NN_scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Net from Scratch\n",
    "An example of a Neural Net from scrath. After the usual imports, we define our neural net and then test it on a basic example. This neural net uses a sigmoid at every stage (even the last one)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from pylab import *\n",
    "import random\n",
    "import time\n",
    "import sys\n",
    "from multiprocessing import Process, Queue\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1.0 / (1.0 + np.exp(-x))\n",
    "\n",
    "def tanh(x):\n",
    "    return np.tanh(x)\n",
    "#    return 1.72*np.tanh(2.0*x/3)\n",
    "\n",
    "def identity(x):\n",
    "    return x\n",
    "\n",
    "def relu(x):\n",
    "    rellu = lambda x: x if x>0 else 0\n",
    "    return np.array([rellu(xi) for xi in x])\n",
    "\n",
    "def chainDiff(v,f):\n",
    "    if f == sigmoid:\n",
    "        return v*(1.0 - v)\n",
    "    elif f == relu:\n",
    "        return 1 if v>0 else 0\n",
    "    elif f == tanh:\n",
    "        return 1-v**2\n",
    "#        return 2.0/3*(1.72-v**2/1.72)\n",
    "    else:\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "Class NeuralNel\n",
    "\n",
    "arguments: nbrNeurons is a list specifying the number of neurons in each layer, \n",
    "           eg: [2,2,3] is a NN with inputs of length 2, one hidden layer with 2 nodes,\n",
    "               and outputs of length 3.\n",
    "            activations is a list of functions wich are the activation functions on each layer\n",
    "            eg: [sigmoid, identity] applies a sigmoid on the first level and nothing on the second\n",
    "            \n",
    "further improvements could be to allow [lambda x: x] and other directly defined functions when\n",
    "creating the NN.\n",
    "\n",
    "'''\n",
    "\n",
    "class NeuralNet:\n",
    "    \n",
    "    def __init__(self, nbrNeurons, activations = None, weights = None, biases = None):\n",
    "        \n",
    "        if activations == None:\n",
    "            self.activations = [sigmoid for _ in range(nbrNeurons)-1]\n",
    "        else:\n",
    "            self.activations = activations\n",
    "            \n",
    "        self.nbrNeurons = nbrNeurons\n",
    "        self.nbrOutputs = nbrNeurons[-1]\n",
    "        self.nbrLayers = len(nbrNeurons)-1\n",
    "        \n",
    "        '''self.neurons = [ [layer,neuron] for layer in range(len(nbrNeurons)) \n",
    "                                        for neuron in range(nbrNeurons[layer])]\n",
    "        self.edges = [[layer, n_arrive, n_depart] for layer in range(self.nbrLayers) \n",
    "                                                  for n_arrive in range(self.nbrNeurons[layer+1])\n",
    "                                                  for n_depart in range(self.nbrNeurons[layer]) ]\n",
    "        '''\n",
    "        if weights == None:\n",
    "        # initial weigths set as random numbers in (0,1)\n",
    "            self.weights = []\n",
    "            for i in range(self.nbrLayers):\n",
    "                self.weights.append(np.random.rand(self.nbrNeurons[i+1], self.nbrNeurons[i]))\n",
    "        else:\n",
    "            self.weights = weights\n",
    "                \n",
    "        if biases == None:\n",
    "            self.biases = []\n",
    "            for i in range(self.nbrLayers):\n",
    "                self.biases.append(np.random.rand(self.nbrNeurons[i+1]))\n",
    "        else:\n",
    "            self.biases = biases\n",
    "    \n",
    "    def show_neurons(self):\n",
    "        print(self.neurons)\n",
    "        \n",
    "    def show_weights(self):\n",
    "        for layer in range(self.nbrLayers):\n",
    "            print(self.weights[layer])\n",
    "            print(self.biases[layer])\n",
    "        \n",
    "    def predict(self, x):\n",
    "        if len(x) != self.nbrNeurons[0] :\n",
    "            print(\"Wrong size of input !\")\n",
    "        else:\n",
    "            for i in range(self.nbrLayers):\n",
    "                x = self.activations[i](np.dot(self.weights[i],x) + self.biases[i])\n",
    "            return x\n",
    "    \n",
    "    def error(self, X, Y):\n",
    "        err = 0\n",
    "        for i in range(len(X)):\n",
    "            pred = self.predict(X[i])\n",
