{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Memory: A Cognitive Modeling Perspective\n", "\n", "From a modelling stand-point, different types of memory are not super well-defined at a psychological level.\n", "\n", "For the purposes of this lecture, we're just going to focus on time-frame:\n", "- Long-term memory *(t > days)*\n", "- Short-term or working memory *(t < a few minutes)*" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "import nengo\n", "import nengo.spa as spa" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Short-Term: Integrators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Previously showed how integrators could save a scalar." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "dimensions = 3\n", "n_neurons = 50\n", "\n", "feedback = 1.0\n", "feedback_synapse = 0.1\n", "\n", "model = nengo.Network(\"integrator mem\")\n", "with model:\n", " inp = nengo.Node([0, 0, 0])\n", " reset = nengo.Node([0])\n", " state = nengo.networks.EnsembleArray(50, dimensions)\n", " state.add_neuron_input()\n", " \n", " nengo.Connection(inp, state.input)\n", " nengo.Connection(state.output, state.input, transform=feedback, synapse=feedback_synapse)\n", " nengo.Connection(reset, state.neuron_input, transform=-3*np.ones((n_neurons*dimensions, 1)))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo_gui.ipython import IPythonViz\n", "IPythonViz(model, \"configs/integ_mem.py.cfg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: you can [engineer a working memory even further](https://github.com/nengo/nengo/blob/master/nengo/networks/workingmemory.py), by essentially making a flip-flop in neurons. This is not necessary for this tutorial." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A SPA pointer is just a vector of scalars, so a memory can be an array of integrators." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "dimensions = 32\n", "vocab = spa.Vocabulary(dimensions)\n", "vocab.parse(\"CIRCLE+BLUE+SQUARE+RED\")\n", "\n", "model = spa.SPA(vocabs=[vocab], label=\"Simple question answering\")\n", "\n", "with model:\n", " model.color_in = spa.State(dimensions=dimensions)\n", " model.shape_in = spa.State(dimensions=dimensions)\n", " model.conv = spa.State(dimensions=dimensions,\n", " neurons_per_dimension=100,\n", " feedback=1,\n", " feedback_synapse=0.4)\n", " model.cue = spa.State(dimensions=dimensions)\n", " model.out = spa.State(dimensions=dimensions)\n", "\n", " # Connect the state populations\n", " cortical_actions = spa.Actions(\n", " 'conv = color_in * shape_in',\n", " 'out = conv * ~cue'\n", " )\n", " model.cortical = spa.Cortical(cortical_actions)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo_gui.ipython import IPythonViz\n", "IPythonViz(model, \"configs/mem_q.py.cfg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Reading\n", "\n", "- Integrator-based memories to model list memorisation [Choo et al. 2010](http://compneuro.uwaterloo.ca/publications/choo2010a.html)\n", "- Approximating the delay function on a recurrent connection to model temporal memory [Voelker et al. 2018](http://compneuro.uwaterloo.ca/publications/voelker2018.html)\n", "- Creating a stack-like memory in neurons for action planning [Blouw et al. 2016](http://compneuro.uwaterloo.ca/publications/Blouw2016.html)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Long-Term: Cleanup and Associative Memories" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result of an unbinding operation is a noisy result. If this result is going to be used, you often want to clean it up." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cleanup memories are based on the same idea the Basal Ganglia uses. Each population of neurons is a pointer symbol, rather than an action. However, you still only want one symbol to be output." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But a cleanup memory works under fewer constraints. It doesn't need to scale to hundreds of highly similar pointers, so it can trade scale and robustness for response speed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you want to instead output a different pointer instead of just cleaning up the input pointer, you just apply a weight transform on the output." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_similarities(input_data,\n", " output_data,\n", " vocab1,\n", " vocab2=None,\n", " autoscale=False):\n", " if vocab2 is None:\n", " vocab2 = vocab1\n", "\n", " ymin, ymax = -1.2, 1.2\n", " plt.figure(figsize=(12, 4))\n", " plt.subplot(1, 2, 1)\n", " plt.ylim(ymin, ymax)\n", " if autoscale:\n", " plt.autoscale(autoscale, axis='y')\n", " plt.grid(True)\n", " plt.plot(t, spa.similarity(input_data, vocab1))\n", " plt.title(\"Input similarity\")\n", " plt.xlabel(\"Time\")\n", " plt.xlim(right=t[-1])\n", " plt.legend(\n", " vocab1.keys, loc='upper center', bbox_to_anchor=(0.5, -0.13), ncol=3)\n", "\n", " plt.subplot(1, 2, 2)\n", " plt.plot(t, spa.similarity(output_data, vocab2))\n", " plt.title(\"Output similarity\")\n", " plt.xlabel(\"Time\")\n", " plt.xlim(right=t[-1])\n", " plt.ylim(ymin, ymax)\n", " if autoscale:\n", " plt.autoscale(autoscale, axis='y')\n", " plt.grid(True)\n", " plt.legend(\n", " vocab2.keys, loc='upper center', bbox_to_anchor=(0.5, -0.13), ncol=3)\n", " plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim = 16\n", "vocab_numbers = spa.Vocabulary(dimensions=dim)\n", "\n", "# a quicker way to add words to a vocabulary\n", "vocab_numbers.parse('ONE + TWO + THREE + FOUR + FIVE')" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# example using nengo.spa\n", "def input_fun(t):\n", " if t < 0.2:\n", " return 'ONE'\n", " elif t < 0.4:\n", " return 'TWO'\n", " elif t < 0.6:\n", " return 'THREE'\n", " elif t < 0.8:\n", " return 'FOUR'\n", " else:\n", " return '0'\n", "\n", "\n", "# from patterns\n", "input_keys = ['ONE', 'TWO', 'THREE', 'FOUR']\n", "\n", "# to patterns\n", "output_keys = ['TWO', 'THREE', 'FOUR', 'FIVE']\n", "\n", "with spa.SPA('Counting', seed=1) as model:\n", " model.assoc_mem = spa.AssociativeMemory(\n", " input_vocab=vocab_numbers,\n", " output_vocab=vocab_numbers,\n", " input_keys=input_keys,\n", " output_keys=output_keys,\n", " wta_output=True)\n", "\n", " model.am_input = spa.Input(assoc_mem=input_fun)\n", "\n", " input_probe = nengo.Probe(model.assoc_mem.input)\n", " output_probe = nengo.Probe(model.assoc_mem.output, synapse=0.03)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "ename": "NameError", "evalue": "name 'plot_similarities' is not defined", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 6\u001b[0m \u001b[0moutput_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msim\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0moutput_probe\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 8\u001b[1;33m \u001b[0mplot_similarities\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minput_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0moutput_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvocab_numbers\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mautoscale\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;31mNameError\u001b[0m: name 'plot_similarities' is not defined" ] } ], "source": [ "with nengo.Simulator(model) as sim:\n", " sim.run(1.)\n", "t = sim.trange()\n", "\n", "input_data = sim.data[input_probe]\n", "output_data = sim.data[output_probe]\n", "\n", "plot_similarities(input_data, output_data, vocab_numbers, autoscale=True)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo_gui.ipython import IPythonViz\n", "IPythonViz(model, \"configs/bg_count.py.cfg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note**: If you look at the internals of the memory, you'll find a \"bias node\", because it's easier to modify a bias than change neuron intercepts for the purposes of optimization. Looking inside a network and finding something slightly different than you expected for optimisation reasons is a typical experience in Nengo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning Memories" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can we learn a network to perform cleanup and association using PES?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "num_items = 5\n", "\n", "d_key = 2\n", "d_value = 2\n", "\n", "rng = np.random.RandomState(seed=7)\n", "keys = nengo.dists.UniformHypersphere(surface=True).sample(\n", " num_items, d_key, rng=rng)\n", "values = nengo.dists.UniformHypersphere(surface=False).sample(\n", " num_items, d_value, rng=rng)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def cycle_array(x, period, dt=0.001):\n", " \"\"\"Cycles through the elements\"\"\"\n", " i_every = int(round(period / dt))\n", " if i_every != period / dt:\n", " raise ValueError(\"dt (%s) does not divide period (%s)\" % (dt, period))\n", "\n", " def f(t):\n", " i = int(round((t - dt) / dt)) # t starts at dt\n", " return x[int(i / i_every) % len(x)]\n", "\n", " return f" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Model constants\n", "n_neurons = 200\n", "dt = 0.001\n", "period = 0.3\n", "T = period * num_items * 2\n", "\n", "# Model network\n", "model = nengo.Network()\n", "with model:\n", "\n", " # Create the inputs/outputs\n", " stim_keys = nengo.Node(output=cycle_array(keys, period, dt))\n", " stim_values = nengo.Node(output=cycle_array(values, period, dt))\n", " learning = nengo.Node(output=lambda t: -int(t >= T / 2))\n", " recall = nengo.Node(size_in=d_value)\n", "\n", " # Create the memory\n", " memory = nengo.Ensemble(\n", " n_neurons, d_key)\n", "\n", " conn_in = nengo.Connection(\n", " stim_keys, memory, synapse=None)\n", "\n", " # Learn the decoders/values, initialized to a null function\n", " conn_out = nengo.Connection(\n", " memory,\n", " recall,\n", " learning_rule_type=nengo.PES(1e-3),\n", " function=lambda x: np.zeros(d_value))\n", "\n", " # Create the error population\n", " error = nengo.Ensemble(n_neurons, d_value)\n", " nengo.Connection(\n", " learning, error.neurons, transform=[[10.0]] * n_neurons, synapse=None)\n", "\n", " # Calculate the error and use it to drive the PES rule\n", " nengo.Connection(stim_values, error, transform=-1, synapse=None)\n", " nengo.Connection(recall, error, synapse=None)\n", " nengo.Connection(error, conn_out.learning_rule)\n", "\n", " # Setup probes\n", " p_keys = nengo.Probe(stim_keys, synapse=None)\n", " p_values = nengo.Probe(stim_values, synapse=None)\n", " p_learning = nengo.Probe(learning, synapse=None)\n", " p_error = nengo.Probe(error, synapse=0.005)\n", " p_recall = nengo.Probe(recall, synapse=None)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:02. \n" ] } ], "source": [ "with nengo.Simulator(model, dt=dt) as sim:\n", " sim.run(T)\n", "t = sim.trange()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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DwNGdhCEYHZ86VZ1xvfJvFBxZM7jstlcAMk9fMfM5c9z2Y6jVyMfOPFopKfF5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\n/j+mKQvzxTk10gAAAABJRU5ErkJggg==\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.title(\"Keys\")\n", "plt.plot(t, sim.data[p_keys])\n", "plt.ylim(-1, 1)\n", "\n", "plt.figure()\n", "plt.title(\"Values\")\n", "plt.plot(t, sim.data[p_values])\n", "plt.ylim(-1, 1)\n", "\n", "plt.figure()\n", "plt.title(\"Learning\")\n", "plt.plot(t, sim.data[p_learning])\n", "plt.ylim(-1.2, 0.2);" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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fwaN9eGbibLZW+vhlpfUfXbW5goPumcRjkxZY19XDveH3j6qWoY5pUIrBaeyK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\nWrFcUWrBnw/dPWp94N5t6kkSJZuprcXwK3AK8HW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u8hIaJMUzY/k2pizyt71f/cYC1jx8Epe++gOzVwafR/Ln9xYy+adN5dzf/WFD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\nGJTw4i1hKCmxm9bU18lqB8LoifYzf09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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "train = t <= T / 2\n", "test = ~train\n", "\n", "plt.figure()\n", "plt.title(\"Value Error During Training\")\n", "plt.plot(t[train], sim.data[p_error][train])\n", "\n", "plt.figure()\n", "plt.title(\"Value Error During Recall\")\n", "plt.plot(t[test], sim.data[p_recall][test] - sim.data[p_values][test]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PES is proportional to the neurons spiking, but if a neuron is spiking for a bunch of inputs, the decoders of the neuron never converge.\n", "\n", "Let's change the encoders so the neurons are more selective." