{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "467bae8f",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4a6920a",
   "metadata": {},
   "source": [
    "# Artificial Neurons \n",
    "\n",
    "Billions of neurons in our brain form a neural network through which our brain makes decisions. Similarly, an Artificial Neural Network is simply a collection of artificial neurons arranged in layers, where the outputs of some neurons become the inputs to others.\n",
    "The phrase \"neural network\" can refer to the networks of neurons found in our brains (Biological Neural Networks or BNNs) or, in the context of machine learning (ML), to Artificial Neural Networks (ANNs). We usually drop the term \"artificial\" and simply call them neural networks, with the understanding that we are referring to the ML context.\n",
    "\n",
    "You saw what a neuron in our brain looks like. In this section, we will introduce some of the commonly used artificial neurons. \n",
    "\n",
    "## The Perceptron\n",
    "\n",
    "One of the most fundamental artificial neuron is the *perceptron*. Perceptrons were developed in 1957 by Frank Rosenblatt. Take a look at the diagram below:\n",
    "\n",
    "```{image} ./perceptron.png\n",
    ":name: fig-perceptron\n",
    "```\n",
    "<center>\n",
    "<em> Figure: Structure of a Perceptron </em>\n",
    "</center>\n",
    "\n",
    "The input layer of a perceptron, just like the dendrites of a neuron that receive input signals, can take several inputs $x_1, x_2, ..., x_m$. These inputs may be any real numbers. Depending on the importance of each of these inputs, they are assigned corresponding weights $w_1, w_2, ..., w_m$. The weights can also be any real numbers: a positive weight represents an excitatory influence, a negative weight represents an inhibitory influence, and a zero weight indicates no effect. The perceptron then calculates a weighted sum of the inputs: $z = \\sum_{i = 1}^{m} w_i x_i = w_1x_1 + w_2x_2+ ... + w_mx_m$. This value is fed into an activation function $g$ that compares it to a threshold value to produce a binary output:\n",
    "\n",
    "$$\\text{output} = \\begin{cases}\n",
    "0, & \\text{if } \\sum_{i = 1}^{m} w_i x_i \\le \\text{threshold} \\\\\n",
    "1,  & \\text{if } \\sum_{i = 1}^{m} w_i x_i > \\text{threshold}\n",
    "\\end{cases}$$\n",
    "\n",
    "Another way to put this is \n",
    "\n",
    "$$\\text{output} = \\begin{cases}\n",
    "0, & \\text{if } w_0 + \\sum_{i = 1}^{m} w_i x_i \\le 0 \\\\\n",
    "1,  & \\text{if } w_0 + \\sum_{i = 1}^{m} w_i x_i > 0\n",
    "\\end{cases}$$\n",
    "\n",
    "with $w_0 = - \\text{threshold}$. \n",
    "\n",
    "The above rewriting is only for the simplification of notation, which greatly simplifies the mathematics when we have several such layers together. The term $w_0$ is called the **bias** term. Just as biological neurons have different firing thresholds, the bias term controls how easily a perceptron activates. Think of the bias as a measure of how easy it is for a perceptron to output $1$. If the bias has a big positive value, it is extremely easy for $w_0 + \\sum_{i = 1}^{m} w_i x_i$ to exceed the threshold (zero) and thus output $1$. However, if the bias is very negative, then it is difficult for the perceptron to activate.\n",
    "\n",
    "Let us consider a simple example with binary inputs to understand the working of a perceptron. Say you want to classify an email as spam or not spam. You decide to consider three factors to make that decision: $x_1 =$ whether the email contains the word \"lottery\", $x_2 =$ whether the email has more than two links, and $x_3 =$ whether the sender is unknown. Each of these inputs $x_1, x_2,$ and $x_3$ takes the value $0$ for \"No\" or $1$ for \"Yes\".\n",
    "\n",
    "Let us say you believe that the word \"lottery\" in the email is more indicative of spam than the factor of having more than two links, which in turn is more indicative than whether the sender is unknown. Based on this reasoning, we assign the weights $w_1 = 0.6$, $w_2 = 0.4$, and $w_3 = 0.3$, and a bias of $w_0 = -0.5$. So, if the weighted sum exceeds $0$, then we will get the output that the email is indeed spam. Let us say we receive an email that does not have the word \"lottery\", has more than two links, and is from an unknown sender. Then:\n",
    "\n",
    "$$w_0 + w_1x_1 + w_2x_2 + w_3x_3 = -0.5 + 0.6 \\times 0 + 0.4 \\times 1 + 0.3 \\times 1 = 0.2 > 0$$\n",
    "\n",
    "```{image} ./example_perceptron.png\n",
    ":name: fig-perceptron-spam\n",
    "```\n",
    "<center>\n",
    "<em> Figure: Perceptron as a spam filter </em>\n",
    "</center>\n",
    "\n",
    "Thus, the email will be classified as spam. This example reveals an interesting property of how the perceptron makes decisions. With these particular weights and bias, any email containing the word \"lottery\" will automatically be classified as spam. However, if \"lottery\" is absent, then the email must have both more than two links *and* an unknown sender to be classified as spam.\n",
