10_Homework_MNIST_BoltzmannMachine.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework: Boltzmann Machines applied to MNIST\n",
    "\n",
    "This shows how to train a Boltzmann machine, to sample from an observed probability distribution. It uses the MNIST digits images that are included in every keras installation."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example code for the lecture series \"Machine Learning for Physicists\" by Florian Marquardt\n",
    "\n",
    "Lecture 9, Homework (this is discussed in session 10)\n",
    "\n",
    "See https://machine-learning-for-physicists.org and the current course website linked there!\n",
    "\n",
    "This notebook is distributed under the Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license:\n",
    "\n",
    "https://creativecommons.org/licenses/by-sa/4.0/"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to:\n",
    "- use a Boltzmann machine to sample from an observed high-dimensional probability distribution (e.g. produce images that look similar to observed training images); applied to the case of MNIST\n",
    "\n",
    "It also implements some of the tricks discussed by the inventor of RBM, G. Hinton, in\n",
    "\n",
    "https://www.cs.toronto.edu/~hinton/absps/guideTR.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2023-06-16 11:28:11.505073: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  SSE4.1 SSE4.2 AVX AVX2 FMA\n",
      "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "matplotlib.rcParams['figure.dpi']=300 # highres display\n",
    "\n",
    "import tensorflow as tf\n",
    "\n",
    "from IPython.display import clear_output\n",
    "from time import sleep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BoltzmannStep(v,b,w,do_random_sampling=True):\n",
    "    \"\"\"\n",
    "    Perform a single step of the Markov chain,\n",
    "    going from visible units v to hidden units h,\n",
    "    according to biases b and weights w.\n",
    "    \n",
    "    z_j = b_j + sum_i v_i w_ij\n",
    "    \n",
    "    and P(h_j=1|v) = 1/(exp(-z_j)+1)\n",
    "    \n",
    "    Note: you can go from h to v, by inserting\n",
    "    instead of v the h, instead of b the a, and\n",
    "    instead of w the transpose of w\n",
    "    \"\"\"\n",
    "    batchsize=np.shape(v)[0]\n",
    "    hidden_dim=np.shape(w)[1]\n",
    "    z=b+np.dot(v,w)\n",
    "    P=1/(np.exp(-z)+1)\n",
    "    # now, the usual trick to obtain 0 or 1 according\n",
    "    # to a given probability distribution:\n",
    "    # just produce uniform (in [0,1]) random numbers and\n",
    "    # check whether they are below the cutoff given by P\n",
    "    if do_random_sampling:\n",
    "        p=np.random.uniform(size=[batchsize,hidden_dim])\n",
    "        return(np.array(p<=P,dtype='int'))\n",
    "    else:\n",
    "        return(P) # no binary random output, just the prob. distribution itself!\n",
    "    \n",
    "def BoltzmannSequence(v,a,b,w,drop_h_prime=False,do_random_sampling=True,\n",
    "                      do_not_sample_h_prime=False,\n",
    "                     do_not_sample_v_prime=False):\n",
    "    \"\"\"\n",
    "    Perform one sequence of steps v -> h -> v' -> h'\n",
    "    of a Boltzmann machine, with the given\n",
    "    weights w and biases a and b!\n",
    "    \n",
    "    All the arrays have a shape [batchsize,num_neurons]\n",
    "    (where num_neurons is num_visible for v and\n",
    "    num_hidden for h)\n",
    "    \n",
    "    You can set drop_h_prime to True if you want to\n",
    "    use this routine to generate arbitrarily long sequences\n",
    "    by calling it repeatedly (then don't use h')\n",
    "    Returns: v,h,v',h'\n",
    "    \"\"\"\n",
    "    h=BoltzmannStep(v,b,w,do_random_sampling=do_random_sampling)\n",
    "    if do_not_sample_v_prime:\n",
    "        v_prime=BoltzmannStep(h,a,np.transpose(w),do_random_sampling=False)\n",
    "    else:\n",
    "        v_prime=BoltzmannStep(h,a,np.transpose(w),do_random_sampling=do_random_sampling)\n",
    "    if not drop_h_prime:\n",
    "        if do_not_sample_h_prime: # G. Hinton recommends not sampling in the v'->h' step (reduces noise)\n",
