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explain_neuralnet_asifiama_ schoolkid_2.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "explain_neuralnet_asifiama_ schoolkid_2.ipynb",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/alexcpn/4d13ab72c8dcd97d81c296474621197a/explain_neuralnet_asifiama_-schoolkid_2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "WUMcoquq5pRe"
},
"source": [
"The below is the neural net we want to model; Taking inputs x0 to x4 and giving an output "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "sC9m5k2349vT"
},
"source": [
"![image.png](data:image/png;base64,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)![image.png]( )![](https://)"
]
},
{
"cell_type": "code",
"metadata": {
"id": "dihdwBm62yKb"
},
"source": [
"# This x defines our Input; or in Neural Network terms, the training set\n",
"\n",
"x = np.array(\n",
" [\n",
" [0,0,1],\n",
" [0,1,1],\n",
" [1,0,1],\n",
" [1,1,1]\n",
" ])\n"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "isn3yMg36_rd"
},
"source": [
"# and let y be the desired ouput \n",
"# Basically the first row in y represents the exected ouput for the first row of the training set.\n",
"# That is the output becomes1 only when two of the inputs\n",
"# becomes one\n",
"y = np.array(\n",
" [\n",
" [0],\n",
" [1],\n",
" [1],\n",
" [0]\n",
" ])"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "69cIvPwAg-Fz"
},
"source": [
"Now we need to define the weights of the layers of our neural network.\n",
"Note that the input is of shape $4*3$. So the first layer should be of shape that we can take dot product of.\n",
"Let us use $3*4$. The shape of the dot product woud be $4*4$ and the next layer weight should be comptaible with it. Let's take the next layer weights as size $4*1$."
]
},
{
"cell_type": "code",
"metadata": {
"id": "lDXCEUlezpgd"
},
"source": [
"np.random.seed(1)\n",
"\n",
"# randomly initialize our weights with mean 0\n",
"\n",
"weight1 = np.random.random((3,4)) \n",
"weight2 = np.random.random((4,1)) \n"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "17fD9mvZCHjb",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "416b96d4-e0ef-4bf8-f41b-6e6638e4f072"
},
"source": [
"#---------------------------------------------------------------\n",
"# Boiler plate code for calculating Sigmoid, derivative etc\n",
"#---------------------------------------------------------------\n",
"\n",
"import numpy as np\n",
"# seed random numbers to make calculation deterministic \n",
"np.random.seed(1)\n",
"\n",
"# pretty print numpy array\n",
"np.set_printoptions(formatter={'float': '{: 0.3f}'.format})\n",
"\n",
"# let us code our sigmoid funciton\n",
"def sigmoid(x):\n",
" return 1/(1+np.exp(-x))\n",
"\n",
"# let us add a method that takes the derivative of x as well\n",
"def derv_sigmoid(x):\n",
" return sigmoid(x)*(1-sigmoid(x))\n",
"\n",
"#---------------------------------------------------------------\n",
"\n",
"# Two layered NW. Using from (1) and the equations we derived as explanaionns\n",
"# (1) http://iamtrask.github.io/2015/07/12/basic-python-network/\n",
"#---------------------------------------------------------------\n",
"\n",
"# set learning rate as 1 for this toy example\n",
"learningRate = 1\n",
"\n",
"# input x, also used as the training set here\n",
"x = np.array([ [0,0,1],[0,1,1],[1,0,1],[1,1,1] ])\n",
"\n",
"# desired output for each of the training set above\n",
"y = np.array([[0,1,1,0]]).T\n",
"\n",
"# Explanaiton - as long as input has two ones, but not three, ouput is One\n",
"\"\"\"\n",
"Input [0,0,1] Output = 0\n",
"Input [0,1,1] Output = 1\n",
"Input [1,0,1] Output = 1\n",
"Input [1,1,1] Output = 0\n",
"\"\"\"\n",
"\n",
"# Randomly initalised weights\n",
"weight1 = np.random.random((3,4)) \n",
"weight2 = np.random.random((4,1)) \n",
"\n",
"# Activation to layer 0 is taken as input x\n",
"a0 = x\n",
"\n",
"iterations = 1000\n",
"for iter in range(0,iterations):\n",
"\n",
" # Forward pass - Straight Forward\n",
" z1= np.dot(x,weight1)\n",
" a1 = sigmoid(z1) \n",
" z2= np.dot(a1,weight2)\n",
" a2 = sigmoid(z2) \n",
" if iter == 0:\n",
" print(\"Intial Ouput \\n\",a2)\n",
"\n",
" # Backward Pass - Backpropagation \n",
" delta2 = (a2-y)\n",
" #---------------------------------------------------------------\n",
" # Calcluating change of Cost/Loss wrto weight of 2nd/last layer\n",
" # Eq (A) ---> dC_dw2 = delta2*derv_sigmoid(z2)*a1.T\n",
" #---------------------------------------------------------------\n",
"\n",
" dC_dw2_1 = delta2*derv_sigmoid(z2) \n",
" dC_dw2 = a1.T.dot(dC_dw2_1)\n",
" \n",
" #---------------------------------------------------------------\n",
" # Calcluating change of Cost/Loss wrto weight of 2nd/last layer\n",
