AI Foundation

January 26, 2026

AI #

A selection of notes that didn’t fit elsewhere or are being worked on!.

• AI Stages: ANI, AGI, ASI
• AI Stack
• AI Pipeline
• AI Learning Resources

Formula Sheet

March 12, 2026

Formula Sheet #

This page is a quick reference of definitions + formulas, grouped by the modules.

Notation #

• Sample size: \( n \) (sample), \( N \) (population)
• Sample mean: \( \bar{x} \) , population mean: \( \mu \)
• Sample variance: \( s^2 \) , population variance: \( \sigma^2 \)
• Sample SD: \( s \) , population SD: \( \sigma \)
• Complement: \( A^c \)
• Intersection (“and”): \( A\cap B \) , union (“or”): \( A\cup B \)
• Conditional probability: \( P(A\mid B) \)

1. Basic Probability & Statistics #

1.1 Measures of Central Tendency #

Arithmetic mean #

Sample mean (ungrouped):

Supervised Learning

January 3, 2026

Supervised Learning #

Trained using labelled data.
Each example in the training set includes the correct output.
The algorithm learns to generalise and make predictions on unseen data.
Generally more accurate than unsupervised methods.
Requires human intervention for labelling and setup.
Widely used due to its accuracy and efficiency.
Produces highly accurate results when trained on good-quality labelled data.

Classification #

Output is discrete (e.g. Yes/No, Spam/Not Spam).
Used for categorising data into predefined classes.
Support Vector Machine (SVM) is a common classifier (a linear classifier with margin-based separation).

Artificial Intelligence

July 4, 2024

My AI Notes #

Learning how machines learn! My working notes as I learn AI.

flowchart LR
    AI[Artificial Intelligence]
    ML[Machine Learning]
    DL[Deep Learning]
    FM[Foundation Models]
    LLM[LLM Models]

    AI --> ML
    ML --> DL
    DL --> FM
    FM --> LLM

    style AI fill:#E1F5FE
    style ML fill:#C8E6C9
    style DL fill:#90CAF9
    style FM fill:#64B5F6
    style LLM fill:#FFCCBC

• Mathematical Foundations for Machine Learning
• Statistical Methods
• Machine Learning
• Deep Neural Networks

• AI Foundation
  • AI Stages: ANI, AGI, ASI
  • AI Stack
  • AI Pipeline
  • AI Learning Resources
• Mathematical Foundation
  • Linear Algebra
    • Linear Systems
      • Systems of Linear Equations
      • Matrices
      • Matrix Transposition
      • Solving Linear Systems
      • Forward and Backward Substitution
      • Inverse Matrix
      • Convex Combination
    • Vector Spaces
      • Basis and Rank
      • Linear Independence
      • Norm
      • Inner Products and Dot Product
      • Lengths and Distances
      • Angles and Orthogonality
      • Orthonormal Basis
      • Feature Space
      • Cauchy–Schwarz
    • Matrix Decompositions
      • Special Matrices
      • Characteristic Polynomial
      • Determinant and Trace
      • Eigenvalues and Eigenvectors
      • Cholesky Decomposition
      • Eigen Decomposition
      • Diagonalization
      • Singular Value Decomposition (SVD)
      • Matrix Approximation
    • Dimensionality reduction and PCA
      • Primal and Dual Perspective for Linear SVM
      • Mathematical Preliminaries for SVM
      • Nonlinear SVM
  • Calculus
    • Vector Calculus
      • Differentiation of Univariate Functions
      • Partial Differentiation and Gradients
      • Gradients of Vector-Valued and Matrix Functions
      • Useful Gradient Identities
      • Backpropagation and Automatic Differentiation
      • Higher-order derivatives
      • Taylor’s series
      • Maxima and Minima
    • Continuous Optimisation
      • Optimisation using Gradient Descent
      • Constrained Optimisation
      • Lagrange Multipliers
      • Convex Optimisation
    • Nonlinear Optimisation
      • Challenges in Gradient-Based Optimisation
      • Stochastic Gradient Descent (SGD)
      • Momentum-Based Learning
      • Adaptive Methods: AdaGrad, RMSProp, Adam
      • Tuning Hyperparameters and Preprocessing
• Statistics
  • Formula Sheet
  • Stats Formula Sheet
  • Basic Statistics
  • Basic Probability
  • Hypothesis Testing
  • Prediction & Forecasting
  • Gaussian Mixture Model & Expectation Maximization
  • Conditional Probability & Bayes’ Theorem
    • Conditional Probability
    • Bayes’ Theorem
    • Naïve Bayes
  • Probability Distributions
    • Random Variables
    • Common Probability Distributions
• Machine Learning
  • Supervised Learning
  • Semi-Supervised Learning
  • Reinforcement Learning
  • ML Workflow
  • Regression (Linear)
  • Ordinary Least Squares
  • Cost Function
  • Gradient Descent
  • Classification (Linear)
  • Decision Tree
  • Instance-based Learning
  • Support Vector Machine
  • Bayesian Learning
  • Ensemble Learning
  • Unsupervised Learning
  • Evaluation/Comparison
  • ML Pipeline
• Generative AI
  • Foundation Models
  • LLM - Model
  • AI Agents
  • Retrieval-Augmented Generation (RAG)
• Deep Learning
  • Neural Networks
  • Artificial Neuron and Perceptron
  • LNN for Regression
  • Gradient Descent Algorithm
  • LNN for Classification
  • Deep Feedforward Neural Networks (DFNN) for Classification
  • Convolutional Neural Networks
  • Deep CNN Architectures
  • CNN Pipeline
  • Recurrent Neural Networks
  • Deep Recurrent Neural Networks
  • Attention Mechanism
  • Transformer
  • Optimisation of Deep models
  • Gradient Descent and Mini-Batch Gradient Descent
  • Momentum Methods
  • Regularisation for Deep models
  • DNN Formula and Numerical Sheet
• Deep Reinforcement Learning
  • Reinforcement Learning
  • Multi-Armed Bandit Problem
  • Markov Decision Process Framework
  • Rewards, Returns, Policies and Value Functions
• Natural Language Processing
  • Understanding and Generation
  • Vector Semantics and Embedding
  • N-gram Language Modelling
  • NN and Neural Language Modelling
  • LLM and Prompt Engineering
  • Part-of-Speech Tagging and Hidden Markov Models
  • Statistical, ML and Neural Models of POS Tagging
• Artificial and Computational Intelligence
  • Artificial Intelligence
  • Intelligent Agents and Environments
• ML System Optimisation
  • ML and DL System Performance
  • Parallel and Distributed Algorithms
  • Parallel Programming Models

• Machine Learning → The broad field where systems learn patterns from data to make predictions or decisions.
• Neural Networks → A subset of machine learning that uses interconnected artificial neurons to model complex relationships.
• Deep Learning → A subset of neural networks that uses many hidden layers to learn high-level features from large datasets.
• Foundation Models → Large deep learning models trained on massive datasets and reused across many tasks using transfer learning.
• LLMs (Large Language Models) → A specialised type of foundation model focused on understanding and generating human language.

flowchart TD
AI["Artificial<br/>Intelligence"]
ML["Machine<br/>Learning"]
NN["Neural<br/>Networks"]
DL["Deep<br/>Learning"]
FM["Foundation<br/>Models"]
LLM["LLM<br/>Models"]

AI --> ML
ML --> NN
NN --> DL
DL --> FM
FM --> LLM

LR["Linear<br/>Regression"]
DT["Decision<br/>Trees"]
ML --> LR
ML --> DT

MLP["MLP"]
CNN["CNN"]
NN --> MLP
NN --> CNN

CNNDL["CNN<br/>(deep)"]
RNN["RNN"]
DL --> CNNDL
DL --> RNN

BERT["BERT"]
CLIP["CLIP"]
FM --> BERT
FM --> CLIP

GPT["GPT"]
LLAMA["LLaMA"]
LLM --> GPT
LLM --> LLAMA

TEXT["Text"]
IMAGE["Images"]
AUDIO["Audio"]
VIDEO["Video"]
LLM --> TEXT
LLM --> IMAGE
LLM --> AUDIO
LLM --> VIDEO

style AI fill:#90CAF9,stroke:#1E88E5,color:#000
style ML fill:#90CAF9,stroke:#1E88E5,color:#000
style NN fill:#90CAF9,stroke:#1E88E5,color:#000

style DL fill:#CE93D8,stroke:#8E24AA,color:#000
style FM fill:#CE93D8,stroke:#8E24AA,color:#000

style LLM fill:#C8E6C9,stroke:#2E7D32,color:#000
style LR fill:#C8E6C9,stroke:#2E7D32,color:#000
style DT fill:#C8E6C9,stroke:#2E7D32,color:#000
style MLP fill:#C8E6C9,stroke:#2E7D32,color:#000
style CNN fill:#C8E6C9,stroke:#2E7D32,color:#000
style CNNDL fill:#C8E6C9,stroke:#2E7D32,color:#000
style RNN fill:#C8E6C9,stroke:#2E7D32,color:#000
style BERT fill:#C8E6C9,stroke:#2E7D32,color:#000
style CLIP fill:#C8E6C9,stroke:#2E7D32,color:#000
style GPT fill:#C8E6C9,stroke:#2E7D32,color:#000
style LLAMA fill:#C8E6C9,stroke:#2E7D32,color:#000
style TEXT fill:#C8E6C9,stroke:#2E7D32,color:#000
style IMAGE fill:#C8E6C9,stroke:#2E7D32,color:#000
style AUDIO fill:#C8E6C9,stroke:#2E7D32,color:#000
style VIDEO fill:#C8E6C9,stroke:#2E7D32,color:#000

Stats Formula Sheet

February 25, 2026

Stats Formula Sheet #

Keep this page as a quick reference of definitions + formulas.

Notation #

• Sample size: \( n \) (sample), \( N \) (population)
• Mean: \( \bar{x} \) (sample), \( \mu \) (population)
• Variance: \( s^2 \) (sample), \( \sigma^2 \) (population)
• Standard deviation: \( s \) (sample), \( \sigma \) (population)

Module 1: Basic Statistics #

Measures of Central Tendency #

Sample mean (ungrouped):

Semi-Supervised Learning

January 3, 2026

Semi-Supervised Learning #

• A combination of labelled and unlabelled data.
• Useful when labelling large datasets is expensive or time-consuming.
• Works well with high-volume datasets (e.g. millions of images).
• Only a small fraction of data is labelled (e.g. a few thousand).
• The algorithm learns from both labelled examples and structure in unlabelled data.
• Ideal for medical imaging where labelled data is limited.
• For example, a radiologist can label a small set of medical scans,
  and the model uses that to learn from thousands of unlabelled scans.
• Helps improve accuracy and generalisation with minimal manual effort.

Home | Machine Learning

Machine Learning

August 6, 2024

Machine Learning #

stateDiagram-v2

    %% ===== CLASS DEFINITIONS (Math-based colours) =====
    classDef algebra fill:#cfe8ff,stroke:#1e3a8a,stroke-width:1px
    classDef probability fill:#d1fae5,stroke:#065f46,stroke-width:1px
    classDef geometry fill:#ffedd5,stroke:#9a3412,stroke-width:1px
    classDef logic fill:#ede9fe,stroke:#5b21b6,stroke-width:1px
    classDef category font-style:italic,font-weight:bold,fill:#aaaaaa,stroke:#374151,stroke-width:3px

    %% ===== ROOT =====
    ML: Machine Learning

    %% ===== SUPERVISED =====
    ML --> SL:::category
    SL: Supervised Learning

    SL --> Regression
    Regression --> LR:::algebra
    LR: Linear Regression

    LR --> NN:::algebra
    NN: Neural Network

    NN --> DT:::logic
    DT: Decision Tree

    SL --> Classification
    Classification --> NB:::probability
    NB: Naive Bayes

    NB --> KNN:::geometry
    KNN: k-Nearest Neighbours

    KNN --> SVM:::algebra
    SVM: Support Vector Machine
    
    %% ===== UNSUPERVISED =====
    ML --> USL:::category
    USL: Unsupervised Learning

    USL --> Clustering
    Clustering --> KM:::geometry
    KM: K-Means

    KM --> GMM:::probability
    GMM: Gaussian Mixture Model

    GMM --> HMM:::probability
    HMM: Hidden Markov Model

    %% ===== REINFORCEMENT =====
    ML --> RL:::category
    RL: Reinforcement Learning

    RL --> DM:::logic
    DM: Decision Making

Generative AI

December 15, 2025

Generative AI #

Generative Artificial Intelligence (GenAI) refers to a class of AI systems that can generate new content such as text, images, audio, video, or code, rather than only making predictions or classifications.

GenAI systems learn patterns and representations from large datasets and use them to produce novel outputs that resemble the data they were trained on.

How Generative AI Differs from Traditional AI #

Core Idea of Generative AI #

Instead of learning “what label to assign”, Generative AI learns “how data is structured” and then creates new data following that structure.

Deep Learning

April 22, 2026

Deep Learning #

• Subset of ML
• focuses on algorithms inspired by the structure and function of the brain called Artificial Neural Networks.
• A neural network with multiple hidden layers and multiple nodes in each hidden layer is known as a deep learning system or a deep neural network.
• Allows systems to automatically learn hierarchical representations (features) from raw input, such as images, sound, or text.

Operational Steps for Neural Architectures #

• Neural Networks
• Artificial Neuron and Perceptron
• LNN for Regression
• Gradient Descent Algorithm
• LNN for Classification
• Deep Feedforward Neural Networks (DFNN) for Classification
• Convolutional Neural Networks
• Deep CNN Architectures
• CNN Pipeline
• Recurrent Neural Networks
• Deep Recurrent Neural Networks
• Attention Mechanism
• Transformer
• Optimisation of Deep models
• Gradient Descent and Mini-Batch Gradient Descent
• Momentum Methods
• Regularisation for Deep models
• DNN Formula and Numerical Sheet

flowchart LR
    %% Input Layer
    subgraph subGraph0["Input Layer"]
        I1(("Input 1"))
        I2(("Input 2"))
        I3(("Input 3"))
    end

    %% Hidden Layers
    subgraph subGraph1["Hidden Layer 1"]
        H1a(("H1-1"))
        H1b(("H1-2"))
        H1c(("H1-3"))
    end

    subgraph subGraph2["Hidden Layer 2"]
        H2a(("H2-1"))
        H2b(("H2-2"))
        H2c(("H2-3"))
    end

    subgraph subGraph3["Hidden Layer 3"]
        H3a(("H3-1"))
        H3b(("H3-2"))
        H3c(("H3-3"))
    end

    %% Output Layer
    subgraph subGraph4["Output Layer"]
        O(("Output"))
    end

    %% Connections: Input to Hidden Layer 1
    I1 --> H1a & H1b & H1c
    I2 --> H1a & H1b & H1c
    I3 --> H1a & H1b & H1c

    %% Connections: Hidden Layer 1 to Hidden Layer 2
    H1a --> H2a & H2b & H2c
    H1b --> H2a & H2b & H2c
    H1c --> H2a & H2b & H2c

    %% Connections: Hidden Layer 2 to Hidden Layer 3
    H2a --> H3a & H3b & H3c
    H2b --> H3a & H3b & H3c
    H2c --> H3a & H3b & H3c

    %% Connections: Hidden Layer 3 to Output
    H3a --> O
    H3b --> O
    H3c --> O

    %% Styling
    style I1 fill:#C8E6C9
    style I2 fill:#C8E6C9
    style I3 fill:#C8E6C9
    style H1a fill:#BBDEFB
    style H1b fill:#BBDEFB
    style H1c fill:#BBDEFB
    style H2a fill:#90CAF9
    style H2b fill:#90CAF9
    style H2c fill:#90CAF9
    style H3a fill:#64B5F6
    style H3b fill:#64B5F6
    style H3c fill:#64B5F6
    style O fill:#FFCDD2
    style subGraph0 stroke:none,fill:transparent
    style subGraph1 stroke:none,fill:transparent
    style subGraph2 stroke:none,fill:transparent
    style subGraph3 stroke:none,fill:transparent
    style subGraph4 stroke:none,fill:transparent

Types of Neural Networks #

• Standard NN - Small and Standard for a smaller and simpler data (e.g. Real Estate
• CNN - Convolution - used for Images (e.g. Photo Tagging, Object Detection)
• RNN - Recurrent - used for Text (e.g. Speech Recognition, Translation)
• Hybrid NN (e.g. Autonoumous Driving)

Components of DL #

• Data
• Learning Algorithm : How to transform data
• Loss Function: Objective function that quantifies how well is model doing? lower the loss function, the better the model. So loss function will try to quantify how well or badly the model is learning or the model is doing.
• Optimnisation Algorithm: in order to adjust the loss function, Learning Algorithm will try to optimize our algorithm. searching for the best possible parameters for minimizing the loss function. Popular optimization algorithms for deep learning are based on an approach called gradient descent.
• Model

Operational Steps for Neural Architectures #

Applications #

• Computer Vision (e.g., face detection, medical imaging)
• Natural Language Processing (e.g., ChatGPT, translation)
• Self Driving Cars
• Speech Assistants (e.g., Alexa, Siri)

Intution #

Deep Learning is the methodology, DNN is a model.

Reinforcement Learning

Reinforcement Learning (RL) #

RL is learning by trial and error.

Reinforcement Learning (RL) is a type of machine learning where an autonomous agent learns to make decisions by interacting with an environment.

Instead of being told the correct answer, the agent:

• takes actions
• observes outcomes
• receives rewards or penalties
• gradually learns a strategy that maximises long-term reward

Reinforcement Learning teaches an agent how to act, not what to predict.