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Volume 4 — Deep Learning

Deep learning is the engine behind modern AI. By stacking layers of simple parametric transformations, deep networks learn hierarchical representations directly from raw data — pixels become edges become objects; characters become tokens become meaning. This volume builds that understanding from first principles, deriving every equation before touching a line of code, then translating theory into clean, production-ready PyTorch.

We begin with the biological motivation for artificial neurons and build up to full multi-layer perceptrons trained via backpropagation. We then explore the engineering machinery that makes deep networks trainable at scale: optimisers, normalisation, regularisation, and mixed-precision arithmetic. The final two chapters cover the two most important architectural families before the Transformer era — Convolutional Neural Networks for structured spatial data and Recurrent Networks for sequential data — setting the stage for Volume 5.

Chapter Map

# Chapter Core Topics Estimated Time
1 Neural Networks from Scratch Perceptron, MLP, backpropagation, NumPy & PyTorch 4 h
2 Training Deep Networks Optimisers, schedulers, BatchNorm, dropout, mixed precision 3 h
3 Convolutional Neural Networks Convolution, pooling, ResNet, transfer learning, augmentation 3.5 h
4 Recurrent Networks & LSTMs RNN, BPTT, LSTM, GRU, seq2seq, attention 3 h

Dependency Graph

graph TD
    V3["Volume 3 — Classical ML"] --> C1
    C1["Ch 1 — Neural Networks"] --> C2
    C1 --> C3
    C1 --> C4
    C2["Ch 2 — Training"] --> C3
    C2 --> C4
    C3["Ch 3 — CNNs"] --> V5_C1
    C4["Ch 4 — RNNs"] --> V5_C1
    V5_C1["Volume 5 — Transformers"]

    style V3 fill:#e8f4f8,stroke:#2196F3
    style C1 fill:#fff3e0,stroke:#FF9800
    style C2 fill:#fff3e0,stroke:#FF9800
    style C3 fill:#fff3e0,stroke:#FF9800
    style C4 fill:#fff3e0,stroke:#FF9800
    style V5_C1 fill:#e8f5e9,stroke:#4CAF50

Prerequisites

What You Should Already Know

  • Linear algebra: matrix multiplication, transpose, eigenvalues (Volume 1, Chapter 2)
  • Calculus: partial derivatives, chain rule (Volume 1, Chapter 3)
  • Probability: distributions, MLE, cross-entropy (Volume 1, Chapter 4)
  • Classical ML: regression, gradient descent, overfitting (Volume 3)
  • Python & NumPy: array operations, broadcasting (Volume 2)

Learning Outcomes

By completing this volume you will be able to:

  1. Derive and implement forward and backward passes for a multi-layer perceptron entirely from scratch in NumPy, without relying on automatic differentiation.
  2. Select and configure optimisers, learning-rate schedules, and regularisation strategies appropriate for a given training regime.
  3. Design CNN architectures using convolutions, pooling, skip connections, and transfer learning for computer vision tasks.
  4. Build and train LSTM-based sequence models and explain why they outperform vanilla RNNs on long-range dependencies.
  5. Connect the historical thread from RNNs with attention to the motivation for the Transformer, and articulate the key limitations that drove each transition.

Notation Reference

Symbol Meaning
\(x \in \mathbb{R}^n\) Input feature vector
\(W^{(l)} \in \mathbb{R}^{d_l \times d_{l-1}}\) Weight matrix at layer \(l\)
\(b^{(l)} \in \mathbb{R}^{d_l}\) Bias vector at layer \(l\)
\(h^{(l)}\) Post-activation at layer \(l\)
\(z^{(l)}\) Pre-activation (logit) at layer \(l\)
\(\sigma(\cdot)\) Activation function (context-specific)
\(\mathcal{L}\) Scalar loss
\(\odot\) Element-wise (Hadamard) product
\(\nabla_\theta \mathcal{L}\) Gradient of loss w.r.t. parameters \(\theta\)

How to Use This Volume

Each chapter is self-contained with derivations, code, and exercises. Read the derivations before running the code — the NumPy implementations are intentional: they force you to think in matrix shapes rather than relying on autograd magic. The PyTorch versions follow immediately so you can compare.