01_MachineLearning_Basics_NeuralNetworksPython.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Networks with Pure Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example code for the lecture series \"Machine Learning for Physicists\" by Florian Marquardt\n",
    "\n",
    "Lecture 1\n",
    "\n",
    "See https://machine-learning-for-physicists.org and the current course website linked there!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to:\n",
    "- implement the forward-pass (evaluation) of a deep, fully connected neural network in a few lines of python\n",
    "- do that efficiently using batches\n",
    "- illustrate the results for randomly initialized neural networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports: only numpy and matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the \"numpy\" library for linear algebra\n",
    "\n",
    "# In the lecture videos, I do this:\n",
    "#\n",
    "# from numpy import *\n",
    "#\n",
    "# WARNING: It is generally considered bad\n",
    "# programming style to \"import *\", as it\n",
    "# can lead to confusion. For me, I\n",
    "#  (1) ALWAYS import numpy\n",
    "#  (2) NEVER import any other package in this * way\n",
    "# Therefore, there is never confusion for me, and\n",
    "# it makes my code a bit more readable (for me).\n",
    "# However, since 99% of people are using the \n",
    "# syntax \"import numpy as np\" and then\n",
    "# access \"np.exp()\" etc., you\n",
    "# should probably also use \"np\" once you start\n",
    "# exchanging code with others. I convert\n",
    "# back to the np. syntax when I turn my\n",
    "# converged code into a module.\n",
    "#\n",
    "# It is apparently officially accepted to explicitly\n",
    "# list all the functions you need from numpy:\n",
    "\n",
    "from numpy import array, zeros, exp, random, dot, shape, reshape, meshgrid, linspace\n",
    "\n",
    "import matplotlib.pyplot as plt # for plotting\n",
    "import matplotlib\n",
    "matplotlib.rcParams['figure.dpi']=300 # highres display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A very simple neural network (no hidden layer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A network with N0 input neurons and N1 output neurons (no hidden layer)\n",
    "\n",
    "$$y^{\\rm out}_j = f(\\sum_k w_{jk} y^{\\rm in}_k + b_j)$$\n",
    "\n",
    "where $w$ is the weight matrix, $b$ is the bias vector, and $f$ would be the activation function (e.g. the sigmoid here), which is applied independently for each $j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N0=3 # input layer size\n",
    "N1=2 # output layer size\n",
    "\n",
    "# initialize random weights: array dimensions N1xN0\n",
    "w=random.uniform(low=-1,high=+1,size=(N1,N0))\n",
    "# initialize random biases: N1 vector\n",
    "b=random.uniform(low=-1,high=+1,size=N1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# input values\n",
    "y_in=array([0.2,0.4,-0.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# evaluate network by hand, in two steps\n",
    "z=dot(w,y_in)+b # result: the vector of 'z' values, length N1\n",
    "y_out=1/(1+exp(-z)) # the 'sigmoid' function (applied elementwise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "network input y_in: [ 0.2  0.4 -0.1]\n",
      "weights w: [[-0.10438302  0.90536501  0.34479841]\n",
      " [ 0.14795581  0.96366737 -0.78710148]]\n",
      "bias vector b: [0.62298635 0.49342234]\n",
      "linear superposition z: [0.92977591 0.9871906 ]\n",
      "network output y_out: [0.71702982 0.72853266]\n"
     ]
    }
   ],
   "source": [
    "print(\"network input y_in:\", y_in)\n",
    "print(\"weights w:\", w)\n",
    "print(\"bias vector b:\", b)\n",
    "print(\"linear superposition z:\", z)\n",
    "print(\"network output y_out:\", y_out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize network result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still stay with the simple network, but define a function that evaluates the network, and visualize the  output for various inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# a function that applies the network\n",
    "def apply_net(y_in):\n",
    "    global w, b\n",
    "    \n",
    "    z=dot(w,y_in)+b    \n",
    "    return(1/(1+exp(-z)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "N0=2 # input layer size\n",
    "N1=1 # output layer size\n",
    "\n",
    "w=random.uniform(low=-10,high=+10,size=(N1,N0)) # random weights: N1xN0\n",
