Systems of Linear Equations

• Introduction to systems of equations and why they matter in ML
• Matrix notation: representing systems as Ax = b
• Geometric interpretation: lines, planes, and hyperplanes in n-dimensional space
• Real-world ML connections: how regression problems map to linear systems

Solving Systems & Matrix Rank

• Elimination method and row echelon form (RREF)
• Matrix rank: understanding independent equations
• Gaussian elimination algorithm

Vectors & Linear Transformations

• Vector addition, scalar multiplication, dot product
• Vector norms, unit vectors, distance in high-dimensional space
• Matrices as linear transformations: rotation, scaling, projection
• Matrix multiplication as composition of transformations

Determinants & Eigenvectors

• Determinants: computation and geometric meaning
• Eigenvalues via the characteristic polynomial
• Eigenvectors: directions unchanged by a transformation
• Applications: PCA, graph Laplacians, stability of dynamical systems

Derivatives & Optimization

• Differentiation rules: power, product, quotient, chain
• Derivatives of key functions: polynomials, exponentials, sigmoid
• Finding minima/maxima; second derivative test

Gradients & Gradient Descent

• Partial derivatives and the gradient vector
• Gradient descent: iterative parameter updates
• Learning rate and convergence behaviour
• Stochastic and mini-batch gradient descent
• Applied to linear regression: minimising mean squared error

Optimization in Neural Networks

• Computational graphs: representing networks as directed acyclic graphs
• Backpropagation: chain rule applied recursively through layers
• Automatic differentiation (autograd) as used in PyTorch
• Newton's Method: using the Hessian for faster convergence

Probability & Distributions

• Sample spaces, conditional probability, Bayes' theorem
• Discrete distributions: Bernoulli, Binomial, Poisson
• Continuous distributions: Uniform, Exponential, Gaussian
• PDFs, CDFs, and probability mass functions

Multivariate Probability

• Expected value, variance, skewness, kurtosis
• Joint and marginal probability distributions
• Covariance and correlation
• Multivariate Gaussian distribution

Sampling & Point Estimation

• Population vs. sample; random sampling methods
• Central Limit Theorem
• Maximum Likelihood Estimation (MLE)
• Bias, variance, and consistency of estimators

Hypothesis Testing & Inference

• Confidence intervals for the mean
• Hypothesis testing: null/alternative hypotheses, p-values
• Type I & Type II errors, statistical power
• t-tests (one-sample, two-sample, paired)
• Chi-squared tests for categorical data

What is CNO?

• CNO stands for Cognitive Network Optimizer
• Learns patterns from KPI optimisation efforts carried out across the network
• Learns patterns of dos and don'ts versus extent of improvement / deterioration
• Builds recommendations for optimisation with probability of improvement
• Built on Deep Neural Network (DNN) — 4-layer architecture — to conserve learning and provide recommendations based on current network situations

DNN Architecture — Four Layers

CNO vs Human — Head to Head

Ecosystem Built

Three core teams working in a continuous feedback loop:

• Optimisation Team — domain experts using CNO tool, feeding manual learnings back into the system
• CNO Tool — central recommendation engine, continuously improving from usage feedback
• Development Team — Data Scientists, Developers, and SMEs contributing domain knowledge and usability improvements

Results by Issue Type (CNO)

Improvement Distribution — CNO vs Manual

Training Trials

Solution quality legend used across all trials:

Trial 1 — 3 months · KPI1: 12K · KPI2: 19K samples

Trial 2 — 2 months · KPI1: 26K · KPI2: 40K samples

Improvisations Taken Forward

• Regression-based estimation including alarms impact
• Prediction over ranges not part of original learning set
• Redefining thresholds and methodology for KPI classification
• Arbitration mechanism introduced
• Separate neighbour cell handling module
• Clustering based on performance metrics
• Revised learning and KPI improvement approach
• Ease of implementation across multiple operators

Course Summary

• Advanced Generative AI products using cutting-edge models and frameworks
• Proficiency with HuggingFace, LangChain, and Gradio
• State-of-the-art techniques: RAG, QLoRA fine-tuning, and Agents
• Transition from inference to training — fine-tuning both frontier and open-source models
• Deployment to production with polished UIs and advanced capabilities

The journey

• Foundations & first projects — Transformer fundamentals, six frontier models, a Gen AI product that scrapes the web and creates formatted sales brochures
• Frontier APIs & chatbots — a customer-service chatbot interacting with text, images, audio, plus tools and agents
• Open-source models — HuggingFace, 10 common Gen AI use cases, a meeting-minutes generator from recordings
• LLM selection & code generation — Python → C++ translation with 60,000× performance gains
• Retrieval-Augmented Generation — vector embeddings, open-source vector stores, a full business RAG solution
• Transitioning to training — fine-tuning a frontier model on a real business problem
• Advanced training — QLoRA fine-tuning an open-source model to outperform frontier models on specific tasks
• Deployment & finalization — a productionized, agentized, fine-tuned LLM with a polished UI

Projects covered

• AI-powered brochure generator that intelligently scrapes and navigates company websites
• Multi-modal customer support agent for an airline with UI and function-calling
• Meeting minutes & action items from audio, using both open- and closed-source models
• AI that converts Python to optimized C++ — 60,000× faster
• AI knowledge-worker using RAG to become an expert on all company matters
• Capstone A — predict product prices from short descriptions using frontier models
• Capstone B — fine-tuned open-source model competing with frontier on price prediction
• Capstone C — autonomous agent system that spots deals and notifies you of bargains