    "            h_prime=BoltzmannStep(v_prime,b,w,do_random_sampling=False)\n",
    "        else:\n",
    "            h_prime=BoltzmannStep(v_prime,b,w,do_random_sampling=do_random_sampling)\n",
    "    else:\n",
    "        h_prime=np.zeros(np.shape(h))\n",
    "    return(v,h,v_prime,h_prime)\n",
    "\n",
    "def trainStep(v,a,b,w,do_random_sampling=True,do_not_sample_h_prime=False,\n",
    "             do_not_sample_v_prime=False):\n",
    "    \"\"\"\n",
    "    Given a set of randomly selected training samples\n",
    "    v (of shape [batchsize,num_neurons_visible]), \n",
    "    and given biases a,b and weights w: update\n",
    "    those biases and weights according to the\n",
    "    contrastive-divergence update rules:\n",
    "    \n",
    "    delta w_ij = eta ( <v_i h_j> - <v'_i h'_j> )\n",
    "    delta a_i  = eta ( <v_i> - <v'_i>)\n",
    "    delta b_j  = eta ( <h_j> - <h'_j>)\n",
    "    \n",
    "    Returns delta_a, delta_b, delta_w, but without the eta factor!\n",
    "    It is up to you to update a,b,w!\n",
    "    \"\"\"\n",
    "    v,h,v_prime,h_prime=BoltzmannSequence(v,a,b,w,do_random_sampling=do_random_sampling,\n",
    "                                         do_not_sample_h_prime=do_not_sample_h_prime,\n",
    "                                         do_not_sample_v_prime=do_not_sample_v_prime)\n",
    "    return( np.average(v,axis=0)-np.average(v_prime,axis=0) ,\n",
    "            np.average(h,axis=0)-np.average(h_prime,axis=0) ,\n",
    "            np.average(v[:,:,None]*h[:,None,:],axis=0)-\n",
    "               np.average(v_prime[:,:,None]*h_prime[:,None,:],axis=0) )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def produce_sample_images(batchsize,num_visible,x_train,threshold=0.7,do_digitize=True):\n",
    "    \"\"\"\n",
    "    Produce 'batchsize' samples, of length num_visible.\n",
    "    Returns array v of shape [batchsize,num_visible]\n",
    "    \"\"\"\n",
    "    j=np.random.randint(low=0,high=np.shape(x_train)[0],size=batchsize) # pick random samples\n",
    "    \n",
    "    # reshape suitably, and digitize (so output is 0/1 values)\n",
    "    if do_digitize:\n",
    "        return( np.array( np.reshape(x_train[j,:,:],[batchsize,num_visible])>threshold, dtype='int' ) )\n",
    "    else:\n",
    "        return(  np.reshape(x_train[j,:,:],[batchsize,num_visible]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
      "11490434/11490434 [==============================] - 11s 1us/step\n"
     ]
    }
   ],
   "source": [
    "# Load the MNIST data using tensorflow/keras\n",
    "(x_train,y_train),(x_test,y_test)=tf.keras.datasets.mnist.load_data(path=\"mnist.npz\")\n",
    "\n",
    "x_train=x_train/256."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 28, 28) (60000,) (10000, 28, 28) (10000,)\n"
     ]
    }
   ],
   "source": [
    "# Show the shape of these arrays\n",
    "print(np.shape(x_train),np.shape(y_train),np.shape(x_test),np.shape(y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 3000x300 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display a few images, for fun\n",
    "nimages=10\n",
    "fig,ax=plt.subplots(ncols=nimages,nrows=1,figsize=(nimages,1))\n",
    "for n in range(nimages):\n",
    "    ax[n].imshow(x_train[n,:,:])\n",
    "    ax[n].set_title(str(y_train[n])) # the label\n",
    "    ax[n].axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2100x300 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pick a few random samples:\n",
    "nimages=7\n",
    "Npixels=28\n",
    "samples=produce_sample_images(batchsize=nimages,num_visible=Npixels**2,x_train=x_train)\n",
    "# now unpack them again and display them:\n",
    "fig,ax=plt.subplots(ncols=nimages,nrows=1,figsize=(nimages,1))\n",
    "for n in range(nimages):\n",
    "    ax[n].imshow(np.reshape(samples[n,:],[Npixels,Npixels]))\n",
    "    ax[n].axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1920x1440 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a little trick (useful later): show them all at once, in one imshow\n",
    "# some weird reshape/transpose gymnastics, found by trial and error\n",
