🧠 Neural Networks from Scratch

Welcome to Neural Networks from Scratch!
This repository is your structured guide to understanding, building, and training neural networks from the ground up — without high-level libraries.

We’ll cover everything: 🔢 math → 🏗️ implementation → 🤖 applications.

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📚 Table of Contents

1. 🌟 Introduction to Neural Networks
2. 🧬 Biological Inspiration
3. 🔗 Neurons & Perceptrons
4. ⚡ Activation Functions
5. 🔄 Forward Propagation
6. 📉 Loss Functions
7. 🔧 Gradient Descent & Backpropagation
8. 🚀 Optimization Algorithms
9. 🛡️ Regularization Techniques
10. 🏗️ Deep Neural Networks
11. 🖼️ Convolutional Neural Networks (CNNs)
12. ⏳ Recurrent Neural Networks (RNNs)
13. 🏋️ Training Best Practices
14. 🧩 Projects & Applications
15. 📖 References & Further Reading

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🌟 1. Introduction to Neural Networks

• 🤔 What is a Neural Network?
• 🕰️ History (Perceptron → Deep Learning)
• 🛠️ Why build from scratch?

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🧬 2. Biological Inspiration

• 🧠 Neurons in the human brain
• ⚖️ Synaptic weights & signals
• 🤖 Artificial neuron modeling

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🔗 3. Neurons & Perceptrons

• 🧩 Structure of a perceptron
• ➕ Weighted sum & bias
• ↔️ Linear separability
• ❌ XOR problem limitations

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⚡ 4. Activation Functions

• 🟢 Sigmoid → Probability mapping
• 🔵 Tanh → Centered outputs
• 🟠 ReLU → Sparse activations & fast learning
• 🟣 Leaky ReLU, ELU, GELU
• 🧭 When to use which function

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🔄 5. Forward Propagation

• 📊 Layer-wise computation
• 🧮 Matrix representation
• 📦 Batch inputs
• 📝 Example with a small NN

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📉 6. Loss Functions

• 🔢 Regression: Mean Squared Error (MSE)
• 🎯 Classification: Cross-Entropy Loss
• ⚖️ Hinge Loss, KL Divergence
• 🎯 Intuition: why minimize loss?

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🔧 7. Gradient Descent & Backpropagation

• 🌀 Gradient intuition
• 📐 Derivatives of activation functions
• 🔗 Chain rule in backprop
• 🚧 Vanishing & exploding gradients

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🚀 8. Optimization Algorithms

• 📦 Batch Gradient Descent
• 🎲 Stochastic Gradient Descent (SGD)
• 🏃 Momentum
• 📉 RMSProp
• ⚡ Adam Optimizer
• ⏳ Learning rate schedules

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🛡️ 9. Regularization Techniques

• 📉 Overfitting vs Underfitting
• ➖ L1 / L2 Regularization
• 🎲 Dropout
• 📊 Batch Normalization
• ⏱️ Early Stopping
• 🖼️ Data Augmentation

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🏗️ 10. Deep Neural Networks

• 🏗️ Stacking multiple layers
• 🌍 Universal Approximation Theorem
• ⚖️ Initialization (Xavier, He)
• ↔️ Depth vs Width trade-offs

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🖼️ 11. Convolutional Neural Networks (CNNs)

• 🔍 Convolution operation
• 🧩 Filters & feature maps
• 📏 Pooling layers
• 🏆 Architectures: LeNet, AlexNet, ResNet

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⏳ 12. Recurrent Neural Networks (RNNs)

• ⏱️ Sequential data handling
• 🔄 Vanilla RNNs
• 🧠 LSTM (Long Short-Term Memory)
• 🚪 GRU (Gated Recurrent Units)
• 💬 Applications: NLP, time-series

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🏋️ 13. Training Best Practices

• 🧹 Data preprocessing & normalization
• 📦 Mini-batch training
• 🎛️ Hyperparameter tuning
• 📊 Metrics: Accuracy, F1, ROC-AUC
• 🐞 Debugging training issues

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🧩 14. Projects & Applications

• ✍️ Handwritten digit recognition (MNIST)
• 🖼️ Image classification
• 💬 Sentiment analysis
• 📈 Time-series forecasting
• 🎨 Neural style transfer

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📖 15. References & Further Reading

• 📘 Books
  • Deep Learning – Ian Goodfellow
  • Neural Networks and Deep Learning – Michael Nielsen
• 🎓 Courses
  • Andrew Ng – Deep Learning Specialization
  • Stanford CS231n – CNNs for Visual Recognition
  • MIT 6.S191 – Intro to Deep Learning
• 📄 Research Papers
  • Perceptron (Rosenblatt, 1958)
  • Backpropagation (Rumelhart et al., 1986)
  • Deep Residual Learning (He et al., 2015)

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🎯 Goal

By completing this journey, you will:

• 🧮 Understand neural networks mathematically & conceptually
• 🛠️ Implement networks using only NumPy
• 🔍 Build intuition to debug & optimize deep learning models

✨ Let’s start building Neural Networks from Scratch 🚀