    "            err += np.linalg.norm(pred-Y[i])\n",
    "        return err / len(X)\n",
    "            \n",
    "            \n",
    "    def train(self, X, Y, step = 1, epoch = 1):\n",
    "        for _ in range(epoch):\n",
    "            order = list(range(len(X)))\n",
    "            np.random.shuffle(order)\n",
    "            '''\n",
    "            with Pool(5) as p:\n",
    "                A = ([X[order[i],Y[i]] for i in range())\n",
    "                X = p.starmap(self.train_once, A)\n",
    "            '''    \n",
    "            for i in order:\n",
    "                self.train_once(X[i], Y[i], step = step)\n",
    "    \n",
    "    def train_once(self, x, y, step = 1):\n",
    "        \"\"\"\n",
    "        training on 1 entry\n",
    "        this updates the weights of the model according to the step size and the gradient \n",
    "        of the neural net at the error = NN(x)-y\n",
    "        \"\"\"\n",
    "        if len(x) != self.nbrNeurons[0] or len(y)!= self.nbrNeurons[-1]:\n",
    "            print(\"Wrong size of x or y !\")\n",
    "        else:\n",
    "            values = []\n",
    "            values.append(np.array(x, dtype=float))\n",
    "            for i in range(self.nbrLayers):\n",
    "                x = self.activations[i](np.dot(self.weights[i],x) + self.biases[i])\n",
    "                values.append(x)\n",
    "            pred = x[-1]\n",
    "            \n",
    "            # initialize influence at zero because the first layer of neurons doesn't have\n",
    "            # influences (this is mainly to keep indices consistent)\n",
    "            influence = [0]\n",
    "            \n",
    "            #selection du neurone \n",
    "            for layer in range(1,self.nbrLayers+1):\n",
    "                infl_layer = []\n",
    "                \n",
    "                for neuron in range(self.nbrNeurons[layer]):\n",
    "                    infl_neuron = []\n",
    "                    \n",
    "                    #selection de l'arete\n",
    "                    for k in range(layer):\n",
    "                        infl = np.zeros([self.nbrNeurons[k+1],self.nbrNeurons[k]])\n",
    "                        # i boucle sur les neurones d'arrivee et j sur ceux de depart.\n",
    "                        for (i,j) in [(i,j) for i in range(self.nbrNeurons[k+1]) \n",
    "                                            for j in range(self.nbrNeurons[k])]:\n",
    "                            \n",
    "                            # Cas a separer pour avoir une activation differente sur \n",
    "                            # certaine couche.\n",
    "                            if layer-k == 1:\n",
    "                                if i != neuron:\n",
    "                                    infl[i,j] = 0\n",
    "                                else:\n",
    "                                    #chainDiff(v)\n",
    "                                    v = values[layer][neuron]\n",
    "                                    infl[i,j] = chainDiff(v, self.activations[layer-1])*values[k][j]\n",
    "                            else:\n",
    "                                # if the edge is too far, we use the chain rule\n",
    "                                v = values[layer][neuron]\n",
    "                                w = np.array([influence[layer-1][n][k][i,j] for n in range(self.nbrNeurons[layer-1])])\n",
    "                                infl[i,j] = chainDiff(v, self.activations[layer-1])*np.dot(self.weights[layer-1][neuron,:], w)\n",
    "                                \n",
    "                        infl_neuron.append(infl)\n",
    "\n",
    "                    #fin de selection d'arete\n",
    "                    infl_layer.append(infl_neuron)\n",
    "                influence.append(infl_layer)\n",
    "            \n",
    "            influence_B = [0]\n",
    "            \n",
    "            #selection du neurone \n",
    "            for layer in range(1,self.nbrLayers+1):\n",
    "                infl_layer = []\n",
    "                \n",
    "                for neuron in range(self.nbrNeurons[layer]):\n",
    "                    infl_neuron = []\n",
    "                    \n",
    "                    #selection du B\n",
    "                    for k in range(layer):\n",
