# Core AI and ML Topics Covered in Chapters 6-10 of the Maths-CS-AI Compendium

> Explore core AI and ML topics from chapters 6-10 of the Maths-CS-AI Compendium. Master classical ML, NLP, computer vision, audio processing, and multimodal architectures.

- Repository: [Henry Ndubuaku/maths-cs-ai-compendium](https://github.com/HenryNdubuaku/maths-cs-ai-compendium)
- Tags: deep-dive
- Published: 2026-07-16

---

**Chapters 6 through 10 of the HenryNdubuaku/maths-cs-ai-compendium form a comprehensive curriculum covering classical machine learning, computational linguistics, computer vision, audio processing, and multimodal learning architectures.**

These five chapters progress from foundational algorithms to state-of-the-art deep learning systems. According to the source code in the repository, they provide a full-stack view of modern AI, starting with probabilistic models and optimization theory, advancing through domain-specific architectures for text and image data, and culminating in unified multimodal systems. The compendium emphasizes both mathematical rigor and practical implementation using frameworks like JAX.

## Chapter 6: Machine Learning Foundations

Chapter 6 establishes the mathematical groundwork for all subsequent topics, divided into classical algorithms and gradient-based optimization methods.

### Classical Algorithms and Decision Trees

The repository covers traditional supervised and unsupervised methods including **Naïve Bayes**, **k-Nearest Neighbors**, **Decision Trees**, **Random Forests**, **SVM**, **k-means**, and **Gaussian Mixture Models (GMM)**. In `chapter 06: machine learning/01. classical machine learning.md`, the implementation details for decision tree splits using **Gini impurity** are provided:

```python
import jax.numpy as jnp

def gini_impurity(y):
    _, counts = jnp.unique(y, return_counts=True)
    probs = counts / len(y)
    return 1.0 - jnp.sum(probs ** 2)

def information_gain(y, left_mask):
    parent = gini_impurity(y)
    left, right = y[left_mask], y[~left_mask]
    n = len(y)
    if len(left) == 0 or len(right) == 0:
        return 0.0
    child = (len(left)/n)*gini_impurity(left) + (len(right)/n)*gini_impurity(right)
    return float(parent - child)

```

This code demonstrates how the compendium implements fundamental splitting criteria for decision trees using JAX.

### Gradient-Based Optimization and Modern Optimizers

The second part of Chapter 6 focuses on **Linear** and **Logistic Regression**, **Softmax** classifiers, and optimization algorithms. The source file `chapter 06: machine learning/02. gradient machine learning.md` covers loss functions (MSE, BCE, Hinge, MAE, Huber) and regularization techniques (L1/L2, Elastic Net), along with modern optimizers including **SGD**, **Momentum**, **Adam**, **LION**, and **Muon**.

Below is the Adam optimizer implementation on an elongated quadratic loss surface:

```python
import jax, jax.numpy as jnp
import matplotlib.pyplot as plt

def loss(w):
    return 0.5*w[0]**2 + 10*w[1]**2       # elongated bowl

grad = jax.grad(loss)

def run_adam(w0, lr=0.05, steps=80):
    w, m, v = w0, jnp.zeros_like(w0), jnp.zeros_like(w0)
    path = [w]
    for t in range(1, steps+1):
        g = grad(w)
        m = 0.9*m + 0.1*g
        v = 0.999*v + 0.001*g**2
        m_hat = m/(1-0.9**t)
        v_hat = v/(1-0.999**t)
        w = w - lr*m_hat/(jnp.sqrt(v_hat)+1e-8)
        path.append(w)
    return jnp.stack(path)

traj = run_adam(jnp.array([8.0, 3.0]))
plt.plot(traj[:,0], traj[:,1], 'o-', color='#e74c3c')
plt.title('Adam on elongated quadratic')
plt.xlabel('w₁'); plt.ylabel('w₂')
plt.show()

```

This example illustrates the adaptive learning rate behavior that makes Adam effective for poorly conditioned optimization landscapes.

## Chapter 7: Computational Linguistics and Modern NLP

Chapter 7 bridges linguistic theory and modern deep learning for natural language processing.

### Linguistic Foundations and Text Preprocessing

The compendium covers **phonetics**, **morphology**, and **syntax** as prerequisites for computational modeling. In `chapter 07: computational linguistics/01. linguistic foundations.md`, the text preprocessing pipeline includes **tokenisation**, **stemming**, and **stop-word removal**, leading to classical representations like **Bag-of-Words** and **TF-IDF**.

### Transformers and Large Language Models

The progression moves from static embeddings (**Word2Vec**, **GloVe**) to modern architectures. The file `chapter 07: computational linguistics/04. transformers and language models.md` contains the theoretical foundations of **self-attention mechanisms**, **scaling laws**, and the architecture patterns that underpin large language models.

## Chapter 8: Computer Vision and Deep Learning Architectures

Chapter 8 addresses visual data processing, from pixel fundamentals to generative architectures.

### Convolutional Neural Networks

The source file `chapter 08: computer vision/02. convolutional networks.md` explains **image fundamentals** (pixels, color spaces), **receptive fields**, and classic architectures including **LeNet** and **ResNet**. The compendium details **pooling operations** and the inductive biases that make CNNs effective for spatial data.

