Writing an LLM from scratch, part 14 -- the complexity of self-attention at scale

Between reading chapters 3 and 4 of Sebastian Raschka's book "Build a Large Language Model (from Scratch)", I'm taking a break to solidify a few things that have been buzzing through my head as I've worked through it. Last time I posted about how I currently understand the "why" of the calculations we do for self-attention. This time, I want to start working through my budding intuition on how this algorithm behaves as we scale up context length.. As always, this is to try to get my own thoughts clear in my head, with the potential benefit of helping out anyone else at the same stage as me -- if you want expert explanations, I'm afraid you'll need to look elsewhere :-)

The particular itch I want to scratch is around the incredible increases in context lengths over the last few years. When ChatGPT first came out in late 2022, it was pretty clear that it had a context length of a couple of thousand tokens; conversations longer than that became increasingly surreal. But now it's much better -- OpenAI's GPT-4.1 model has a context window of 1,047,576 tokens, and Google's Gemini 1.5 Pro is double that. Long conversations just work -- and the only downside is that you hit rate limits faster if they get too long.

It's pretty clear that there's been some impressive engineering going into achieving that. And while understanding those enhancements to the basic LLM recipe is one of the side quests I'm trying to avoid while reading this book, I think it's important to make sure I'm clear in my head what the problems are, even if I don't look into the solutions.

So: why is context length a problem?

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Writing an LLM from scratch, part 13 -- the 'why' of attention, or: attention heads are dumb

Now that I've finished chapter 3 of Sebastian Raschka's book "Build a Large Language Model (from Scratch)" -- having worked my way through multi-head attention in the last post -- I thought it would be worth pausing to take stock before moving on to Chapter 4.

There are two things I want to cover, the "why" of self-attention, and some thoughts on context lengths. This post is on the "why" -- that is, why do the particular set of matrix multiplications described in the book do what we want them to do?

As always, this is something I'm doing primarily to get things clear in my own head -- with the possible extra benefit of it being of use to other people out there. I will, of course, run it past multiple LLMs to make sure I'm not posting total nonsense, but caveat lector!

Let's get into it. As I wrote in part 8 of this series:

I think it's also worth noting that [what's in the book is] very much a "mechanistic" explanation -- it says how we do these calculations without saying why. I think that the "why" is actually out of scope for this book, but it's something that fascinates me, and I'll blog about it soon.

That "soon" is now :-)

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