squared.neurons)\n", " A_squared_probe = nengo.Probe(A_squared, synapse=0.02)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(2)\n", "\n", "plt.figure(figsize=(10, 6.5))\n", "plt.subplot(3, 2, 1)\n", "plt.plot(sim.trange(), sim.data[A_probe])\n", "plt.axhline(0, color='k')\n", "plt.title(\"A\")\n", "plt.xticks(())\n", "plt.xlim(0, 2)\n", "\n", "plt.subplot(3, 2, 3)\n", "plt.plot(sim.trange(), sim.data[minusA_probe])\n", "plt.axhline(0, color='k')\n", "plt.title(\"-A\")\n", "plt.xticks(())\n", "plt.xlim(0, 2)\n", "\n", "plt.subplot(3, 2, 5)\n", "plt.plot(sim.trange(), sim.data[A_squared_probe])\n", "plt.axhline(0, color='k')\n", "plt.title(\"(-A)^2\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.xlim(0, 2)\n", "\n", "ax = plt.subplot(3, 2, 2)\n", "rasterplot(sim.trange(), sim.data[A_spikes], ax)\n", "plt.xlim(0, 2)\n", "plt.title(\"A\")\n", "plt.xticks(())\n", "plt.ylabel(\"Neuron\")\n", "\n", "ax = plt.subplot(3, 2, 4)\n", "rasterplot(sim.trange(), sim.data[minusA_spikes], ax)\n", "plt.xlim(0, 2)\n", "plt.title(\"-A\")\n", "plt.xticks(())\n", "plt.ylabel(\"Neuron\")\n", "\n", "ax = plt.subplot(3, 2, 6)\n", "rasterplot(sim.trange(), sim.data[A_squared_spikes], ax)\n", "plt.xlim(0, 2)\n", "plt.title(\"(-A)^2\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.ylabel(\"Neuron\");\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 23, "text": [ "" ] }, { "output_type": "display_data", "png": 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GdsIe1MbXaG605jEkqXlLO9pUpxdexzUODe3/0nLdfNPGdMKfL2+HlKaNADj3cyU08n0h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\nJ74ORz8E+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"text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Principle 3: Dynamics\n", "\n", "So far, we have been considering the values represented by ensembles as generic \"signals.\" However, if we think of them instead as state variables in a dynamical system, then we can apply the methods of control theory or dynamic systems theory to brain models. Nengo automatically translates from standard dynamical systems descriptions to descriptions consistent with neural dynamics.\n", "\n", "In order to get interesting dynamics, we can connect populations recurrently (i.e., to themselves).\n", "\n", "Below is a simple harmonic oscillator implemented using this third principle. It needs is a bit of input to get it started." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = nengo.Network(label=\"NEF summary\")\n", "with model:\n", " input = nengo.Node(lambda t: [1,0] if t < 0.1 else [0,0])\n", " oscillator = nengo.Ensemble(200, dimensions=2)\n", " nengo.Connection(input, oscillator)\n", " nengo.Connection(oscillator, oscillator,\n", " transform=[[1, 1], [-1, 1]], synapse=0.1)\n", " oscillator_probe = nengo.Probe(oscillator, synapse=0.02)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "with nengo.Simulator(model) as sim:\n", " sim.run(3)\n", "\n", "plt.figure(figsize=(10, 3.5))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(sim.trange(), sim.data[oscillator_probe])\n", "plt.ylim(-1.2, 1.2)\n", "plt.xlabel('Time (s)')\n", "\n", "plt.subplot(1,2,2)\n", "plt.plot(sim.data[oscillator_probe][:,0], sim.data[oscillator_probe][:,1])\n", "plt.grid()\n", "plt.axis([-1.2, 1.2, -1.2, 1.2])\n", "plt.xlabel('$x_1$')\n", "plt.ylabel('$x_2$');\n", "hide_input()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " Show Input\n", "\n", " \n", " " ], "output_type": "pyout", "prompt_number": 25, "text": [ "" ] }, { "output_type": "display_data", "png": 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u0+pJ6bb7UI5OjcDHOwq91+i85qTnj8HoFbRp9Dhe1oz4UPNvIytBif9cnIUl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\ntHofgtWm6PMNB9h5s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