    "plt.imshow(np.transpose(np.reshape(np.transpose(np.reshape(samples,[nimages,Npixels,Npixels]),\n",
    "                                                axes=[0,2,1]),[nimages*Npixels,Npixels])))\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic training, according to the simple principle of an RBM presented in the lecture (all units are binary 0 or 1 all the time, randomly chosen according to the calculated probability distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "09999 / 10000   \r"
     ]
    }
   ],
   "source": [
    "# Now: the training\n",
    "# here: purely using random binary sampling of all\n",
    "# units at all times (this is not the most efficient way,\n",
    "# but implements directly the basic principle shown in the lecture)\n",
    "\n",
    "Npixels=28\n",
    "num_visible=Npixels**2\n",
    "num_hidden=60\n",
    "batchsize=50\n",
    "eta=0.1\n",
    "nsteps=10000\n",
    "skipsteps=10\n",
    "\n",
    "a=np.random.randn(num_visible)\n",
    "b=np.random.randn(num_hidden)\n",
    "w=0.01*np.random.randn(num_visible,num_hidden)\n",
    "\n",
    "# test_samples=np.zeros([num_visible,nsteps])\n",
    "\n",
    "for j in range(nsteps):\n",
    "    v=produce_sample_images(batchsize,num_visible,x_train)\n",
    "    da,db,dw=trainStep(v,a,b,w)\n",
    "    a+=eta*da\n",
    "    b+=eta*db\n",
    "    w+=eta*dw\n",
    "    print(\"{:05d} / {:05d}\".format(j,nsteps),end=\"   \\r\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/PIL/ImageFile.py:515\u001b[0m, in \u001b[0;36m_save\u001b[0;34m(im, fp, tile, bufsize)\u001b[0m\n\u001b[1;32m    514\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[0;32m--> 515\u001b[0m     fh \u001b[39m=\u001b[39m fp\u001b[39m.\u001b[39;49mfileno()\n\u001b[1;32m    516\u001b[0m     fp\u001b[39m.\u001b[39mflush()\n",
      "\u001b[0;31mAttributeError\u001b[0m: '_idat' object has no attribute 'fileno'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m/Users/fwb251/Documents/GitHub/machine-learning-for-physicists/10_Homework_MNIST_BoltzmannMachine.ipynb Cell 14\u001b[0m in \u001b[0;36m<cell line: 16>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     <a href='vscode-notebook-cell:/Users/fwb251/Documents/GitHub/machine-learning-for-physicists/10_Homework_MNIST_BoltzmannMachine.ipynb#X16sZmlsZQ%3D%3D?line=22'>23</a>\u001b[0m plt\u001b[39m.\u001b[39mimshow(np\u001b[39m.\u001b[39mtranspose(np\u001b[39m.\u001b[39mreshape(np\u001b[39m.\u001b[39mtranspose(np\u001b[39m.\u001b[39mreshape(test_samples,[num_samples,Npixels,Npixels]),\n\u001b[1;32m     <a href='vscode-notebook-cell:/Users/fwb251/Documents/GitHub/machine-learning-for-physicists/10_Homework_MNIST_BoltzmannMachine.ipynb#X16sZmlsZQ%3D%3D?line=23'>24</a>\u001b[0m                                         axes\u001b[39m=\u001b[39m[\u001b[39m0\u001b[39m,\u001b[39m2\u001b[39m,\u001b[39m1\u001b[39m]),[num_samples\u001b[39m*\u001b[39mNpixels,Npixels])),\n\u001b[1;32m     <a href='vscode-notebook-cell:/Users/fwb251/Documents/GitHub/machine-learning-for-physicists/10_Homework_MNIST_BoltzmannMachine.ipynb#X16sZmlsZQ%3D%3D?line=24'>25</a>\u001b[0m           interpolation\u001b[39m=\u001b[39m\u001b[39m'\u001b[39m\u001b[39mnone\u001b[39m\u001b[39m'\u001b[39m)\n\u001b[1;32m     <a href='vscode-notebook-cell:/Users/fwb251/Documents/GitHub/machine-learning-for-physicists/10_Homework_MNIST_BoltzmannMachine.ipynb#X16sZmlsZQ%3D%3D?line=25'>26</a>\u001b[0m plt\u001b[39m.\u001b[39maxis(\u001b[39m'\u001b[39m\u001b[39moff\u001b[39m\u001b[39m'\u001b[39m)\n\u001b[0;32m---> <a href='vscode-notebook-cell:/Users/fwb251/Documents/GitHub/machine-learning-for-physicists/10_Homework_MNIST_BoltzmannMachine.ipynb#X16sZmlsZQ%3D%3D?line=26'>27</a>\u001b[0m plt\u001b[39m.\u001b[39;49mshow()\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/matplotlib/pyplot.py:446\u001b[0m, in \u001b[0;36mshow\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    402\u001b[0m \u001b[39m\u001b[39m\u001b[39m\"\"\"\u001b[39;00m\n\u001b[1;32m    403\u001b[0m \u001b[39mDisplay all open figures.\u001b[39;00m\n\u001b[1;32m    404\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    443\u001b[0m \u001b[39mexplicitly there.