    "\n",
    "\n",
    "## The Sigmoid Neuron\n",
    "\n",
    "Another common type of artificial neuron is *The Sigmoid Neuron*. Just like a perceptron, the sigmoid neuron has inputs $x_i$'s, weights $w_i$'s and a bias term $w_0$. However, the output of a sigmoid neuron need not be binary ($0$ or $1$). Instead of applying a step function as the activation function, we use the *sigmoid function* which is defined by:\n",
    "\n",
    "$$\n",
    "\\sigma(z) = \\dfrac{1}{1 + e^{-z}}\n",
    "$$\n",
    "\n",
    "Let us visualize how the sigmoid function looks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b1ca4c36",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the sigmoid function\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "# Generate input values\n",
    "z = np.linspace(-10, 10, 400)  # from -10 to 10\n",
    "\n",
    "# Compute sigmoid outputs\n",
    "y = sigmoid(z)\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(z, y, color = '#800000', linewidth=2)\n",
    "plt.title('Sigmoid Function', fontsize=14)\n",
    "plt.xlabel('z')\n",
    "plt.ylabel('σ(z)')\n",
    "plt.grid(True, linestyle='--', alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16325664",
   "metadata": {},
   "source": [
    "Does it remind of you a function you have already seen? Yes, the logistic function used in logistic regression! It is the same exact idea here. \n",
    "\n",
    "The output of a sigmoid neuron with inputs $x_i$'s and weights $w_i$'s and bias $w_0$ is: \n",
    "\n",
    "$$\\dfrac{1}{1 + e^{-(w_0 + \\sum_{i = 1} w_i x_i)}}$$\n",
    "\n",
    "The sigmoid function \"squashes\" any input value into the range $[0,1]$. When the value of the weighted sum $z = w_0 + w_1x_1 + w_2x_2 + ... + w_mx_m$ is a large positive the number, the output of the sigmoid neuron, $\\sigma(z)$, approaches 1. Conversely, when the weighted sum $z$ is a large negative number, the output approaches 0.\n",
    "\n",
    "So far we have seen two kinds of activation functions: the step function, and the sigmoid function. There are other activation functions too, for example:\n",
    "\n",
    "- **Hyperbolic Tangent function**: Its mathematical formula is given by:\n",
    "  \n",
    "$$\n",
    "f(z) = \\tanh(z) = \\dfrac{2}{1 + e^{-2z}} - 1 = 2 \\times \\sigma(2z) - 1\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3c577bd0",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate input values\n",
    "z = np.linspace(-10, 10, 400)  # from -10 to 10\n",
    "\n",
    "# Compute the outputs\n",
    "y = np.tanh(z)\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(z, y, color = '#800000', linewidth=2)\n",
    "plt.title('Hyperbolic Tangent Function', fontsize=14)\n",
    "plt.xlabel('z')\n",
    "plt.ylabel('f(z)')\n",
    "plt.grid(True, linestyle='--', alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cfa534b",
   "metadata": {},
   "source": [
    "Hyperbolic tangent function looks similar to the sigmoid function but it stretches along the $y$-axis. The output values are centered around $0$ and ranges from $-1$ to $1$. \n",
    "\n",
    "- **Rectified Linear Unit (ReLU) function**: Its mathematical formula is given by: \n",
    "\n",
    "$$\n",
    "f(z) = \\max(0,z)\n",
    "$$\n",
    "\n",
    "The ReLU function is basically the identity function $f(z) = z$ for all the positive values $z$ and is a constant function $f(z) = 0$ for all non-positive values $z$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cc2e7ab5",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate input values\n",
    "z = np.linspace(-10, 10, 400) # from -10 to 10\n",
    "\n",
    "# Generate output values\n",
    "y = [max(0, x) for x in z]\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(z, y, color = '#800000', linewidth=2)\n",
    "plt.title('Rectified Linear Unit (ReLU) Function', fontsize=14)\n",
    "plt.xlabel('z')\n",
    "plt.ylabel('f(z)')\n",
    "plt.grid(True, linestyle='--', alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6d832f0",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "**Can activation functions be linear?**\n",
    "\n",
    "Theoretically, yes. But if a neuron uses a linear activation function, its output is just a linear combination of its inputs. Even if you stack multiple such neurons together (neural network), the result is still a linear function, essentially the same as applying linear regression to the inputs.\n",
    "\n",
    "The world around us is highly non-linear, and real-world data often requires curved or complex decision boundaries. Non-linear activation functions introduce non-linearity at the neuron level, allowing the neuron to model more complex patterns than a simple linear function could. \n",
    ":::"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Edit Metadata",
  "kernelspec": {
   "display_name": "base",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