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "intercepts = [0.7] * n_neurons\n", "encoders = []\n", "\n", "for n_i in range(n_neurons):\n", " k_i = n_i%len(keys)\n", " tmp_enc = keys[k_i] + np.random.normal(0, 0.1, size=2)\n", " encoders.append(tmp_enc / np.linalg.norm(tmp_enc))\n", "\n", "encoders = np.array(encoders)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(keys[:, 0], keys[:, 1], s=150, label=\"keys\")\n", "plt.scatter(enc[:, 0], enc[:, 1], label=\"encoders\")\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Model network\n", "model = nengo.Network()\n", "with model:\n", "\n", " # Create the inputs/outputs\n", " stim_keys = nengo.Node(output=cycle_array(keys, period, dt))\n", " stim_values = nengo.Node(output=cycle_array(values, period, dt))\n", " learning = nengo.Node(output=lambda t: -int(t >= T / 2))\n", " recall = nengo.Node(size_in=d_value)\n", "\n", " # Create the memory\n", " memory = nengo.Ensemble(\n", " n_neurons, d_key, intercepts=intercepts, encoders=encoders)\n", "\n", " conn_in = nengo.Connection(\n", " stim_keys, memory, synapse=None)\n", "\n", " # Learn the decoders/values, initialized to a null function\n", " conn_out = nengo.Connection(\n", " memory,\n", " recall,\n", " learning_rule_type=nengo.PES(1e-3),\n", " function=lambda x: np.zeros(d_value))\n", "\n", " # Create the error population\n", " error = nengo.Ensemble(n_neurons, d_value)\n", " nengo.Connection(\n", " learning, error.neurons, transform=[[10.0]] * n_neurons, synapse=None)\n", "\n", " # Calculate the error and use it to drive the PES rule\n", " nengo.Connection(stim_values, error, transform=-1, synapse=None)\n", " nengo.Connection(recall, error, synapse=None)\n", " nengo.Connection(error, conn_out.learning_rule)\n", "\n", " # Setup probes\n", " p_keys = nengo.Probe(stim_keys, synapse=None)\n", " p_values = nengo.Probe(stim_values, synapse=None)\n", " p_learning = nengo.Probe(learning, synapse=None)\n", " p_error = nengo.Probe(error, synapse=0.005)\n", " p_recall = nengo.Probe(recall, synapse=None)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:02. \n" ] } ], "source": [ "with nengo.Simulator(model, dt=dt) as sim:\n", " sim.run(T)\n", "t = sim.trange()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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rRVu465NF8M2D8OsrfPfeY0xbvCUF0idJ8GJy52Pju+6lkfD2WPB6YOU3qZNn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\n", 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o3MVfAw8zImMJHW/PZ82SufSYdtIej/9L+blcGnibjrJ3ua7eDx3Oif6vGV86\niRez7gDgmW63c/yah3g0dArSYQDPre/MFf7/cXPGVAA2mxY084fJCVcfeLbN5NJa6j7D3Ne5Izh8\np30avKP8Yk68bDLH9t23rssi8qUxpvrjYRUS9vxFxA88CJwMFABzRWSGMSY2Y9pPgK3GmANEZALw\nZ+C8ROtWLEL1x0SXhR8qwj6ZGX447DxY/h4smFbLUe6xcYdbOe6fmbMGvwgrCq2githxNQA99h9Q\n6/G/yXhhn+o90W+fZiPCD3BRwe/BB7/3PQVbYXJ25WPayg4IE5e9EX4gKvwAkzKe5vTH+3HsXT/f\nq3PsLckYLzEUyDfGrDDGlAFTgXFVyowDnvKWXwRGSUMFttKIyFNcaE/pRutAQ/wy2Rn7/tcTIXq7\ni3a/Hfdg9YIt6j6T215x3K/27bhr5lTfNubPMP6J2o/99XfM6XwhJaYiTrytuKxa2MYFYkNIEhu+\nysqlrGtyet41di7MifNfSTLJiPl3BdbGrBcAw2oqY4wJikgR0BbYFFtIRCYCEwF69NCBMnWlqli/\n5KWIbpEV4OSDOnLDSQeyenMxx/Ztx4Mf5NO2eSZ9O7bgnH99xllHdKVfpxbc7cXbrzimN5NOH8iE\nR2YzZ8UW2jTP5LObT4w29AZDYXaWBnlp3vdcMKwH20vKmb+2iKum5HFY99Y8cvFgOra0LtJtryzk\nmTm2ATTT7+PbP47llpcWcnDXltExDTtLg3z3ww6Ky0Is27CD95b+wB/GHUyvts258NHPOaBDLtee\ncADD73qPv44/lB8N7ERWho/svFXwFkRvA744f+VuQyrFePfIz+fBA1XmcWjdsyKL5GEXwPzn7PKo\nSXDoedCyC9zVrW7nP3AMdBgA5z0LnQ+D+7x0IwefDbkdoMvhsOZz+PBPEMiGPidC83bw/p3Qrh/k\ndohEv6PEzg7nMsZUfO7QqNthypgUWtMwTAi9Xu91JEP84/mJVV3PupTBGPMI8AjYmH/ipqUXBusN\nRlJOfH7rKHIy7U8cGRx27QkHRMsv+v1osgM+/D7hyF5t6N2ueXQGsscvO5IH3s/n+lF9K/XwCfh9\ntM7JjKauyM7wc/LAbJbcMabawJ87zzyEO888pNK2u86uvJ6bFYgOlDvmgHbR8wI8P7Gi733+H8cS\niB1kF2mritz5ROD6BfDx36zg794C4SrzH094Hr55FRZMrbx9zN3Qtg90HQzff2m3jb4LjroG3vi1\nHTF81r+sIPf2EgW294aZXvsFFK2F5yZA2JtP+dYfYPWntvw3r0Dz9tDLG0cy4DT7PrnKxCRt9rev\nw8+vvL3bkdDR3igkboDPdSpZujCdAAAX8klEQVTLQHbv4TWUSz7BbsPwt+yCfPNyg9XZkCQj7FMA\ndI9Z7wZU7WYRLSMiAaAVoLNu1wORrnhAVPhrIjcrQMDvQ0QY3HO/SlNP5mQGuGlM/xq7dlYlWSM+\nayJQbXR1RBRi5HC/nnDGP+AX82yKhRE3wk9n2dDKzWug/ylw5r/gvGdg0lY4+1G4cDoM/5k9/pJX\n7RPAb1ZWbDv1HrjM88IO/TG0qNJFtX0/OOAkmLQJLnzRHp+RDQeMsjekg86qEP59Yf+R9gkAQCQa\nBrn8iS+qFT3bN4uJ/tcAQwZBjpSldGQLh0k+bSni94EnaEEx5/hm4fOC1ZmUEyDIaN9c2hN/LuQA\nQVqyi2xK6SE/cL6/ooF5oKzieN98sigjizImHZ2Nn1D03O0o4lBZTh/5nh77NaMzmzlEVtCtdTYd\n2MqUjLs40TePB84/grdvGMFRXloUIcwxvoUECBOIGZEsIvyt79MVxvU+vm7fY//Tqm878qqK5VZe\npKHfKQCEj/01gSvfRs59EoZfU/3Yg86OLm7seRrGn1m9TCyZufbpL4aSEbdBTtvqZXsdZ/+f9Uwy\nPP+5QF8R6Q18D0wALqhSZgZwKTAbGA+8b5LRzUiphDGwq7SWzJ6bl9uwQquu8Nat0G8sdDkC/tTF\nCs34JyCnDZTugA/vtuGNzodWrsSEbTqE9v1sORGYdY+NhWe3Ap93IwiWgQnBhkW2S2a3wbBrEzRr\nUzEbkzH2+GApILBkBgwcZ8M4K2dZr7ltH3jtlzDi13Y5chzEb6Botp/NsROh82EVyz5fRd6fQ39c\n+bisFva1r/Q9ed+PrQOxF8wHy+yALh9hpmb+gaG+ipnefpvxfI3nuDRgQ0V/4+GEbLkr47H4O+bB\nFdnxd7EbiOwrqVge4V8IL9vR2c8TU8YjHKicwfZXF54BxSuhqAA6HQIrP4K8J2DkLfBQ1Yizx4Rn\nYXKVFBKn/BXm2kF1nHYvPDseDjsfzn++sld84u9syG7Gz2HIT2xZgNF/hJIiOnTwGqKfPA1WfWxF\nvmVXa09mc3jlZ/bmM+A0+KPnPBw6gewTb4Shl8GuQvjqGXutHHExdBjYILOVJSz+Xgz/OmwE1g88\nboxZLCJ3AHnGmBnAY8DTIpKP9fgnJFqvUkFs2/nW4jJ+GXiRS9vnw9OPwvL393zw7H9WLK/4EP7S\nG370R3j71sr7Ox8GOwthxx76zseeKxGmVx4cRSAbgiUVMfeWXWF7pO95+gRC7CeNvQUYVlQZHOYi\nvlbdq2/MaWNfYJ2W/Ufa5S6DYN0864jsfwI8Fcfjv2mVdRAitO1rb9y/+Bra9K5ePjMHBl1ihTnW\n2WjZxb4iXPQSBHdbByiWc5+qWL5tY+WcUbnt7WvMn6rXW88kZZCXMWYmMLPKtkkxyyXAj6sepyQb\nwytT7ucfmS/BVqjhKb52IsIfy/q6zUlcLwSrdGfcHjPoyF95lKTLVG3wPd9f5cbe+3jWh1qwadU3\n7DDZtJJdHHT6L2DbGlj1CbQ9wDZit+wCi6ZD2z4snfcx/c1ye3yv46Dn0fbJbNMy+wS2aDp0OMg+\nuXU6GJZ/ABsWwMAzoXQH896byqCyL1kz7HZ6bJsLR15pUy/87yZCrboTHng2svIDKNlBYMwf4aun\nocdR0HUQZtN3yGu/INR3DP5xD9i2lWb7wdrP7ZNdUQFkNIPBl9f9Szp/qnV4Im0n45+wT5tQ0aYT\nK/y/WlYxejie8MdSWze4QKZ97bFM3efxqG90hK8DxP4lrw28WnPBjJyGmwyjx9Gw5rN9O/bAsdZ7\nqtowW5Xjb2pUF1N9E+niGunKe23gVYz4kP9bCi1smvLO3mvphu22G2z7GqYxHWIFdWp4Ec/OXs7d\nPx7MOYPj9Fzaf2Tl9Z5HV1p9Z8txnPvRt7w/9GRo+3/e1lEw9Cr82FAA3F5xQL+KuLf0PBoGX0q0\ntcjL00Snyp0C9ooWHSs3mh9cEZvn4ldsiKVS+eppRtIFFX+XKCumn89LlnXQWbBfb9tY1byd9aRi\n44ilO+zNwOeHNXPg8dGQ0w6ueBMWvGCVpttQ63UPOM16U+sXwLG/tF5ksNQ2akbYtsYmz+oQk5dn\ny0p4fgKUFNnY/eUz4ZP7bAhp4Bm2TCTmX7zFhpwALvBE/+x/2/d3J8Mnf7eNszt/gMMvgPVf27aK\nNMJgG3zLgmF6yga6ySYYNTkq/LH079SyTue87bSBTDy+D11qyeZZE78e3Z9zj+xRPZFaYyS7pX0p\ngIq/E0SeRjt+eCMAG7N60GH8E5UfU6s+ssY2bHYdYns+HHM9tO4OJ8YJ+/Q50b4gfu+VeBOYtOkN\n135eeduo38U3PqdN9e6PEU6aXJGPP0KaCb/FfldrtxZznM9r0D5wz+nBayPg9+2z8AP4fRJNKaI0\nLXRGNIdokW9DPk8e+vzeDdP1B2yXxtZxGtaURoMN+xjO/fdsBsoqygK5FeMNFGUvUfF3ADv4pyLJ\nSNtW6om5SKTBd1txOSP98ylseVB6zuSjJAUVf0dohU2E9URwNG2b19LjQGmSiPfav20zOrK1QUe7\nKu6RHuJftst2USsrtn3V47HkNZhbw8CVWP4zCh46uvZy8di9DQq+rFhf9iZ88Z99O1eEzx6gxY7v\n6OClsJ0X7kuLbG3KcRPBJ4YTembgF0Pb9l1qP0RRaiA9VOLV62DxS9CmD2xZDjethnlPQfv+djTd\nW7dUJAA70htg9O/jbY+S8U/YPC3H/coONvrem2PAGAiVw5OnwrE3QP67tlFy1Sd2IvCRN1W345lz\n7PH9T4OjroPnvazWQ6+yvWWePRcKl8Clr1fkkIklHIaNi+H7eXb0a+/j4O3bGJbVhgPEDvZZYbrU\neT5VpWlhvBBPTomd/SuduykqiZMeKrHB6xmxxRvM8t/LYMUH8cuGwzDlDCv8AC96A0zmPlq53NQL\nYdkb3rLXrzgv5snBH7DnWv+1vUl891bFvqWv21eEya3sIBrjxe2fOg3OnWJTGuzeAuc8ZgczffZP\nKIjJ6bLoRVtVsIQDfQWE8ZFvupCr4u80LUu8UdbxelgpSh1xXyUK8mDzd5W31ST8AHfsV/O+WCLC\nXxPv3bHn/VUxVWaFeOGSiuWq6Q6qEAgV01/WUhJoSSmZKv7OYj3/VqUb7Grrnim0RWnquB3z37AI\nHh1VezkHGOOfS4nP9tfWsI+bRPr15JZvopxARW4bRdkH3Bb/b99MXd2HX9jgVUrYZvTUBl83icT8\ns0I7KJbm2s1TSQi3xb+mi6PrYJi0xSaYqoljfgk/eQcmPFdzmYPHx9/evIOdIKQudImZPeqCF2ze\n76pc/ibcVqWXUiT/+LH/F92UFdqF3ydkBdz+WdMX+38OlO+kxK9jOZTEcNdFDIdhccwMPP1Ps5kp\ni9baCRt8fjjxNttbJ5IyGOzkCj+vkvkvwiWvwu6tkNUSeo+wjbD9T4HCb20voU/vr5z//rfr4b5D\nbMPc+VNh2Uw74UizNvDI8fY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "train = t <= T / 2\n", "test = ~train\n", "\n", "plt.figure()\n", "plt.title(\"Value Error During Training\")\n", "plt.plot(t[train], sim.data[p_error][train])\n", "\n", "plt.figure()\n", "plt.title(\"Value Error During Recall\")\n", "plt.plot(t[test], sim.data[p_recall][test] - sim.data[p_values][test]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But this assumes our memory knows all the vocabulary ahead of time. Can we learn the encoders instead?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Voja\n", "\n", "Voja: Vector Oja [Voelker et al. 2016](http://compneuro.uwaterloo.ca/publications/voelker2016b.html)\n", "\n", "$$\n", "\\Delta e_i = \\kappa a_i (x - e_i)\n", "$$\n", "\n", "where $e_i$ is the encoder of the $i^{th}$ neuron, $\\kappa$ is a modulatory learning rate (positive to move towards, and negative to move away), $a_i$ is the filtered activity of the $i^{th}$ neuron, and $x$ is the input vector encoded by each neuron." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Model network\n", "model = nengo.Network()\n", "with model:\n", "\n", " # Create the inputs/outputs\n", " stim_keys = nengo.Node(output=cycle_array(keys, period, dt))\n", " stim_values = nengo.Node(output=cycle_array(values, period, dt))\n", " learning = nengo.Node(output=lambda t: -int(t >= T / 2))\n", " recall = nengo.Node(size_in=d_value)\n", "\n", " # Create the memory\n", " memory = nengo.Ensemble(\n", " n_neurons, d_key, intercepts=intercepts)\n", "\n", " # Learn the encoders/keys\n", " voja = nengo.Voja(post_tau=None, learning_rate=5e-2)\n", " conn_in = nengo.Connection(\n", " stim_keys, memory, synapse=None, learning_rule_type=voja)\n", " nengo.Connection(learning, conn_in.learning_rule, synapse=None)\n", "\n", " # Learn the decoders/values, initialized to a null function\n", " conn_out = nengo.Connection(\n", " memory,\n", " recall,\n", " learning_rule_type=nengo.PES(1e-3),\n", " function=lambda x: np.zeros(d_value))\n", "\n", " # Create the error population\n", " error = nengo.Ensemble(n_neurons, d_value)\n", " nengo.Connection(\n", " learning, error.neurons, transform=[[10.0]] * n_neurons, synapse=None)\n", "\n", " # Calculate the error and use it to drive the PES rule\n", " nengo.Connection(stim_values, error, transform=-1, synapse=None)\n", " nengo.Connection(recall, error, synapse=None)\n", " nengo.Connection(error, conn_out.learning_rule)\n", "\n", " # Setup probes\n", " p_keys = nengo.Probe(stim_keys, synapse=None)\n", " p_values = nengo.Probe(stim_values, synapse=None)\n", " p_learning = nengo.Probe(learning, synapse=None)\n", " p_error = nengo.Probe(error, synapse=0.005)\n", " p_recall = nengo.Probe(recall, synapse=None)\n", " p_encoders = nengo.Probe(conn_in.learning_rule, 'scaled_encoders')" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:02. \n" ] } ], "source": [ "with nengo.Simulator(model, dt=dt) as sim:\n", " sim.run(T)\n", "t = sim.trange()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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eQsv5acPeTZGPeQt6pWNHrAQR5cZDNSrgFjQIH3vxGMOK0qQdoozM55UlZfyy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\nvqcP8W83bGs0VTrnXehkVp1pFJ7DHur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O8JNN/NMyuzeS699SYa67r3S/L+pIYhGJerPZXfw+SVrBSe8qRNk2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\n4UXi1i4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "train = t <= T / 2\n", "test = ~train\n", "\n", "plt.figure()\n", "plt.title(\"Value Error During Training\")\n", "plt.plot(t[train], sim.data[p_error][train])\n", "\n", "plt.figure()\n", "plt.title(\"Value Error During Recall\")\n", "plt.plot(t[test], sim.data[p_recall][test] - sim.data[p_values][test]);" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\tools\\Anaconda3\\lib\\site-packages\\matplotlib\\cbook\\deprecation.py:106: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n", " warnings.warn(message, mplDeprecation, stacklevel=1)\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scale = (sim.data[memory].gain / memory.radius)[:, np.newaxis]\n", "\n", "\n", "def plot_2d(text, xy):\n", " plt.figure()\n", " plt.title(text)\n", " plt.scatter(xy[:, 0], xy[:, 1], label=\"Encoders\")\n", " plt.scatter(\n", " keys[:, 0], keys[:, 1], c='red', s=150, alpha=0.6, label=\"Keys\")\n", " plt.xlim(-1.5, 1.5)\n", " plt.ylim(-1.5, 2)\n", " plt.legend()\n", " plt.axes().set_aspect('equal')\n", "\n", "\n", "plot_2d(\"Before\", sim.data[p_encoders][0].copy() / scale)\n", "plot_2d(\"After\", sim.data[p_encoders][-1].copy() / scale)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What happens if the intercepts aren't set?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Reading\n", "\n", "- Alternative Associative Memory architectures optimising for different criteria [Gosmann et al. 2017](http://compneuro.uwaterloo.ca/publications/gosmann2017a.html)\n", "- Scaling up Associative Memories to large corpuses [Kajic et al. 2017](http://compneuro.uwaterloo.ca/publications/kajic2017.html)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Short-Term to Long-Term\n", "\n", "After the break!" ] } ], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }