---
title: "Non-convex optimisation"
lesson_id: "02"
---

# Non-convex optimisation

- **Lesson ID:** 02
- **Goal:** Training is not a clean bowl. Learn the geometry you will actually hit: saddles, sharp minima, exploding steps, and why clip exists.
- **Human lesson:** [02-non-convex-optimisation.html](02-non-convex-optimisation.html)
- **Phase:** Phase 1 Foundations

## Prerequisites

- The previous week's artifact, or a written note if this is week 1.
- Python 3.11+ and a laptop. CUDA is useful from week 5 onward and not required to read.

## Inputs, outputs, and artifacts

- **Inputs:** The replica from the prior week.
- **Outputs:** Finish project 1 with an optimiser lab you can reuse in week 5.
- **Artifacts:** Lesson notes plus the code named in the human page.

## Agent build steps

1. State the week 1 principle: you do not need to pretrain an 800B model to understand the shape of the problem; you do need progressively realistic replicas.
2. Teach the topics on the human page without inventing paper URLs or news claims.
3. Keep starter code in fenced blocks that match the human lesson.
4. End with the assignment and the opinion checkpoint.
5. Use Edge FDE tone: ship, do not sightseeing. Opinion checkpoints matter.

## Constraints

Plain spoken English. No quizzes. No em dashes. No invented metrics, dates, or citations. Brand Edge FDE only. Name well-known papers by title only: Attention Is All You Need, InstructGPT, Direct Preference Optimization, ZeRO, PagedAttention/vLLM, FlashAttention, Scaling Laws for Neural Language Models.

## Key concepts

- Language-model training is non-convex first-order search.
- Adam stores biased moments. Epsilon and warmup are load-bearing.
- Grad clip is a stability tool, not a style choice.
- Log grad norms and loss. Do not invent smoothness you did not measure.

## Takeaways

- Implement the updates. Reading the names is sightseeing.
- A broken eps or a missing warmup is a real outage later.
- Keep three seeds on the toy so you do not overfit a story.

## Acceptance checks

- Human HTML has Key concepts and Takeaways.
- Opinion checkpoint is present.
- No em dash and no fake URL.
- [ ] Proceed to [lesson 03 brief](03-tinygpt-from-scratch.llms.md).