[Majromax]

> At first glance this doesn't seem that surprising. We often use "is" in a way which isn't reversible. e.g.

They appear to only be testing the 'reliable' cases. There schematic example was fine-tuning the model on "<Fictitious name> is the composer of <fictitious album>", yet having the model be unable to answer "Who composed <fictitious album>"?

In this case, English and common sense force symmetry on 'is'. Without further specification, these kinds of prompts imply an exclusive relationship.

Additionally, the authors claim that when they tested it, the model didn't even rate the correct answer more probable than random chance. This suggests that the model isn't being clever about logical implications.

[phire]

To us, it's obvious that "is" in these examples is symmetrical. But LLMs don't have common sense, they have to rely on the training dataset we feed them.

It's entirely possible there is nothing wrong with the logical reasoning abilities of LLM architectures and this result is simply an indication the training data doesn't provide enough infomation for LLMs to learn the symmetrical/commutative nature of these "is" relationships.

Though, based on the find-the-next-token architecture of LLMs, it seems logical that LLM should need to learn facts in both directions. If it's input set contains <Fictitious name>, it makes sense the tokens for "<fictitious album>" and "composer" will show up with high probability. But there is no reason that having the tokens "composer" and "<fictitious album>" in the input set should increase the probability of the "<fictitious name>" token, because that ordering never occurred in the training data.

If true, it would would suggest that LLMs have a massive bias against the very concept of symmetrical logic and commutative operations.

[wongarsu]

The "is" in that sentence still isn't fully symmetric, I'd rather call it reversible. There is a learned relationship that "is composer of" has the same meaning as "composed" (as in "<Name> composed <Album>"). Now you can turn the active verb passive to switch subject and object: <Album> was composed by <Name>.

The final puzzle piece is then recognizing the difference between the question "Who composed <x>" and "Who did <x> compose", one asking for the object of the passive sentence and one for the object of the active sentence.

In a "traditional" system without ML you would represent this with a directional knowledge graph <Artist> --composed--> <Album>, with the system then able to form sentences or answer questions in either arrow direction. But that conversion is generally tricky unless you know how many other arrows exist. That's obvious with categories, but even if you know that one person composed a song that doesn't tell you that only that person composed that song. That can lead to unsatisfying answers, and might be a reason why this is hard for LLMs.

[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.

[diffeomorphism]

English only forces that if there is a definite article "the" (unique composer). If it instead said "a" composer, then it is impossible to answer "who composed" completely; you only know one of the composers.

Jumping to conclusions like "if A then B" to "A=B" is a very common mistake for humans, bad statistics and propaganda. So I am actually positively surprised that models don't make that mistake.