\u001b[39;00m\n\u001b[1;32m    444\u001b[0m \u001b[39m\"\"\"\u001b[39;00m\n\u001b[1;32m    445\u001b[0m _warn_if_gui_out_of_main_thread()\n\u001b[0;32m--> 446\u001b[0m \u001b[39mreturn\u001b[39;00m _get_backend_mod()\u001b[39m.\u001b[39;49mshow(\u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/matplotlib_inline/backend_inline.py:90\u001b[0m, in \u001b[0;36mshow\u001b[0;34m(close, block)\u001b[0m\n\u001b[1;32m     88\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[1;32m     89\u001b[0m     \u001b[39mfor\u001b[39;00m figure_manager \u001b[39min\u001b[39;00m Gcf\u001b[39m.\u001b[39mget_all_fig_managers():\n\u001b[0;32m---> 90\u001b[0m         display(\n\u001b[1;32m     91\u001b[0m             figure_manager\u001b[39m.\u001b[39;49mcanvas\u001b[39m.\u001b[39;49mfigure,\n\u001b[1;32m     92\u001b[0m             metadata\u001b[39m=\u001b[39;49m_fetch_figure_metadata(figure_manager\u001b[39m.\u001b[39;49mcanvas\u001b[39m.\u001b[39;49mfigure)\n\u001b[1;32m     93\u001b[0m         )\n\u001b[1;32m     94\u001b[0m \u001b[39mfinally\u001b[39;00m:\n\u001b[1;32m     95\u001b[0m     show\u001b[39m.\u001b[39m_to_draw \u001b[39m=\u001b[39m []\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/IPython/core/display_functions.py:298\u001b[0m, in \u001b[0;36mdisplay\u001b[0;34m(include, exclude, metadata, transient, display_id, raw, clear, *objs, **kwargs)\u001b[0m\n\u001b[1;32m    296\u001b[0m     publish_display_data(data\u001b[39m=\u001b[39mobj, metadata\u001b[39m=\u001b[39mmetadata, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs)\n\u001b[1;32m    297\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[0;32m--> 298\u001b[0m     format_dict, md_dict \u001b[39m=\u001b[39m \u001b[39mformat\u001b[39;49m(obj, include\u001b[39m=\u001b[39;49minclude, exclude\u001b[39m=\u001b[39;49mexclude)\n\u001b[1;32m    299\u001b[0m     \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m format_dict:\n\u001b[1;32m    300\u001b[0m         \u001b[39m# nothing to display (e.g. _ipython_display_ took over)\u001b[39;00m\n\u001b[1;32m    301\u001b[0m         \u001b[39mcontinue\u001b[39;00m\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/IPython/core/formatters.py:178\u001b[0m, in \u001b[0;36mDisplayFormatter.format\u001b[0;34m(self, obj, include, exclude)\u001b[0m\n\u001b[1;32m    176\u001b[0m md \u001b[39m=\u001b[39m \u001b[39mNone\u001b[39;00m\n\u001b[1;32m    177\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[0;32m--> 178\u001b[0m     data \u001b[39m=\u001b[39m formatter(obj)\n\u001b[1;32m    179\u001b[0m \u001b[39mexcept\u001b[39;00m:\n\u001b[1;32m    180\u001b[0m     \u001b[39m# FIXME: log the exception\u001b[39;00m\n\u001b[1;32m    181\u001b[0m     \u001b[39mraise\u001b[39;00m\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/decorator.py:232\u001b[0m, in \u001b[0;36mdecorate.<locals>.fun\u001b[0;34m(*args, **kw)\u001b[0m\n\u001b[1;32m    230\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m kwsyntax:\n\u001b[1;32m    231\u001b[0m     args, kw \u001b[39m=\u001b[39m fix(args, kw, sig)\n\u001b[0;32m--> 232\u001b[0m \u001b[39mreturn\u001b[39;00m caller(func, \u001b[39m*\u001b[39;49m(extras \u001b[39m+\u001b[39;49m args), \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkw)\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/IPython/core/formatters.py:222\u001b[0m, in \u001b[0;36mcatch_format_error\u001b[0;34m(method, self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    220\u001b[0m \u001b[39m\u001b[39m\u001b[39m\"\"\"show traceback on failed format call\"\"\"\u001b[39;00m\n\u001b[1;32m    221\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[0;32m--> 222\u001b[0m     r \u001b[39m=\u001b[39m method(\u001b[39mself\u001b[39;49m, \u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n\u001b[1;32m    223\u001b[0m \u001b[39mexcept\u001b[39;00m \u001b[39mNotImplementedError\u001b[39;00m:\n\u001b[1;32m    224\u001b[0m     \u001b[39m# don't warn on NotImplementedErrors\u001b[39;00m\n\u001b[1;32m    225\u001b[0m     \u001b[39mreturn\u001b[39;00m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_check_return(\u001b[39mNone\u001b[39;00m, args[\u001b[39m0\u001b[39m])\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/IPython/core/formatters.py:339\u001b[0m, in \u001b[0;36mBaseFormatter.