{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### This code illustrates the fast AI implementation of the unsupervised \"biological\" learning algorithm from [Unsupervised Learning by Competing Hidden Units](https://doi.org/10.1073/pnas.1820458116) on MNIST data set. \n", "If you want to learn more about this work you can also check out this [lecture](https://www.youtube.com/watch?v=4lY-oAY0aQU) from MIT's [6.S191 course](http://introtodeeplearning.com/). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This cell loads the data and normalizes it to the [0,1] range" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import scipy.io\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "mat = scipy.io.loadmat('mnist_all.mat')\n", "\n", "Nc=10\n", "N=784\n", "Ns=60000\n", "M=np.zeros((0,N))\n", "for i in range(Nc):\n", " M=np.concatenate((M, mat['train'+str(i)]), axis=0)\n", "M=M/255.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To draw a heatmap of the weights a helper function is created:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def draw_weights(synapses, Kx, Ky):\n", " yy=0\n", " HM=np.zeros((28*Ky,28*Kx))\n", " for y in range(Ky):\n", " for x in range(Kx):\n", " HM[y*28:(y+1)*28,x*28:(x+1)*28]=synapses[yy,:].reshape(28,28)\n", " yy += 1\n", " plt.clf()\n", " nc=np.amax(np.absolute(HM))\n", " im=plt.imshow(HM,cmap='bwr',vmin=-nc,vmax=nc)\n", " fig.colorbar(im,ticks=[np.amin(HM), 0, np.amax(HM)])\n", " plt.axis('off')\n", " fig.canvas.draw() \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This cell defines paramaters of the algorithm: `eps0` - initial learning rate that is linearly annealed during training; `hid` - number of hidden units that are displayed as an `Ky` by `Kx` array by the helper function defined above; `mu` - the mean of the gaussian distribution that initializes the weights; `sigma` - the standard deviation of that gaussian; `Nep` - number of epochs; `Num` - size of the minibatch; `prec` - parameter that controls numerical precision of the weight updates; `delta` - the strength of the anti-hebbian learning; `p` - Lebesgue norm of the weights; `k` - ranking parameter. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "eps0=2e-2 # learning rate\n", "Kx=10\n", "Ky=10\n", "hid=Kx*Ky # number of hidden units that are displayed in Ky by Kx array\n", "mu=0.0\n", "sigma=1.0\n", "Nep=200 # number of epochs\n", "Num=100 # size of the minibatch\n", "prec=1e-30\n", "delta=0.4 # Strength of the anti-hebbian learning\n", "p=2.0 # Lebesgue norm of the weights\n", "k=2 # ranking parameter, must be integer that is bigger or equal than 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This cell defines the main code. The external loop runs over epochs `nep`, the internal loop runs over minibatches. For every minibatch the overlap with the data `tot_input` is calculated for each data point and each hidden unit. The sorted strengths of the activations are stored in `y`. The variable `yl` stores the activations of the post synaptic cells - it is denoted by g(Q) in Eq 3 of [Unsupervised Learning by Competing Hidden Units](https://doi.org/10.1073/pnas.1820458116), see also Eq 9 and Eq 10. The variable `ds` is the right hand side of Eq 3. The weights are updated after each minibatch in a way so that the largest update is equal to the learning rate `eps` at that epoch. The weights are displayed by the helper function after each epoch. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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