From a11f71b23d7e89b423824ed3d582570e5075f502 Mon Sep 17 00:00:00 2001 From: shantnu <98252196+Shantnu-singh@users.noreply.github.com> Date: Thu, 25 Jul 2024 10:27:44 +0530 Subject: [PATCH] Adding activation functions --- .../Activation Function.md | 107 ++++++++++++++++++ .../activation_functions.ipynb | 100 ++++++++++++++++ 2 files changed, 207 insertions(+) create mode 100644 docs/Deep Learning/Activation Function/Activation Function.md create mode 100644 docs/Deep Learning/Activation Function/activation_functions.ipynb diff --git a/docs/Deep Learning/Activation Function/Activation Function.md b/docs/Deep Learning/Activation Function/Activation Function.md new file mode 100644 index 000000000..f952e202e --- /dev/null +++ b/docs/Deep Learning/Activation Function/Activation Function.md @@ -0,0 +1,107 @@ +# Activation Functions in Deep Learning: LaTeX Equations and Python Implementation + +## Overview + +This project provides LaTeX equations, explanations, and Python implementations for various activation functions used in Artificial Neural Networks (ANN) and Deep Learning. Our goal is to offer clear, visually appealing mathematical representations and practical implementations of these functions for educational and reference purposes. + +## Contents + +1. [Introduction to Activation Functions](#introduction-to-activation-functions) +2. [Activation Functions](#activation-functions) +3. [Mathematical Equations](#mathematical-equations) +4. [Python Implementations](#python-implementations) +5. [Jupyter Notebook](#jupyter-notebook) +7. [Comparison of Activation Functions](#comparison-of-activation-functions) +8. [How to Use This Repository](#how-to-use-this-repository) + + +## Introduction to Activation Functions + +Activation functions are crucial components in neural networks, introducing non-linearity to the model and allowing it to learn complex patterns. They determine the output of a neural network node, given an input or set of inputs. + +## Activation Functions + +This project covers the following activation functions: + +### Non-Linear Activation Functions +Non-linear activation functions introduce non-linearity into the model, enabling the network to learn and represent complex patterns. + +- Essential for deep learning models as they introduce the non-linearity needed to capture complex patterns and relationships in the data. + +- Here are some common non-linear activation functions: +1. Sigmoid +2. Hyperbolic Tangent (tanh) +3. Rectified Linear Unit (ReLU) + +### Linear Activation Functions +A linear activation function is a function where the output is directly proportional to the input. + +- **Linearity:** The function does not introduce any non-linearity. The output is just a scaled version of the input. +- **Derivative:** The derivative of the function is constant, which means it does not vary with the input. + +- Here are some common linear activation functions: + +1. Identity +2. Step Function + +## Mathematical Equations + +We provide LaTeX equations for each activation function. For example: + +1. Sigmoid: $\sigma(x) = \frac{1}{1 + e^{-x}}$ +2. Hyperbolic Tangent: $\tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}$ +3. ReLU: $f(x) = \max(0, x)$ +4. Linear : $f(x) = x$ +5. Step : + +$$ +f(x) = +\begin{cases} +0 & \text{if } x < \text{threshold} \\ +1 & \text{if } x \geq \text{threshold} +\end{cases} +$$ + + +## Python Implementations + +Here are the Python implementations of the activation functions: + +```python +import numpy as np + +# Non-Linear activation functions +def sigmoid(x): + return 1 / (1 + np.exp(-x)) + +def tanh(x): + return (np.exp(x) - np.exp(-x)) / (np.exp(x) + np.exp(-x)) + +def reLu(x): + return np.maximum(x, 0) + +# Linear activation functions +def identity(x): + return x + +def step(x, thres): + return np.where(x >= thres, 1, 0) +``` + + +## How to Use This Repository + +- Clone this repository to your local machine. + +```bash + git clone https://github.com/CodeHarborHub/codeharborhub.github.io/tree/main/docs/Deep%20Learning/Activation function +``` +- For Python implementations and visualizations: + +1. Ensure you have Jupyter Notebook installed + +```bash + pip install jupyter +``` +2. Navigate to the project directory in your terminal. +3. Open activation_functions.ipynb. diff --git a/docs/Deep Learning/Activation Function/activation_functions.ipynb b/docs/Deep Learning/Activation Function/activation_functions.ipynb new file mode 100644 index 000000000..6a7afa397 --- /dev/null +++ b/docs/Deep Learning/Activation Function/activation_functions.ipynb @@ -0,0 +1,100 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Implementation of diff activation fucntion in neural network

" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Non - Linaer activation functions\n", + "def sigmoid(x):\n", + " return 1/(1+(np.exp(-x)))\n", + "\n", + "def tanh(x):\n", + " return((np.exp(x)) - np.exp(-x)) / ((np.exp(x)) + np.exp(-x))\n", + "\n", + "def reLu(x):\n", + " return np.maximum(x , 0)\n", + "\n", + "# Linaer activation functions \n", + "def identity(x):\n", + " return x\n", + "\n", + "def step(x , thres):\n", + " return np.where (x >= thres , 1, 0)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-10 , 10 , 200)\n", + "# plt.figure(figsize= (15 , 5))\n", + "plt.figure(figsize=(10, 6))\n", + "\n", + "plt.plot(x , sigmoid(x) , label = \"sigmoid\" , color = \"red\")\n", + "plt.plot(x , tanh(x) , label = \"Tan - h\" , color = \"blue\")\n", + "plt.plot(x , reLu(x) , label = \"reLu\" , color = \"green\")\n", + "plt.plot(x , step(x , 3) , label = \"Step\" , color = \"yellow\")\n", + "\n", + "plt.title(\"Activation functions\")\n", + "plt.xlabel(\"input\")\n", + "plt.ylabel(\"Output\")\n", + "plt.legend()\n", + "plt.grid(True)\n" + ] + }, + { + "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": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}