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This argument is centered around the belief that language and reasoning flow bidirectionally- language can be understood first (we are here), and reasoning is the next natural rung of the latter (your thesis believes we will get here with LLMs).

I see language more as a medium for transcribing reasoning. While language certainly communicates reasoning, you can have reasoning without language, but not language without reasoning.

This paper seems to imply that current LLM's are just copying the training dataset's reasoning communication, not understand the actual reasoning. I don't think LLM's moving past this is "obvious" or even close to being inevitable.

> Instead, LLMs likely perform a form of probabilistic pattern-matching and searching to find closest seen data during training without proper understanding of concepts. While this process goes beyond naive memorization of words and the models are capable of searching and matching more abstract reasoning steps, it still falls short of true formal reasoning.

I realize there is subtlety to the question of which is first. An infant, crying when it is hungry and pre-linguistic, is applying modus ponens. C -> F crying implies food, so I cry and then I get fed. Language grows in humans just like arms and legs, and so does reasoning. Baby animals do the same behavior but don't use language, so perhaps some logic is wired by instinct. Either way I don't think we need to worry about that detail.

Consider how language input to an LLM is tokenized. Now imagine a tokenization scheme that introduces tokens that track the strict logical reasoning in the language. Thus two completely different English sentences could both tokenize as the application of Modus Ponens over assumption 1 to conclude conclusion 2, for example.

Now consider that we can tokenize formal notation as used in mathematics and logic, and we can train LLMs on mathematical papers, peer review write-ups, etc. We can generate millions of correct proofs and teach it which ones are remarkable and why, etc.

Ultimately we run into the same barrier as mathematical constructivists run into, but I think it's still quite plausible that LLMs trained as I describe would be able to reason quite well and find oversights humans missed. However creating the optimal scheme and implementation is not trivial.

> If trained properly, LLMs can develop advanced representations of logical systems that will surely outpace what humans can do in terms of raw reasoning.

We have already trained the LLMs on most of the human knowledge base (so like 4-5000 years?) - imo training data will become a problem and will soon be more expensive than compute. Sure, you can work around some of this using synthetic training data but I personally would not count on general-purpose LLMs (especially LLMs aka transformer models) developing super-human representations of logical systems anytime soon.

I don't disagree, however I'm optimistic because most of the current reasoning "ability" of LLMs comes from the accidental reasoning embedded in language patterns.

For example, the prompt completion: "The mouse has a unique digestive system compared to other rodents, however the sparrow" on GPT-4o is

"exhibits a highly specialized digestive system adapted for rapid processing of food, particularly seeds and insects, through structures like the crop and gizzard, which are not found in rodents."

Claude 3.5 completes it as

"has a completely different digestive anatomy as a bird. Birds like sparrows have adaptations for flight, including a lightweight skeletal system and a specialized digestive tract. Unlike mice, sparrows have a crop for storing food, a gizzard for grinding it, and generally shorter intestines to reduce weight. They also lack teeth, instead using their beak to manipulate food."

What appears to be a thoughtful contrast is merely a language pattern. Similarly, a prompt like "Assume -B, A->B. Under what circumstances is B true?" will simply follow the gradient to return output that is likely correct. Prompts like "what is 2+2" fail only because nobody bothers to write about it so simple arithmetic was not in the training data.

However the way that multi-modal LLMs handle images is inspiring as it effectively converts from the visual domain into the sequential token domain. The same could be done for symbolic systems, etc.

I don’t see how it’s obvious that LLM’s will be capable of any mathematical, “reasoning.

LLM’s can infer relationships and maintain longer context chains in order to generate their output… it still happens that some times the output is correct depending on the training data, layers, context, etc. And it can get more accurate when we change the parameters of the model. But the algorithm isn’t “doing” anything here. It will generate something regardless of what it’s prompted with.

Maybe it’s right. But the algorithm is an algorithm. It doesn’t care what truth is. It’s generating BS essentially.

A human is doing a lot more work when performing mathematics.

It may be that LLM’s can be a useful tool in mathematical reasoning but it’s not obvious that it will ever be capable of it without a human, let alone be better than a human.

I think models could be designed that in separate layers created "logical system" representations which could feed back into the output, much like how attention works. Attention is about relevance, the logical layers could be based on logical schema-based patterns.

Consider an LLM that happened to have some pre-trained layers that were trained abstractly on all the constructive proofs available for modern mathematics. LLMs with image recognition rely on existing visual pattern recognition layers, fwiw.

There's another blog post that made it to the front-page of this site which sums up the state of the art nicely [0].

It's not obvious that they will be able to do any reasoning, in the formal sense, at all; let alone better than humans. LLMs are simply not sufficient for the kinds of tasks and work done when reasoning about mathematical problems.

There's plenty of research demonstrating that they can be useful in small, constrained tasks -- which isn't anything to raise our noses at!

... it's just not _obvious_ in the sense that there is a clear step from LLM capabilities today to "better than humans." It's more an article of faith that it could be true, some day, if we just figure out X, Y, Z... which folks have been doing for decades to no avail. In other words, it's not obvious at all.

[0] https://garymarcus.substack.com/p/llms-dont-do-formal-reason...

It’s true that current models do not do formal reasoning, my point is that it is possible to use tokenization to do it. See my comment in the other thread.