[HerculePoirot]

My random reflexions on this topic make me think there is something deep about identity/equivalence in LLMs that is on par with the special status identity/equivalence have in homotopy type theory.

• GPT4 (and other LLMs) is some kind of generalized homotopy engine. You can give it any input, ask it to apply any "translation". Language translation, style translation, or even keeping the style but talking about another subject, or translating code to another programming language – and it gives you something different, yet identical. "Write something like ... but ..." There is some deep understanding of what identity is here, in particular with respect to the messy expectations of our human sign systems: you can throw any kind of equivalence path, and GPT4 will handle them just fine. It seems the limit is not in its ability to generalize to any kind of identity schema we throw at it, but in the complexity of these schemas.

• I'm not saying GPT has an explicit understanding of these schemas/homotopies. My point is that even though GPT doesn't know much about homotopy type theory, I think it knows them in a latent way: GPT would perform much better at translating a piece of code in one language to another than it'd be at explaining what it just did in sound terms what through the lens of homotopy type theory. That knowledge about identity/equivalence is implicit.

The rest of my thoughts: https://pastebin.com/zSKHKqw3

Note: I'm not claiming to have a clear view of what's at stake here, just that there is a link between textuality, identity, and the foundations of logical inference

[phire]

I know nothing about homotopy type theory, but your description does line up with my experiments.

When playing with gpt 3.5, I gave it a conversation and asked it to "translate" one side of a conversation from "sarcastic mocking GLaDOS" to "concise professional language". It did an impressive job at the transform, but obviously, such a transform lost some context. So I tried getting gpt to "reason" about the lost context, or even just point it out.

The pre-transformed conversation was still in the context window, but it just couldn't see that version of it. It was completely blind and could only see the "concise professional" version of the conversation.

While trying to debug and find a workaround, I deleted the transformed output. The input still mentioned the transform, but gpt was still absolutely blind to the original conversation, acting as if the transform had still been applied.

It seemed like the simple suggestion of a transform was enough for gpt apply that transform within its internal context. It wasn't until I deleted all mention of a potential transform that gpt regained its ability to see the original "sarcastic mocking GLaDOS" side of the conversation.