    "b=random.uniform(low=-1,high=+1,size=N1) # biases: N1 vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.07188659])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apply_net([0.8,0.3]) # a simple test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note: this is NOT the most efficient way to do this! (but simple)\n",
    "# We will later learn to use array syntax efficiently\n",
    "\n",
    "M=50 # will create picture of size MxM\n",
    "y_out=zeros([M,M]) # array MxM, to hold the result\n",
    "\n",
    "for j1 in range(M):\n",
    "    for j2 in range(M):\n",
    "        # out of these integer indices, generate\n",
    "        # two values in the range -0.5...0.5\n",
    "        # and then apply the network to those two\n",
    "        # input values\n",
    "        value0=float(j1)/M-0.5\n",
    "        value1=float(j2)/M-0.5\n",
    "        y_out[j1,j2]=apply_net([value0,value1])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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37CJj2EwdZl4UVfU9SX5osPlFrbX/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H7Orc5rrX1MkmcsHbqW5KcKS7v/fu7Izhqpdy4d/v+y00h9S/X9rZtmKgAAAAAcb89N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\nmSpJkiRJkiRJHfx/28LGyWXfs+IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1102b6438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display image\n",
    "plt.imshow(y_out,origin='lower',extent=(-0.5,0.5,-0.5,0.5))\n",
    "plt.colorbar()\n",
    "plt.title(\"NN output as a function of input values\")\n",
    "plt.xlabel(\"y_2\")\n",
    "plt.ylabel(\"y_1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now visualize a network with one hidden layer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea here is to have multiple weight matrices (for each pair of subsequent layers there is one weight matrix). The function that \"applies a layer\", i.e. goes from one layer to the next, is essentially the same as the function evaluating the simple network above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# a function that evaluates one layer based\n",
    "# on the neuron values in the preceding layer\n",
    "def apply_layer(y_in,w,b): \n",
    "    z=dot(w,y_in)+b\n",
    "    return(1/(1+exp(-z)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "N0=2 # input layer size\n",
    "N1=30 # hidden layer size\n",
    "N2=1 # output layer size\n",
    "\n",
    "# weights and biases\n",
    "# from input layer to hidden layer:\n",
    "w1=random.uniform(low=-10,high=+10,size=(N1,N0)) # random weights: N1xN0\n",
    "b1=random.uniform(low=-1,high=+1,size=N1) # biases: N1 vector\n",
    "\n",
    "# weights+biases from hidden layer to output layer:\n",
    "w2=random.uniform(low=-10,high=+10,size=(N2,N1)) # random weights\n",
    "b2=random.uniform(low=-1,high=+1,size=N2) # biases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# evaluate the network by subsequently\n",
    "# evaluating the two steps (input to hidden and\n",
    "# hidden to output)\n",
    "def apply_net(y_in):\n",
    "    global w1,b1,w2,b2\n",
    "    \n",
    "    y1=apply_layer(y_in,w1,b1)\n",
    "    y2=apply_layer(y1,w2,b2)\n",
    "    return(y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Again, obtain values for a range of inputs\n",
    "# Note: this is NOT the most efficient way to do this! (but simple)\n",
    "\n",
    "M=50 # will create picture of size MxM\n",
    "y_out=zeros([M,M]) # array MxM, to hold the result\n",
    "\n",
    "for j1 in range(M):\n",
    "    for j2 in range(M):\n",
    "        value0=float(j1)/M-0.5\n",
    "        value1=float(j2)/M-0.5\n",
    "        y_out[j1,j2]=apply_net([value0,value1])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ndexwVXVKVf1ukrfk8IXUJDk9yXcn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eRjuWmYNMb1SX4lyfP8I8Fmm9Kc3o6q+s9JfvIQPxKmAmtLmApMVlUdn+R/5aZ/gf5s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\nH7GQArtGUMmjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef94d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display image\n",
    "plt.imshow(y_out,origin='lower',extent=(-0.5,0.5,-0.5,0.5))\n",
    "plt.colorbar()\n",
    "plt.title(\"NN output as a function of input values\")\n",
    "plt.xlabel(\"y_2\")\n",
    "plt.ylabel(\"y_1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obviously, the shape of the output is already more 'complex' than that of a simple network without hidden layer! Let's go further in that direction..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applying a network to a 'batch' of samples (python trickery)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Goal: apply network to many samples in parallel (no 'for' loops!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Small excursion: matrix-vector multiplication and python broadcasting of array dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7, 30)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# See how the dot product works: \n",