__call__\u001b[0;34m(self, obj)\u001b[0m\n\u001b[1;32m    337\u001b[0m     \u001b[39mpass\u001b[39;00m\n\u001b[1;32m    338\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[0;32m--> 339\u001b[0m     \u001b[39mreturn\u001b[39;00m printer(obj)\n\u001b[1;32m    340\u001b[0m \u001b[39m# Finally look for special method names\u001b[39;00m\n\u001b[1;32m    341\u001b[0m method \u001b[39m=\u001b[39m get_real_method(obj, \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mprint_method)\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/IPython/core/pylabtools.py:151\u001b[0m, in \u001b[0;36mprint_figure\u001b[0;34m(fig, fmt, bbox_inches, base64, **kwargs)\u001b[0m\n\u001b[1;32m    148\u001b[0m     \u001b[39mfrom\u001b[39;00m \u001b[39mmatplotlib\u001b[39;00m\u001b[39m.\u001b[39;00m\u001b[39mbackend_bases\u001b[39;00m \u001b[39mimport\u001b[39;00m FigureCanvasBase\n\u001b[1;32m    149\u001b[0m     FigureCanvasBase(fig)\n\u001b[0;32m--> 151\u001b[0m fig\u001b[39m.\u001b[39;49mcanvas\u001b[39m.\u001b[39;49mprint_figure(bytes_io, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkw)\n\u001b[1;32m    152\u001b[0m data \u001b[39m=\u001b[39m bytes_io\u001b[39m.\u001b[39mgetvalue()\n\u001b[1;32m    153\u001b[0m \u001b[39mif\u001b[39;00m fmt \u001b[39m==\u001b[39m \u001b[39m'\u001b[39m\u001b[39msvg\u001b[39m\u001b[39m'\u001b[39m:\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/matplotlib/backend_bases.py:2366\u001b[0m, in \u001b[0;36mFigureCanvasBase.print_figure\u001b[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[1;32m   2362\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[1;32m   2363\u001b[0m     \u001b[39m# _get_renderer may change the figure dpi (as vector formats\u001b[39;00m\n\u001b[1;32m   2364\u001b[0m     \u001b[39m# force the figure dpi to 72), so we need to set it again here.\u001b[39;00m\n\u001b[1;32m   2365\u001b[0m     \u001b[39mwith\u001b[39;00m cbook\u001b[39m.\u001b[39m_setattr_cm(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mfigure, dpi\u001b[39m=\u001b[39mdpi):\n\u001b[0;32m-> 2366\u001b[0m         result \u001b[39m=\u001b[39m print_method(\n\u001b[1;32m   2367\u001b[0m             filename,\n\u001b[1;32m   2368\u001b[0m             facecolor\u001b[39m=\u001b[39;49mfacecolor,\n\u001b[1;32m   2369\u001b[0m             edgecolor\u001b[39m=\u001b[39;49medgecolor,\n\u001b[1;32m   2370\u001b[0m             orientation\u001b[39m=\u001b[39;49morientation,\n\u001b[1;32m   2371\u001b[0m             bbox_inches_restore\u001b[39m=\u001b[39;49m_bbox_inches_restore,\n\u001b[1;32m   2372\u001b[0m             \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n\u001b[1;32m   2373\u001b[0m \u001b[39mfinally\u001b[39;00m:\n\u001b[1;32m   2374\u001b[0m     \u001b[39mif\u001b[39;00m bbox_inches \u001b[39mand\u001b[39;00m restore_bbox:\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/matplotlib/backend_bases.py:2232\u001b[0m, in \u001b[0;36mFigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   2228\u001b[0m     optional_kws \u001b[39m=\u001b[39m {  \u001b[39m# Passed by print_figure for other renderers.\u001b[39;00m\n\u001b[1;32m   2229\u001b[0m         \u001b[39m\"\u001b[39m\u001b[39mdpi\u001b[39m\u001b[39m\"\u001b[39m, \u001b[39m\"\u001b[39m\u001b[39mfacecolor\u001b[39m\u001b[39m\"\u001b[39m, \u001b[39m\"\u001b[39m\u001b[39medgecolor\u001b[39m\u001b[39m\"\u001b[39m, \u001b[39m\"\u001b[39m\u001b[39morientation\u001b[39m\u001b[39m\"\u001b[39m,\n\u001b[1;32m   2230\u001b[0m         \u001b[39m\"\u001b[39m\u001b[39mbbox_inches_restore\u001b[39m\u001b[39m\"\u001b[39m}\n\u001b[1;32m   2231\u001b[0m     skip \u001b[39m=\u001b[39m optional_kws \u001b[39m-\u001b[39m {\u001b[39m*\u001b[39minspect\u001b[39m.\u001b[39msignature(meth)\u001b[39m.\u001b[39mparameters}\n\u001b[0;32m-> 2232\u001b[0m     print_method \u001b[39m=\u001b[39m functools\u001b[39m.\u001b[39mwraps(meth)(\u001b[39mlambda\u001b[39;00m \u001b[39m*\u001b[39margs, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs: meth(\n\u001b[1;32m   2233\u001b[0m         \u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49m{k: v \u001b[39mfor\u001b[39;49;00m k, v \u001b[39min\u001b[39;49;00m kwargs\u001b[39m.