" # Eq (B)---> dC_dw1 = derv_sigmoid(z1)*delta2*derv_sigmoid(z2)*weight2*a0.T\n",
" # dC_dw1 = derv_sigmoid(z1)*dC_dw2*weight2_1*a0.T\n",
" #---------------------------------------------------------------\n",
"\n",
" dC_dw1 = np.multiply(dC_dw2_1,weight2.T) * derv_sigmoid(z1)\n",
" dC_dw1 = a0.T.dot(dC_dw1)\n",
"\n",
" #---------------------------------------------------------------\n",
" #Gradinent descent\n",
" #---------------------------------------------------------------\n",
" \n",
" weight2 = weight2 - learningRate*(dC_dw2)\n",
" weight1 = weight1 - learningRate*(dC_dw1)\n",
"\n",
"\n",
"print(\"New ouput\",a2)\n",
"\n",
"#---------------------------------------------------------------\n",
"# Training is done, weight2 and weight2 are primed for output y\n",
"#---------------------------------------------------------------\n",
"\n",
"# Lets test out, two ones in input and one zero, ouput should be One\n",
"x = np.array([[1,0,1]])\n",
"z1= np.dot(x,weight1)\n",
"a1 = sigmoid(z1) \n",
"z2= np.dot(a1,weight2)\n",
"a2 = sigmoid(z2) \n",
"print(\"Ouput after Training is \\n\",a2)\n",
" \n"
],
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": [
"Intial Ouput \n",
" [[ 0.758]\n",
" [ 0.771]\n",
" [ 0.791]\n",
" [ 0.801]]\n",
"New ouput [[ 0.028]\n",
" [ 0.925]\n",
" [ 0.925]\n",
" [ 0.090]]\n",
"Ouput after Training is \n",
" [[ 0.925]]\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Rg-nU_ZNrD-s"
},
"source": [
"Lets model the above via Tensorflow framework"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 642
},
"id": "-1SsJY0mGWJm",
"outputId": "85fd33a3-f225-45b8-a927-a85b0454faf0"
},
"source": [
"import tensorflow as tf\n",
"from tensorflow import keras\n",
"from tensorflow.keras import layers\n",
"import numpy as np\n",
"from matplotlib import pyplot\n",
"\n",
"# Define Sequential model with 3 layers\n",
"# https://keras.io/api/layers/core_layers/dense/\n",
"\n",
"model = keras.Sequential()\n",
"model.add(layers.Dense(3, activation=\"sigmoid\", name=\"layer1\",input_shape=(4,3)))\n",
"model.add(layers.Dense(4, activation=\"sigmoid\", name=\"layer2\"))\n",
"model.add(layers.Dense(1, activation=\"sigmoid\", name=\"layer3\"))\n",
"\n",
"opt = tf.keras.optimizers.SGD(learning_rate=1.0)\n",
"model.compile(optimizer=opt, loss='mse',metrics=[['accuracy'], ['mse']])\n",
"# Call model on a test input\n",
"x = np.array(\n",
" [\n",
" [0,0,1],\n",
" [0,1,1],\n",
" [1,0,1],\n",
" [1,1,1]\n",
" ])\n",
"y = np.array([[0,1,1,0]]).T\n",
"model.output_shape\n",
"model.summary()\n",
"history =model.fit(x, y, epochs=1000, batch_size=1,verbose=0)\n",
"pyplot.plot(history.history['accuracy'])\n",
"pyplot.show()\n",
"pred = model.predict(x) \n",
"print(\"prediction\",pred)"
],
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"text": [
"Model: \"sequential_1\"\n",
"_________________________________________________________________\n",
"Layer (type) Output Shape Param # \n",
"=================================================================\n",
"layer1 (Dense) (None, 4, 3) 12 \n",
"_________________________________________________________________\n",
"layer2 (Dense) (None, 4, 4) 16 \n",
"_________________________________________________________________\n",
"layer3 (Dense) (None, 4, 1) 5 \n",
"=================================================================\n",
"Total params: 33\n",
"Trainable params: 33\n",
"Non-trainable params: 0\n",
"_________________________________________________________________\n",
"WARNING:tensorflow:Model was constructed with shape (None, 4, 3) for input KerasTensor(type_spec=TensorSpec(shape=(None, 4, 3), dtype=tf.float32, name='layer1_input'), name='layer1_input', description=\"created by layer 'layer1_input'\"), but it was called on an input with incompatible shape (1, 3).\n",
"WARNING:tensorflow:Model was constructed with shape (None, 4, 3) for input KerasTensor(type_spec=TensorSpec(shape=(None, 4, 3), dtype=tf.float32, name='layer1_input'), name='layer1_input', description=\"created by layer 'layer1_input'\"), but it was called on an input with incompatible shape (1, 3).\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
},
{
"output_type": "stream",
"text": [
"WARNING:tensorflow:Model was constructed with shape (None, 4, 3) for input KerasTensor(type_spec=TensorSpec(shape=(None, 4, 3), dtype=tf.float32, name='layer1_input'), name='layer1_input', description=\"created by layer 'layer1_input'\"), but it was called on an input with incompatible shape (None, 3).\n",
"prediction [[0.03814456]\n",
" [0.9462323 ]\n",
" [0.9463794 ]\n",
" [0.05433232]]\n"
],
"name": "stdout"
}
]
}
]
}
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