Please see instructions for this assignment in the word document. You may complete this in Jupyter Notebook for coding parts and other short answer questions, thesis.

1 answer below »
Please see instructions for this assignment in the word document. You may complete this in Jupyter Notebook for coding parts and other short answer questions, thesis.
Answered 2 days AfterFeb 25, 2021

Answer To: Please see instructions for this assignment in the word document. You may complete this in Jupyter...

Vicky answered on Feb 27 2021
148 Votes
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# import libraries\n",
"from itertools import cycle\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. According to the following AND, OR, NOT symbols used in logical computations of electrical brain, can you express A ⊕ (¬B), Try to have at least two different ways to realize this operation results."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"class MLP:\n",
" \"\"\"\n",
" Create a multi-layer perceptron.\n",
" train_data: A 4x2 matrix with the input data.\n",
" target: A 4x1 matrix with expected outputs\n",
" lr: the learning rate. Defaults to 0.1\n",
" num_epochs: the number of times the training data goes through the model\n",
" while training\n",
" num_input: the number of nodes in the input layer of the MLP.\n",
" Should be equal to the second dimension of train_data.\n",
" \n",
" num_hidden: the number of nodes in the hidden layer of the MLP.\n",
" num_output: the number of nodes in the output layer of the MLP.\n",
" Should be equal to the second dimension of target.\n",
" \"\"\"\n",
" def __init__(self, train_data, target, lr=0.1, num_epochs=100, num_input=2, num_hidden=2, num_output=1):\n",
" self.train_data = train_data\n",
" self.target = target\n",
" self.lr = lr\n",
" self.num_epochs = num_epochs\n",
"\n",
" # initialize both sets of weights and biases randomly\n",
" # - weights_01: weights between input and hidden layer\n",
" # - weights_12: weights between hidden and output layer\n",
" self.weights_01 = np.random.uniform(size=(num_input, num_hidden))\n",
" self.weights_12 = np.random.uniform(size=(num_hidden, num_output))\n",
"\n",
" # - b01: biases for the hidden layer\n",
" # - b12: bias for the output layer\n",
" self.b01 = np.random.uniform(size=(1,num_hidden))\n",
" self.b12 = np.random.uniform(size=(1,num_output))\n",
"\n",
" self.losses = []\n",
"\n",
" def update_weights(self):\n",
" \n",
" # Calculate the squared error\n",
" loss = 0.5 * (self.target - self.output_final) ** 2\n",
" print(loss)\n",
" self.losses.append(np.sum(loss))\n",
"\n",
" error_term = (self.target - self.output_final)\n",
"\n",
" # the gradient for the hidden layer weights\n",
" grad01 = self.train_data.T @ (((error_term * self._delsigmoid(self.output_final)) * self.weights_12.T) * self._delsigmoid(self.hidden_out))\n",
" print(\"grad01: \", grad01)\n",
" print(grad01.shape)\n",
"\n",
" # the gradient for the output layer weights\n",
" grad12 = self.hidden_out.T @ (error_term * self._delsigmoid(self.output_final))\n",
"\n",
" print(\"grad12: \", grad12)\n",
" print(grad12.shape)\n",
"\n",
" # updating the weights by the learning rate times their gradient\n",
" self.weights_01 += self.lr * grad01\n",
" self.weights_12 += self.lr * grad12\n",
"\n",
" # update the biases the same way\n",
" self.b01 += np.sum(self.lr * ((error_term * self._delsigmoid(self.output_final)) * self.weights_12.T) * self._delsigmoid(self.hidden_out), axis=0)\n",
" self.b12 += np.sum(self.lr * error_term * self._delsigmoid(self.output_final), axis=0)\n",
"\n",
" def _sigmoid(self, x):\n",
" \"\"\"\n",
" The sigmoid activation function.\n",
" \"\"\"\n",
" return 1 / (1 + np.exp(-x))\n",
"\n",
" def _delsigmoid(self, x):\n",
" \"\"\"\n",
" The first derivative of the sigmoid function wrt x\n",
" \"\"\"\n",
" return x * (1 - x)\n",
"\n",
" def forward(self, batch):\n",
" \"\"\"\n",
" A single forward pass through the network.\n",
" Implementation of wX + b\n",
" \"\"\"\n",
"\n",
" self.hidden_ = np.dot(batch, self.weights_01) + self.b01\n",
" self.hidden_out = self._sigmoid(self.hidden_)\n",
"\n",
" self.output_ = np.dot(self.hidden_out, self.weights_12) + self.b12\n",
" self.output_final = self._sigmoid(self.output_)\n",
"\n",
" return self.output_final\n",
"\n",
" def classify(self, datapoint):\n",
" \"\"\"\n",
" Return the class to which a datapoint belongs based on\n",
" the perceptron's output for that point.\n",
" \"\"\"\n",
" datapoint = np.transpose(datapoint)\n",
" if self.forward(datapoint) >= 0.5:\n",
" return 1\n",
"\n",
" return 0\n",
"\n",
" def plot(self, h=0.01):\n",
" \"\"\"\n",
" Generate plot of input data and decision boundary.\n",
" \"\"\"\n",
" # setting plot properties like size, theme and axis limits\n",
" sns.set_style('darkgrid')\n",
" plt.figure(figsize=(20, 20))\n",
"\n",
" plt.axis('scaled')\n",
" plt.xlim(-0.1, 1.1)\n",
" plt.ylim(-0.1, 1.1)\n",
"\n",
" colors = {\n",
" 0: \"ro\",\n",
" 1: \"go\"\n",
" }\n",
"\n",
" # plotting the four datapoints\n",
" for i in range(len(self.train_data)):\n",
" plt.plot([self.train_data[i][0]],\n",
" [self.train_data[i][1]],\n",
" colors[self.target[i][0]],\n",
" markersize=20)\n",
"\n",
" x_range = np.arange(-0.1, 1.1, h)\n",
" y_range = np.arange(-0.1, 1.1, h)\n",
"\n",
" # creating a mesh to plot decision boundary\n",
" xx, yy = np.meshgrid(x_range, y_range, indexing='ij')\n",
" Z = np.array([[self.classify([x, y]) for x in x_range] for y in y_range])\n",
"\n",
" # using the contourf function to create the plot\n",
" plt.contourf(xx, yy, Z, colors=['red', 'green', 'green', 'blue'], alpha=0.4)\n",
"\n",
" def train(self):\n",
" \"\"\"\n",
" Train an MLP. Runs through the data num_epochs number of times.\n",
" A forward pass is done first, followed by a backward pass (backpropagation)\n",
" where the networks parameter's are updated.\n",
" \"\"\"\n",
" for _ in range(self.num_epochs):\n",
" self.forward(self.train_data)\n",
" self.update_weights()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"train_data = np.array(\n",
" [\n",
" [0, 0],\n",
" [0, 1],\n",
" [1, 0],\n",
" [1, 1]])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"target = np.array(\n",
" [\n",
" [1],\n",
" [0],\n",
" [0],\n",
" [1]])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
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