\u001b[39;49mitems() \u001b[39mif\u001b[39;49;00m k \u001b[39mnot\u001b[39;49;00m \u001b[39min\u001b[39;49;00m skip}))\n\u001b[1;32m   2234\u001b[0m \u001b[39melse\u001b[39;00m:  \u001b[39m# Let third-parties do as they see fit.\u001b[39;00m\n\u001b[1;32m   2235\u001b[0m     print_method \u001b[39m=\u001b[39m meth\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/matplotlib/backends/backend_agg.py:509\u001b[0m, in \u001b[0;36mFigureCanvasAgg.print_png\u001b[0;34m(self, filename_or_obj, metadata, pil_kwargs)\u001b[0m\n\u001b[1;32m    462\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mprint_png\u001b[39m(\u001b[39mself\u001b[39m, filename_or_obj, \u001b[39m*\u001b[39m, metadata\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m, pil_kwargs\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m):\n\u001b[1;32m    463\u001b[0m \u001b[39m    \u001b[39m\u001b[39m\"\"\"\u001b[39;00m\n\u001b[1;32m    464\u001b[0m \u001b[39m    Write the figure to a PNG file.\u001b[39;00m\n\u001b[1;32m    465\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    507\u001b[0m \u001b[39m        *metadata*, including the default 'Software' key.\u001b[39;00m\n\u001b[1;32m    508\u001b[0m \u001b[39m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 509\u001b[0m     \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_print_pil(filename_or_obj, \u001b[39m\"\u001b[39;49m\u001b[39mpng\u001b[39;49m\u001b[39m\"\u001b[39;49m, pil_kwargs, metadata)\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/matplotlib/backends/backend_agg.py:458\u001b[0m, in \u001b[0;36mFigureCanvasAgg._print_pil\u001b[0;34m(self, filename_or_obj, fmt, pil_kwargs, metadata)\u001b[0m\n\u001b[1;32m    453\u001b[0m \u001b[39m\u001b[39m\u001b[39m\"\"\"\u001b[39;00m\n\u001b[1;32m    454\u001b[0m \u001b[39mDraw the canvas, then save it using `.image.imsave` (to which\u001b[39;00m\n\u001b[1;32m    455\u001b[0m \u001b[39m*pil_kwargs* and *metadata* are forwarded).\u001b[39;00m\n\u001b[1;32m    456\u001b[0m \u001b[39m\"\"\"\u001b[39;00m\n\u001b[1;32m    457\u001b[0m FigureCanvasAgg\u001b[39m.\u001b[39mdraw(\u001b[39mself\u001b[39m)\n\u001b[0;32m--> 458\u001b[0m mpl\u001b[39m.\u001b[39;49mimage\u001b[39m.\u001b[39;49mimsave(\n\u001b[1;32m    459\u001b[0m     filename_or_obj, \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49mbuffer_rgba(), \u001b[39mformat\u001b[39;49m\u001b[39m=\u001b[39;49mfmt, origin\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mupper\u001b[39;49m\u001b[39m\"\u001b[39;49m,\n\u001b[1;32m    460\u001b[0m     dpi\u001b[39m=\u001b[39;49m\u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49mfigure\u001b[39m.\u001b[39;49mdpi, metadata\u001b[39m=\u001b[39;49mmetadata, pil_kwargs\u001b[39m=\u001b[39;49mpil_kwargs)\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/matplotlib/image.py:1689\u001b[0m, in \u001b[0;36mimsave\u001b[0;34m(fname, arr, vmin, vmax, cmap, format, origin, dpi, metadata, pil_kwargs)\u001b[0m\n\u001b[1;32m   1687\u001b[0m pil_kwargs\u001b[39m.\u001b[39msetdefault(\u001b[39m\"\u001b[39m\u001b[39mformat\u001b[39m\u001b[39m\"\u001b[39m, \u001b[39mformat\u001b[39m)\n\u001b[1;32m   1688\u001b[0m pil_kwargs\u001b[39m.\u001b[39msetdefault(\u001b[39m\"\u001b[39m\u001b[39mdpi\u001b[39m\u001b[39m\"\u001b[39m, (dpi, dpi))\n\u001b[0;32m-> 1689\u001b[0m image\u001b[39m.\u001b[39;49msave(fname, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mpil_kwargs)\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/PIL/Image.py:2432\u001b[0m, in \u001b[0;36mImage.save\u001b[0;34m(self, fp, format, **params)\u001b[0m\n\u001b[1;32m   2429\u001b[0m         fp \u001b[39m=\u001b[39m builtins\u001b[39m.