    "# 'contracts' (sums over) the innermost index\n",
    "W=zeros([7,8])\n",
    "y=zeros([8,30]) \n",
    "# here '30' would stand for the number of samples\n",
    "# in our envisaged network applications\n",
    "shape(dot(W,y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (7,30) (7,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-17-3d0ac521c66d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;31m# in the most naive way (beware!)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mresult\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mB\u001b[0m \u001b[0;31m# will produce an error!\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (7,30) (7,) "
     ]
    }
   ],
   "source": [
    "# now try to add the bias vector entries,\n",
    "# in the most naive way (beware!)\n",
    "B=zeros(7)\n",
    "result=dot(W,y)+B # will produce an error!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 7)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# But with a re-ordering of indices, this works!\n",
    "# So, let's take the dimension of size 30 to be\n",
    "# the very first one:\n",
    "y=zeros([30,8])\n",
    "W=zeros([8,7])\n",
    "shape(dot(y,W))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 7)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and now try again adding the bias vector,\n",
    "# again in a naive way\n",
    "B=zeros(7)\n",
    "result=dot(y,W)+B \n",
    "# will give the desired result, \n",
    "# because B is 'broadcast' to shape (30,7)\n",
    "shape(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining the functions that evaluate a layer and evaluate the network, with batch processing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up for batch processing, i.e. parallel evaluation of many input samples!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_layer_new(y_in,w,b): # a function that applies a layer    \n",
    "    z=dot(y_in,w)+b # note different order in matrix product!\n",
    "    return(1/(1+exp(-z)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_net_new(y_in): # same as before, but with new layer function\n",
    "    global w1,b1,w2,b2\n",
    "    \n",
    "    y1=apply_layer_new(y_in,w1,b1)\n",
    "    y2=apply_layer_new(y1,w2,b2)\n",
    "    return(y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "N0=2 # input layer size\n",
    "N1=5 # hidden layer size\n",
    "N2=1 # output layer size\n",
    "\n",
    "# from input layer to hidden layer:\n",
    "w1=random.uniform(low=-10,high=+10,size=(N0,N1)) # NEW ORDER!! N0xN1\n",
    "b1=random.uniform(low=-1,high=+1,size=N1) # biases: N1 vector\n",
    "\n",
    "# from hidden layer to output layer:\n",
    "w2=random.uniform(low=-10,high=+10,size=(N1,N2)) # NEW ORDER N1xN2\n",
    "b2=random.uniform(low=-1,high=+1,size=N2) # biases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "batchsize=10000\n",
    "y=random.uniform(low=-1,high=1,size=(batchsize,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_out=apply_net_new(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 1)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape(y_out) \n",
    "# these were 10000 samples evaluated in parallel!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now visualize multi-layer net again, but more efficiently!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the pixels in the image are samples, process all of them together!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "M=50\n",
    "# Generate a 'mesh grid', i.e. x,y values in an image\n",
    "v0,v1=meshgrid(linspace(-0.5,0.5,M),linspace(-0.5,0.5,M))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef944a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(1,2)\n",
    "ax[0].imshow(v0,origin='lower')\n",
    "ax[0].set_title(\"input value v0\")\n",
    "ax[1].imshow(v1,origin='lower')\n",
    "ax[1].set_title(\"input value v1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2500,)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0flat=v0.flatten() # make 1D array out of 2D array\n",
    "v1flat=v1.flatten() \n",
    "# that means: MxM matrix becomes M^2 vector\n",
    "shape(v0flat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "batchsize=shape(v0flat)[0] # number of samples = number of pixels\n",
    "y_in=zeros([batchsize,2])\n",
