Maths and computer science · Ambitious · Dissertation or artefact

How a neural network learns: a maths EPQ idea

Why it works as an EPQ

Gradient descent and the chain rule are A Level ideas at heart; building a tiny network shows exactly where they appear.

Scope and difficulty

Ambitious. Ambitious. A network with one hidden layer on a small problem, written and explained by you.

The maths

Builds on these A Level topics: Differentiation · Numerical methods · Algebra and functions.

You would learn:

• Partial derivatives
• Gradient descent
• Backpropagation as the chain rule

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Fit a straight line by gradient descent and explain each step.
2. Build a one-hidden-layer network and derive its updates with the chain rule.
3. Train it on a simple data set and study the learning rate.
4. Judge how far 'just calculus' explains modern systems.

Pitfalls

• Using a library you cannot explain.
• Claims about large AI systems without sources.

Where to start reading

• Mathematics for Machine Learning (Deisenroth, Faisal and Ong)
• Search for: backpropagation chain rule worked example

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

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Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.