### Vision Transformers and Advanced Architectures

Moving beyond convolutions, `chapter 08: computer vision/04. vision transformers and generation.md` covers **Vision Transformers (ViT)**, **object detection** (YOLO, Mask R-CNN), **segmentation**, and **video/3-D vision** for action recognition and depth estimation.

The minimal ViT forward pass implementation demonstrates patch embedding and positional encoding:

```python
import jax.numpy as jnp
from einops import rearrange

def vit_forward(patch_embeddings, cls_token, pos_embed, mlp):
    # patch_embeddings: (B, N, D)

    x = jnp.concatenate([cls_token, patch_embeddings], axis=1) + pos_embed
    # simple transformer block (omitted for brevity)

    # ...

    return mlp(x[:,0])   # classification token output

```

## Chapter 9: Audio, Speech, and Signal Processing

Chapter 9 focuses on sequential signal data, covering both digital signal processing fundamentals and modern speech ML systems.

### Digital Signal Processing Fundamentals

According to `chapter 09: audio and speech/01. digital signal processing.md`, the core topics include **Fourier transforms**, **spectrograms**, and the spectral analysis techniques that form the input representations for audio ML.

### Speech Recognition and Synthesis

The compendium covers **ASR pipelines** and **CTC loss** for sequence-to-sequence speech recognition, **text-to-speech (TTS)** and **voice synthesis**, as well as **speaker diarisation**, **emotion recognition**, **source separation**, and **noise reduction** techniques.

## Chapter 10: Multimodal Learning and Cross-Modal Integration

Chapter 10 synthesizes the preceding domains into systems that process heterogeneous data types simultaneously.

### Multimodal Representations and Vision-Language Models

The file `chapter 10: multimodal learning/01. multimodal representations.md` introduces **joint embeddings** and **contrastive learning**. The compendium implements **CLIP-style** training objectives that align image and text representations:

```python
import jax.numpy as jnp

def contrastive_loss(image_emb, text_emb, temperature=0.07):
    # Normalise

    image_emb = image_emb / jnp.linalg.norm(image_emb, axis=1, keepdims=True)
    text_emb  = text_emb  / jnp.linalg.norm(text_emb,  axis=1, keepdims=True)
    logits = image_emb @ text_emb.T / temperature
    labels = jnp.arange(logits.shape[0])
    loss_i = -jnp.mean(jnp.log(jnp.exp(jnp.diag(logits)) / jnp.sum(jnp.exp(logits), axis=1)))
    loss_t = -jnp.mean(jnp.log(jnp.exp(jnp.diag(logits)) / jnp.sum(jnp.exp(logits), axis=0)))
    return (loss_i + loss_t) / 2

```

This symmetric loss function trains models to maximize similarity between paired image-text embeddings while minimizing it for unpaired samples.

### Unified Multimodal Architectures

The final section in `chapter 10: multimodal learning/05. unified multimodal architectures.md` covers **cross-modal generation** (image-to-text, text-to-image) and **unified architectures** like **Perceiver** and **Gato** that handle arbitrary modality mixtures through attention mechanisms.

## Summary

- **Chapters 6-10** provide a comprehensive AI/ML curriculum spanning from classical algorithms to modern multimodal systems according to the HenryNdubuaku/maths-cs-ai-compendium source code.
- **Chapter 6** establishes foundations with decision trees, ensemble methods, and optimizers including Adam, LION, and Muon implemented in `chapter 06: machine learning/`.
- **Chapter 7** transitions from linguistic theory to transformers and large language models in `chapter 07: computational linguistics/`.
- **Chapter 8** covers computer vision through CNNs and Vision Transformers detailed in `chapter 08: computer vision/`.
- **Chapter 9** addresses audio processing, speech recognition, and signal processing fundamentals in `chapter 09: audio and speech/`.
- **Chapter 10** integrates these domains through multimodal representations and unified architectures like CLIP and Perceiver found in `chapter 10: multimodal learning/`.

## Frequently Asked Questions

### What optimization algorithms are covered in Chapter 6 beyond standard SGD?

Chapter 6 includes modern adaptive optimizers such as **Adam**, **LION**, and **Muon** alongside classical momentum and SGD. The `run_adam()` function in `chapter 06: machine learning/02. gradient machine learning.md` demonstrates the adaptive learning rate mechanism using bias-corrected first and second moment estimates.

### How does the compendium explain the difference between CNNs and Vision Transformers?

The repository contrasts these architectures across two files: `chapter 08: computer vision/02. convolutional networks.md` covers CNNs with their inductive biases for spatial locality, while `chapter 08: computer vision/04. vision transformers and generation.md` explains how ViTs replace convolutional operations with self-attention over image patches, requiring less domain-specific engineering but more data.

### What are the key components of the multimodal learning approach in Chapter 10?

Chapter 10 focuses on **joint embedding spaces** and **contrastive learning** objectives that align representations across modalities. The `contrastive_loss()` function implements the symmetric cross-entropy loss used in CLIP-style training, while the section on unified architectures covers models like **Perceiver** and **Gato** that process arbitrary modality combinations through attention mechanisms.

### Does Chapter 9 include practical implementations for speech recognition?

Yes, Chapter 9 covers practical ASR pipelines including **CTC loss** for alignment-free sequence training and spectrogram-based feature extraction. The source file `chapter 09: audio and speech/01. digital signal processing.md` provides the signal processing foundations necessary for implementing modern speech recognition systems.