    "                        infl = np.zeros(self.nbrNeurons[k+1])\n",
    "                        \n",
    "                        # i boucle sur les neurones d'arrivee du B.\n",
    "                        for i in range(self.nbrNeurons[k+1]):\n",
    "                            \n",
    "                            if layer-k == 1:\n",
    "                                if i != neuron:\n",
    "                                    infl[i] = 0\n",
    "                                else:\n",
    "                                    #chainDiff(v)\n",
    "                                    v = values[layer][neuron]\n",
    "                                    infl[i] = chainDiff(v, self.activations[layer-1])\n",
    "                            else:\n",
    "                                # if the edge is too far, we use the chain rule\n",
    "                                v = values[layer][neuron]\n",
    "                                w = np.array([influence_B[layer-1][n][k][i] for n in range(self.nbrNeurons[layer-1])])\n",
    "                                infl[i] = chainDiff(v, self.activations[layer-1])*np.dot(self.weights[layer-1][neuron,:], w)\n",
    "                        infl_neuron.append(infl)\n",
    "\n",
    "                    #fin de selection d'arete\n",
    "                    infl_layer.append(infl_neuron)\n",
    "                influence_B.append(infl_layer)\n",
    "\n",
    "\n",
    "            # use the gradients to calculate the new weights\n",
    "            delta_weights = []\n",
    "            delta_biases = []\n",
    "            for layer in range(self.nbrLayers):\n",
    "                delta_biases.append(step * influence_B[-1][0][layer]*(pred - y))\n",
    "                delta_weights.append(step * influence[-1][0][layer]*(pred - y))\n",
    "                \n",
    "            for layer in range(self.nbrLayers):\n",
    "                self.biases[layer] -= delta_biases[layer]\n",
    "                self.weights[layer] -= delta_weights[layer]\n",
    "            \n",
    "            return delta_weights, delta_biases\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#creation du neural net\n",
    "NN = NeuralNet([2,3,1], [sigmoid, tanh])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.94907315])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NN.predict([2,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0910290260701021"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#nos données test avec l'erreur du neural net\n",
    "X = np.array([ [0,0],[0,1],[-3,2],[-3,-3],[2,-3],[5,-4],[2,0],[-5,3],[0,5],[5,5],[5,3],[7,0],[8,2],[10,-3]])\n",
    "#Y = np.array([ [0]  ,[0]  ,[0]   ,[0]    ,[0]   ,[0]   ,[0]  ,[0]   ,[1]  ,[1]  ,[1]  ,[1]  ,[1]  ,[1]  ])\n",
    "Y = np.array([ [-1] ,[-1] ,[-1]  ,[-1]   ,[-1]  ,[-1]  ,[-1] ,[-1]   ,[1]  ,[1]  ,[1]  ,[1]  ,[1]  ,[1]  ])\n",
    "NN.error(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.87635309731880773"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#premier round d'entrainement\n",
    "NN.train(X,Y)\n",
    "NN.error(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.025161307460455491"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plus de round d'entrainement\n",
    "NN.train(X,Y, step=0.1, epoch=500)\n",
    "NN.error(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.015435875365113302"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#c'est beaucoup mieux, reposons des donnees test\n",
    "X_test = np.array([ [-1,-1],[0,-1],[-4,0],[-3,-1],[1,5],[4,4],[9,2],[6,1]])\n",
    "#Y_test = np.array([ [0]    ,[0]   ,[0]   ,[0]    ,[1]  ,[1]  ,[1]  ,[1]  ])\n",
    "Y_test = np.array([ [-1]    ,[-1]   ,[-1]   ,[-1]    ,[1]  ,[1]  ,[1]  ,[1]  ])\n",
    "NN.error(X_test,Y_test)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On voit que l'erreur sur le test set est similaire à l'erreur sur le train set, donc pas trop d'overfit. De plus, l'erreur est bien plus basse qu'avant trainning. Peut-on entrainer le modèle plus longtemps?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0020915678647154745"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plus de round d'entrainement\n",
    "NN.train(X,Y, step=0.1,epoch=10000)\n",
    "NN.error(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0019912093697984547"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# overfit ??\n",