\u001b[39mopen(filename, \u001b[39m\"\u001b[39m\u001b[39mw+b\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m   2431\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[0;32m-> 2432\u001b[0m     save_handler(\u001b[39mself\u001b[39;49m, fp, filename)\n\u001b[1;32m   2433\u001b[0m \u001b[39mexcept\u001b[39;00m \u001b[39mException\u001b[39;00m:\n\u001b[1;32m   2434\u001b[0m     \u001b[39mif\u001b[39;00m open_fp:\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/PIL/PngImagePlugin.py:1407\u001b[0m, in \u001b[0;36m_save\u001b[0;34m(im, fp, filename, chunk, save_all)\u001b[0m\n\u001b[1;32m   1405\u001b[0m     _write_multiple_frames(im, fp, chunk, rawmode, default_image, append_images)\n\u001b[1;32m   1406\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[0;32m-> 1407\u001b[0m     ImageFile\u001b[39m.\u001b[39;49m_save(im, _idat(fp, chunk), [(\u001b[39m\"\u001b[39;49m\u001b[39mzip\u001b[39;49m\u001b[39m\"\u001b[39;49m, (\u001b[39m0\u001b[39;49m, \u001b[39m0\u001b[39;49m) \u001b[39m+\u001b[39;49m im\u001b[39m.\u001b[39;49msize, \u001b[39m0\u001b[39;49m, rawmode)])\n\u001b[1;32m   1409\u001b[0m \u001b[39mif\u001b[39;00m info:\n\u001b[1;32m   1410\u001b[0m     \u001b[39mfor\u001b[39;00m info_chunk \u001b[39min\u001b[39;00m info\u001b[39m.\u001b[39mchunks:\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/PIL/ImageFile.py:519\u001b[0m, in \u001b[0;36m_save\u001b[0;34m(im, fp, tile, bufsize)\u001b[0m\n\u001b[1;32m    517\u001b[0m     _encode_tile(im, fp, tile, bufsize, fh)\n\u001b[1;32m    518\u001b[0m \u001b[39mexcept\u001b[39;00m (\u001b[39mAttributeError\u001b[39;00m, io\u001b[39m.\u001b[39mUnsupportedOperation) \u001b[39mas\u001b[39;00m exc:\n\u001b[0;32m--> 519\u001b[0m     _encode_tile(im, fp, tile, bufsize, \u001b[39mNone\u001b[39;49;00m, exc)\n\u001b[1;32m    520\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mhasattr\u001b[39m(fp, \u001b[39m\"\u001b[39m\u001b[39mflush\u001b[39m\u001b[39m\"\u001b[39m):\n\u001b[1;32m    521\u001b[0m     fp\u001b[39m.\u001b[39mflush()\n",
      "File \u001b[0;32m~/miniconda3/envs/mlp/lib/python3.8/site-packages/PIL/ImageFile.py:538\u001b[0m, in \u001b[0;36m_encode_tile\u001b[0;34m(im, fp, tile, bufsize, fh, exc)\u001b[0m\n\u001b[1;32m    535\u001b[0m \u001b[39mif\u001b[39;00m exc:\n\u001b[1;32m    536\u001b[0m     \u001b[39m# compress to Python file-compatible object\u001b[39;00m\n\u001b[1;32m    537\u001b[0m     \u001b[39mwhile\u001b[39;00m \u001b[39mTrue\u001b[39;00m:\n\u001b[0;32m--> 538\u001b[0m         errcode, data \u001b[39m=\u001b[39m encoder\u001b[39m.\u001b[39;49mencode(bufsize)[\u001b[39m1\u001b[39m:]\n\u001b[1;32m    539\u001b[0m         fp\u001b[39m.\u001b[39mwrite(data)\n\u001b[1;32m    540\u001b[0m         \u001b[39mif\u001b[39;00m errcode:\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# Now: visualize the typical samples generated (from some starting point)\n",
    "# run several times to continue this. It basically is a random walk\n",
    "# through the space of all possible configurations, hopefully according\n",
    "# to the probability distribution that has been trained!\n",
    "\n",
    "nsteps=1000\n",
    "num_samples=20\n",
    "test_samples=np.zeros([num_samples,num_visible])\n",
    "skipsteps=1\n",
    "substeps=400 # how many steps to take before showing a new picture\n",
    "\n",
    "v_prime=np.zeros(num_visible)\n",
    "h=np.zeros(num_hidden)\n",
    "h_prime=np.zeros(num_hidden)\n",
    "\n",
    "for j in range(nsteps):\n",
    "    for k in range(substeps):\n",
    "        v,h,v_prime,h_prime=BoltzmannSequence(v,a,b,w,drop_h_prime=True) # step from v via h to v_prime!\n",
    "    test_samples[j%num_samples,:]=v[0,:]\n",
    "    v=np.copy(v_prime) # use the new v as a starting point for next step!\n",
    "    if j%skipsteps==0 or j==nsteps-1:\n",
    "        clear_output(wait=True)\n",
    "        plt.imshow(np.transpose(np.reshape(np.transpose(np.reshape(test_samples,[num_samples,Npixels,Npixels]),\n",
    "                                                axes=[0,2,1]),[num_samples*Npixels,Npixels])),\n",
    "                  interpolation='none')\n",
    "        plt.axis('off')\n",
    "        plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More advanced training: do not randomly sample h' and v'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "299999 / 300000   \r"
     ]
    }
   ],
   "source": [
    "# Now: the training\n",
    "#\n",
    "# Here we use the more sophisticated approach, where\n",