    "y_in[:,0]=v0flat # fill first component (index 0)\n",
    "y_in[:,1]=v1flat # fill second component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# apply net to all these samples simultaneously!\n",
    "y_out=apply_net_new(y_in) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2500, 1)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape(y_out) # this is not a vector but a funny matrix batchsize x 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# turn this back into a 2D matrix (image)\n",
    "y_2D=reshape(y_out[:,0],[M,M]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Hu0MtTr6V5Pa11heu98LaxuC5c9Y2Vy5J/kyz3W43HTyvST60YKzfTJvhZNpXk9y61vqS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\nziVPvsIocfbuu+IocS7xtXE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hAgAAANBJQgUAAACgk4QKAAAAQCcJFQAAAIBOEioAAAAA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\nDKhIkiRJkiR1ZEBFkiRJkiSpo/8P4z3xEcJJVzgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef94b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(y_2D,origin='lower')\n",
    "plt.title(\"NN output (one hidden layer)\")\n",
    "plt.xlabel(\"v0\")\n",
    "plt.ylabel(\"v1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For fun: a network with MANY hidden layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nlayers=20 # not counting the input layer & the output layer\n",
    "LayerSize=100\n",
    "\n",
    "Weights=random.uniform(low=-3,high=3,size=[Nlayers,LayerSize,LayerSize])\n",
    "Biases=random.uniform(low=-1,high=1,size=[Nlayers,LayerSize])\n",
    "\n",
    "# for the first hidden layer (coming in from the input layer)\n",
    "WeightsFirst=random.uniform(low=-1,high=1,size=[2,LayerSize])\n",
    "BiasesFirst=random.uniform(low=-1,high=1,size=LayerSize)\n",
    "\n",
    "# for the final layer (i.e. the output neuron)\n",
    "WeightsFinal=random.uniform(low=-1,high=1,size=[LayerSize,1])\n",
    "BiasesFinal=random.uniform(low=-1,high=1,size=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_multi_net(y_in):\n",
    "    global Weights, Biases, WeightsFinal, BiasesFinal, Nlayers\n",
    "    \n",
    "    y=apply_layer_new(y_in,WeightsFirst,BiasesFirst)    \n",
    "    for j in range(Nlayers):\n",
    "        y=apply_layer_new(y,Weights[j,:,:],Biases[j,:])\n",
    "    output=apply_layer_new(y,WeightsFinal,BiasesFinal)\n",
    "    return(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate a 'mesh grid', i.e. x,y values in an image\n",
    "M=40\n",
    "v0,v1=meshgrid(linspace(-0.5,0.5,M),linspace(-0.5,0.5,M))\n",
    "batchsize=M**2 # number of samples = number of pixels = M^2\n",
    "y_in=zeros([batchsize,2])\n",
    "y_in[:,0]=v0.flatten() # fill first component (index 0)\n",
    "y_in[:,1]=v1.flatten() # fill second component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use the MxM input grid that we generated above \n",
    "y_out=apply_multi_net(y_in) # apply net to all these samples!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_2D=reshape(y_out[:,0],[M,M]) # back to 2D image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
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nuZcNbf/1SCqa8q2h7TNLKctmmPH4oe3ZjIocKY1GAAAAgHliUMcy2fPboPan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\nAIDZGdT+r4E40Hk4ZGk07mp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uImsbn7+tWfap75vLhKVDe+jyNu8tSbL8/nY/e9t/sM1z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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a9c6b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(y_2D,origin='lower',extent=[-0.5,0.5,-0.5,0.5],interpolation='nearest')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now do the same, but high-resolution (400x400 picture)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "M=400\n",
    "# Generate a 'mesh grid', i.e. x,y values in an image\n",
    "v0,v1=meshgrid(linspace(-0.5,0.5,M),linspace(-0.5,0.5,M))\n",
    "batchsize=M**2 # number of samples = number of pixels = M^2\n",
    "y_in=zeros([batchsize,2])\n",
    "y_in[:,0]=v0.flatten() # fill first component (index 0)\n",
    "y_in[:,1]=v1.flatten() # fill second component"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next function takes a few seconds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use the MxM input grid that we generated above \n",
    "y_out=apply_multi_net(y_in) # apply net to all these samples!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_2D=reshape(y_out[:,0],[M,M]) # back to 2D image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11aa2b1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[10,10])\n",
