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Comment by FloorEgg | Hacker News Reader

Ever since I learned about category theory and its relationship with symbolic reasoning I've suspected that AGI will come from elegantly combining symbolic reasoning and probabilistic reasoning. This is the first project I've seen that seems to be positioned that way. Very cool.

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When LLMs code in order to reason, isn’t that a combination of probabilistic reasoning and symbolic reasoning?

Neural networks are actually somewhere in between. They don't directly operate on symbolic expressions or explicit logical rules. And while they rely on probabilistic aspects for training (and sometimes for inference), they rely more on continuous-valued transformations in extremely high dimensional spaces. But if your goal is human-like intelligence, they are a pretty good bet, because we know the human brain also doesn't perform symbolic reasoning at its core and these things only emerge as high-level behaviour from a sufficiently complex system. But it also makes neural networks (and us too) prone to failure modes that you would not see in strictly symbolic reasoning processes.

Yes, this seems to be what the symbolists always forget. We don’t use symbolism like this, we just have very dense neural connections that emerge from scale and approximate it

That's not really what symbolists actually argue. Read Fodor and Pylylshyn 1988 to better understand how symbolists view the relationship between symbolic representation and connectionist models. What you're saying is akin to saying there's no point in doing neuroscience or trying to understand neural-networks as its just particle physics deep down.

Connectionism and cognitive architecture: A critical analysis https://www.semanticscholar.org/paper/Connectionism-and-cogn...

Fodor and Pylyshyn's Critique of Connectionism and the Brain as Basis of the Mind https://arxiv.org/abs/2307.14736

So if inventing the airplane how long should one stick with a flapping bird wing design?

That is not a good analogy. Symbolism has given us lots of useful things, including SAT/SMT and theorem provers.

The point is that while biology has been a great source of inspiration toward technical advances it’s only a guide, it can’t guarantee there isn’t a better way.

https://www.brunogavranovic.com/posts/2024-03-13-my-thesis-i...

http://forestdb.org is quite old and includes some toy examples that IMHO elegantly combine symbolic and probabilistic reasoning.

Related: Graph&Category-Theory-based Neuro-Symbolic AI

> The work uses graphs developed using methods inspired by category theory as a central mechanism to teach the model to understand symbolic relationships in science.

https://news.mit.edu/2024/graph-based-ai-model-maps-future-i...

I know a tiny bit about category theory but nothing about symbolic reasoning. Would anyone mind ELI5ing the connection between the two?

I'm not qualified to offer an accurate eli5, just a hand-wavy explanation...

Category theory can be leveraged to make faster theorem provers (making complex symbolic reasoning practical at larger scales).

Don't ask me how, hopefully someone who studies it will chime in and correct me / expand.

There is a long history of efforts to combine symbolic and connectionist approaches. This is hardly the first!

If you know of other modern NS languages/integrations, please share !

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