    "NN.error(X_test,Y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow, toujours pas d'overfit!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "126.22336888313293\n",
      "0.0552125390997\n",
      "0.0732500537504\n"
     ]
    },
    {
     "data": {
      "image/png": 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c5KyEEwkaIKSxEJPYTwH4MwBv7iye/nXdPSmInaN/Yw4O7MhoYFAtPtlwXSZV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\nVRdi50TsBUcdiXFtvLApl83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fAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0ea17ec390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# More complicated test \n",
    "# lets define a function and say: above = 1, under = 0\n",
    "def courbe(x):\n",
    "    return 2*np.sin(2*x)\n",
    "\n",
    "'''\n",
    "X=np.linspace(-5,5,100)\n",
    "Y=courbe(X)\n",
    "plt.plot(X,Y)\n",
    "plt.show()\n",
    "'''\n",
    "nbrPoints = 600\n",
    "    \n",
    "#creation du train and test set\n",
    "X_train = 10*np.random.rand(nbrPoints,2)-5\n",
    "X_test = 10*np.random.rand(nbrPoints,2)-5\n",
    "\n",
    "f = lambda x: 1 if x[1]>courbe(x[0]) else 0\n",
    "Y_train = np.array([[f(x)] for x in X_train])\n",
    "Y_test  = np.array([[f(x)] for x in X_test])\n",
    "\n",
    "for i in range(nbrPoints):\n",
    "    color=\"r\"\n",
    "    if Y_train[i]==1:\n",
    "        color=\"b\"\n",
    "    plt.scatter(X_train[i,0],X_train[i,1], s=20,color = color)\n",
    "    \n",
    "    \n",
    "#creation du neural net\n",
    "NN = NeuralNet([2,10,1], activations = [sigmoid, sigmoid], weights = NNweights, biases = NNbiases)\n",
    "\n",
    "startTime = time.time()\n",
    "NN.train(X_train,Y_train, step=0.5,epoch=500)\n",
    "endTime = time.time()\n",
    "\n",
    "print(endTime - startTime)\n",
    "\n",
    "NNbiases = NN.biases\n",
    "NNweights = NN.weights\n",
    "print(NN.error(X_train,Y_train))\n",
    "print(NN.error(X_test,Y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NVuyjKc25Qo6hksHR0QJq9RK18ws0lq2kl8SVWxHr2/fFEXbdC6icWcV7+i94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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0eaa835860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nbrSpots = 500\n",
    "phi_m = np.linspace(-5, 5, nbrSpots)\n",
    "phi_p = np.linspace(-5, 5, nbrSpots)\n",
    "X,Y = np.meshgrid(phi_p, phi_m)\n",
    "Z=np.zeros([nbrSpots,nbrSpots])\n",
    "for i in range(nbrSpots):\n",
    "    for j in range(nbrSpots):\n",
    "        Z[j,i] = NN.predict([phi_m[i],phi_p[j]])\n",
    "        \n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "p = ax.pcolor(X, Y, Z, cmap=cm.RdBu, vmin=abs(Z).min(), vmax=abs(Z).max())\n",
    "cb = fig.colorbar(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(-0.5758066333301306, 4), (-1.5136049906158564, 3)]\n",
      "(1.8185948536513634, 2)\n",
      "0.0010313987731933594\n"
     ]
    }
   ],
   "source": [
    "# More complicated test \n",
    "# lets define a function and say: above = 1, under = 0\n",
    "\n",
    "from multiprocessing import Pool\n",
    "\n",
    "def courbe(x,y):\n",
    "    return 2*np.sin(2*x), y\n",
    "\n",
    "with Pool(5) as p:\n",
    "    X = p.starmap(courbe, [(8,4),(2,3)])\n",
    "\n",
    "print(X)\n",
    "startTime = time.time()\n",
    "res = []\n",
    "for i in range(7):\n",
    "    res.append(courbe(i,2))\n",
    "print(res[1])\n",
    "endTime = time.time()\n",
    "\n",
    "print(endTime - startTime)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([  1.68433228,  28.58524243, -13.74025668,  17.91628909,\n",
       "         13.03645404,  19.53530872,  -4.97127594, -11.86363178,\n",
       "        -12.67799085, -10.96090392]), array([ 34.46581975])]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NNbiases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'list' object has no attribute 'shape'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-51-1a4c89301e58>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mNNbiases\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: 'list' object has no attribute 'shape'"
     ]
    }
   ],
   "source": [
    "NNbiases.shape()"
   ]
  },
  {
   "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": "3.5.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}