Building Neural Networks Through Mathematical Intuition
"The best way to understand something is to build it from scratch."
This repository takes you on a journey from basic calculus to modern transformer architectures, implementing every component from the ground up. No magic frameworks, no black boxes - just pure mathematical understanding translated into clean, readable Python.
Chapter 1: Autodiff Engine - Build a scalar-based automatic differentiation system
Chapter 2: Text Generation - Create character-level language models
Chapter 3: Neural Architectures - Implement feedforward networks with proper training
Chapter 4: Training Dynamics - Master gradient flow and normalization techniques
Chapter 5: Gradient Mastery - Hand-implement backpropagation for deep understanding
Chapter 6: Hierarchical Learning - Build convolutional and tree-structured networks
Chapter 7: Attention Mechanisms - Implement the transformer architecture from scratch
Chapter 8: Optimization Strategies - Advanced training techniques and regularization
Chapter 9: Scaling Laws - Distributed training and efficient architectures
Chapter 10: Production Systems - Deployment patterns and real-world considerations
# Clone the repository
git clone https://github.com/pradosh94/deep-learning-from-first-principles.git
cd deep-learning-from-first-principles
# Create virtual environment
python -m venv venv
source venv/bin/activate # On Windows: venv\Scripts\activate
# Install dependencies
pip install -r requirements.txt
# Run examples
python chapter_01_autodiff/gradient_engine.py- Mathematical Intuition: Understanding backpropagation through computational graphs
- Implementation Skills: Building neural networks without high-level frameworks
- Debugging Techniques: Identifying and fixing training issues
- Architecture Design: Creating efficient and scalable models
- Optimization Theory: Advanced training strategies and convergence analysis
deep-learning-from-first-principles/
├── chapter_01_autodiff/ # Automatic differentiation engine
├── chapter_02_text_generation/ # Language modeling fundamentals
├── chapter_03_neural_nets/ # Multi-layer perceptrons
├── chapter_04_training_dynamics/ # Gradient flow and normalization
├── chapter_05_gradient_mastery/ # Manual backpropagation
├── chapter_06_hierarchical/ # Convolutional architectures
├── chapter_07_attention/ # Transformer implementation
├── chapter_08_optimization/ # Advanced training techniques
├── chapter_09_scaling/ # Distributed and efficient training
├── chapter_10_production/ # Deployment and serving
├── utils/ # Shared utilities and visualizations
└── notebooks/ # Interactive Jupyter examples
- Programming: Intermediate Python knowledge
- Mathematics: Basic calculus and linear algebra
- Mindset: Curiosity and willingness to implement everything from scratch
This is an educational resource built for the community. Contributions, suggestions, and improvements are welcome!
- Fork the repository
- Create a feature branch (
git checkout -b feature/amazing-improvement) - Commit your changes (
git commit -m 'Add amazing improvement') - Push to the branch (
git push origin feature/amazing-improvement) - Open a Pull Request
If you find this educational material helpful in your research or learning, please cite:
@misc{deep_learning_first_principles,
title={Deep Learning from First Principles: A Mathematical Journey},
author={Pradosh P. Dash},
year={2025},
url={https://github.com/pradosh94/deep-learning-from-first-principles}
}This project is licensed under the MIT License - see the LICENSE file for details.
- Built with inspiration from mathematical elegance and pedagogical clarity from [Andrej Karpathy][https://github.com/karpathy]
- Special thanks to the open-source community for foundational tools
- Dedicated to learners who prefer understanding over memorization
"In the end, we want to understand not just how to use these tools, but how they work at the deepest level."