Comment by D-Machine
2 days ago
"Aristotle integrates three main components: a Lean proof search system, an informal reasoning system that generates and formalizes lemmas, and a dedicated geometry solver"
It is far more than an LLM, and math != "language".
> Aristotle integrates three main components (...)
The second one being backed by a model.
> It is far more than an LLM
It's an LLM with a bunch of tools around it, and a slightly different runtime that ChatGPT. It's "only" that, but people - even here, of all places - keep underestimating just how much power there is in that.
> math != "language".
How so?
Transformer != LLM. See my edited top-level post. Just because Aristotle uses a transformer doesn't mean it is an LLM, just as Vision Transformers and AlphaFold use transformers but are not LLMs.
LLM = Large Language Model. Large refers to both the number of parameters (and in practice, depth) of the model, and also implicitly the amount of data used for training, and "language" means human (i.e. written, spoken) language. A Vision Transformer is not an LLM because it is trained on images, and AlphaFold is not an LLM because it is trained molecular configurations.
Aristotle works heavily with formalized LEAN statements and expressions. While you can certainly argue this is a language of sorts, it is not at all the same "language" as the "language" in LLMs. Calling Aristotle an "LLM" just because it has a transformer is more misleading than truthful, because every other single aspect of it is far more clever and involved.
The paper you keep linking literally says they're using a large language model (search for that very string in it).
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I kind of agree, "math" can be a "language". Same as "images" can be a language. You can use anything as tokens.
In this context, we're not even talking about "math" (as a broad, abstract concept). We're strictly talking about converting English to Lean. Both are just languages. Lean isn't just something that can be a language. It's a language.
There is no reason or framing where you can say Aristotle isn't a language model.
That's true, and a good fundamental point. But here it's much simpler than that: math is a language the same way code is, and if there's one thing LLMs excel at, it's reading and writing code and translating back and forth between code and natural language.