    "plt.axes([0,0,1,1]) # fill all of the picture with the image\n",
    "plt.imshow(y_2D,origin='lower',extent=[-0.5,0.5,-0.5,0.5],interpolation='nearest')\n",
    "plt.axis('off') # no axes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Try another nonlinearity: rectified linear units!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Sh5PcleS2uq5bd90ZAgAAAHRvdz62Iu//1i3FO32bmzJt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\njvx1wZPFOy84dI+841WHF+8AUJYhAQAAAKAX+eE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cKSf5DKqqen6S83ZVHwAAAHqyr/3m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\nR/17aRRzXjdxM0UTp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110a4fb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=linspace(-1,1,100)\n",
    "plt.plot(x,x*(x>0),linewidth=5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_layer_new_relu(y_in,w,b): # a function that applies a layer    \n",
    "    z=dot(y_in,w)+b # note different order in matrix product!\n",
    "    return(z*(z>0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_multi_net_relu(y_in):\n",
    "    global Weights, Biases, WeightsFinal, BiasesFinal, Nlayers\n",
    "    \n",
    "    y=apply_layer_new_relu(y_in,WeightsFirst,BiasesFirst)    \n",
    "    for j in range(Nlayers):\n",
    "        y=apply_layer_new_relu(y,Weights[j,:,:],Biases[j,:])\n",
    "    output=apply_layer_new_relu(y,WeightsFinal,BiasesFinal)\n",
    "    return(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nlayers=20 # not counting the input layer & the output layer\n",
    "LayerSize=100\n",
    "\n",
    "Weights=random.uniform(low=-1,high=1,size=[Nlayers,LayerSize,LayerSize])\n",
    "Biases=0*random.uniform(low=-1,high=1,size=[Nlayers,LayerSize])\n",
    "\n",
    "# for the first hidden layer (coming in from the input layer)\n",
    "WeightsFirst=random.uniform(low=-1,high=1,size=[2,LayerSize])\n",
    "BiasesFirst=0*random.uniform(low=-1,high=1,size=LayerSize)\n",
    "\n",
    "# for the final layer (i.e. the output neuron)\n",
    "WeightsFinal=random.uniform(low=-1,high=1,size=[LayerSize,1])\n",
    "BiasesFinal=0*random.uniform(low=-1,high=1,size=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "M=400\n",
    "# Generate a 'mesh grid', i.e. x,y values in an image\n",
    "v0,v1=meshgrid(linspace(-0.5,0.5,M),linspace(-0.5,0.5,M))\n",
    "batchsize=M**2 # number of samples = number of pixels = M^2\n",
    "y_in=zeros([batchsize,2])\n",
    "y_in[:,0]=v0.flatten() # fill first component (index 0)\n",
    "y_in[:,1]=v1.flatten() # fill second component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use the MxM input grid that we generated above \n",
    "y_out=apply_multi_net_relu(y_in) # apply net to all these samples!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_2D=reshape(y_out[:,0],[M,M]) # back to 2D image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110392780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[10,10])\n",
    "plt.axes([0,0,1,1]) # fill all of the picture with the image\n",
    "plt.imshow(y_2D,origin='lower',extent=[-0.5,0.5,-0.5,0.5],interpolation='nearest')\n",
    "plt.axis('off') # no axes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now zoom out!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "M=400\n",
    "# Generate a 'mesh grid', i.e. x,y values in an image\n",
    "v0,v1=meshgrid(linspace(-10,10,M),linspace(-10,10,M))\n",
    "batchsize=M**2 # number of samples = number of pixels = M^2\n",
    "y_in=zeros([batchsize,2])\n",
    "y_in[:,0]=v0.flatten() # fill first component (index 0)\n",
    "y_in[:,1]=v1.flatten() # fill second component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use the MxM input grid that we generated above \n",
    "y_out=apply_multi_net_relu(y_in) # apply net to all these samples!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_2D=reshape(y_out[:,0],[M,M]) # back to 2D image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119d6fda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[10,10])\n",
    "plt.axes([0,0,1,1]) # fill all of the picture with the image\n",
    "plt.imshow(y_2D,origin='lower',extent=[-0.5,0.5,-0.5,0.5],interpolation='nearest')\n",
    "plt.axis('off') # no axes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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M1O91qb9Tj/dBjNpOt23M3uwYJnvD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\nHyXnXkHfC/QfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a92a6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y_2D[:,200])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}