    "# h' and v' are not binary (not randomly sampled), rather\n",
    "# they are taken as the probability distribution (numbers\n",
    "# between 0 and 1). This is a trick recommend by G. Hinton\n",
    "# in his review of Boltzmann Machines. It effectively means\n",
    "# less sampling noise.\n",
    "#\n",
    "# Also, we initialize the biases and weights according to the\n",
    "# tricks given in that review!\n",
    "\n",
    "Npixels=28\n",
    "num_visible=Npixels**2\n",
    "num_hidden=60\n",
    "batchsize=10\n",
    "eta=0.0001\n",
    "nsteps=10*30000\n",
    "skipsteps=10\n",
    "\n",
    "# get average brightness of training images:\n",
    "p_avg=np.average(np.reshape(x_train,[np.shape(x_train)[0],Npixels**2]),axis=0)\n",
    "a=np.log(p_avg/(1.0+1e-6-p_avg)+1e-6) # recipe for visible biases\n",
    "b=np.zeros(num_hidden) # recipe for hidden biases\n",
    "w=0.01*np.random.randn(num_visible,num_hidden) # recipe for weights\n",
    "\n",
    "# test_samples=np.zeros([num_visible,nsteps])\n",
    "\n",
    "for j in range(nsteps):\n",
    "    v=produce_sample_images(batchsize,num_visible,x_train,\n",
    "                           do_digitize=False)\n",
    "    da,db,dw=trainStep(v,a,b,w,\n",
    "                      do_not_sample_h_prime=True,\n",
    "                       do_not_sample_v_prime=True)\n",
    "    a+=eta*da\n",
    "    b+=eta*db\n",
    "    w+=eta*dw\n",
    "    print(\"{:06d} / {:06d}\".format(j,nsteps),end=\"   \\r\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 6000x3000 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 6000x3000 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now: visualize the typical samples generated (from some starting point)\n",
    "# run several times to continue this. It basically is a random walk\n",
    "# through the space of all possible configurations, hopefully according\n",
    "# to the probability distribution that has been trained!\n",
    "\n",
    "nsteps=20\n",
    "num_samples=20\n",
    "test_samples=np.zeros([num_samples,batchsize,num_visible])\n",
    "test_hidden=np.zeros([num_samples,batchsize,num_hidden])\n",
    "skipsteps=1\n",
    "substeps=400 # how many steps to take before showing a new picture\n",
    "\n",
    "v_prime=np.zeros([batchsize,num_visible])\n",
    "h=np.zeros([batchsize,num_hidden])\n",
    "h_prime=np.zeros([batchsize,num_hidden])\n",
    "\n",
    "v=produce_sample_images(batchsize,num_visible,x_train,\n",
    "                       do_digitize=False)\n",
    "    \n",
    "for j in range(nsteps):\n",
    "    for k in range(substeps):\n",
    "        v,h,v_prime,h_prime=BoltzmannSequence(v,a,b,w,\n",
    "                                  drop_h_prime=True,\n",
    "                                  do_not_sample_v_prime=True) # step from v via h to v_prime!\n",
    "    test_samples[j%num_samples,:,:]=v[:,:]\n",
    "    test_hidden[j%num_samples,:]=h[:,:]\n",
    "    v=np.copy(v_prime) # use the new v as a starting point for next step!\n",
    "    if j%skipsteps==0 or j==nsteps-1:\n",
    "        clear_output(wait=True)\n",
    "        fig,ax=plt.subplots(ncols=1,nrows=batchsize,figsize=(num_samples,batchsize))\n",
    "        for n in range(batchsize):\n",
    "            ax[n].imshow(np.transpose(np.reshape(np.transpose(np.reshape(test_samples[:,n,:],[num_samples,Npixels,Npixels]),\n",
    "                                                    axes=[0,2,1]),[num_samples*Npixels,Npixels])),\n",
    "                      interpolation='none')\n",
    "            ax[n].axis('off')\n",
    "        plt.show()\n",
    "        fig,ax=plt.subplots(ncols=1,nrows=batchsize,figsize=(num_samples,batchsize))\n",
    "        for n in range(batchsize):\n",
    "            ax[n].imshow(np.transpose(np.reshape(np.transpose(np.reshape(test_hidden[:,n,:],[num_samples,6,10]),\n",
    "                                                    axes=[0,2,1]),[num_samples*10,6])),\n",
    "                      interpolation='none')\n",
    "            ax[n].axis('off')\n",
    "        plt.show()        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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