[ainch]

I'm afraid the precise connection you're making isn't totally obvious to me.

As far as prediction - I mean sure the cortex and LLMs do prediction, but then so can RNNs or diffusion models or any other generative model. Really any ML architecture is learning to compress its environment in pursuit of modelling. More broadly, the predictive brain model would suggest that all of the brain, not just the neocortex, is dedicated to prediction. What would you say makes LLMs similar to the neocortex, rather than the basal ganglia or Broca's area?

Similarly, if you agree with the Manifold Hypothesis, then all machine learning models operate on manifolds. I agree it's an exciting thought, but then I don't know what would distinguish an LLM from a VAE or SVM in terms of operating over a low-dimensional manifold embedded in high dimensional spaces - maybe just scale?

[koverstreet]

> More broadly, the predictive brain model would suggest that all of the brain, not just the neocortex, is dedicated to prediction. What would you say makes LLMs similar to the neocortex, rather than the basal ganglia or Broca's area?

The whole brain is most definitely not dedicated to prediction, and I don't think "prediction" is a very useful model anyways. You could say the hippocampus is for "prediction" if you really squint, but that's underselling what it's doing. And the basal ganglia operates off of prediction error, but it's more about regulating short timescale feedback loop learning than learning itself - speaking somewhat loosely because it's a particularly ancient structure in the brain and things get muddied.

LLMs obviously don't have functional equivalents to either of those - sure they can remember facts, but they can't intake new facts the way we can, the hippocampus is set up completely differently. But higher reasoning is humans is the neocortex, and that LLMs can do, and there's even structural parallels - LLMs and the neocortex are both implemented in layers, and you can even (with a shit ton of analysis) watch how LLMs walk the geometry across layers. The neocortex needs a lot fewer layers than LLMs, but that's because it's not pure feedforward across layers; the neocortex already does what the "looped LLM" people are trying to do.

> Similarly, if you agree with the Manifold Hypothesis, then all machine learning models operate on manifolds. I agree it's an exciting thought, but then I don't know what would distinguish an LLM from a VAE or SVM in terms of operating over a low-dimensional manifold embedded in high dimensional spaces - maybe just scale?

I view things more mathematically, and in math and physics it frequently turns out that there's really only one solution to a problem, or correct way to model something - and then everything else is just isomorphisms (which may be interesting objects in their own right!).

My interpretation/guess (informed by research, but with a lot of still unanswered questions) is that the manifold is fundamentally the structure that emerges from natural language: natural language has a computational model, just like Church/Turing machines have a computational model. Reimannian manifold is also underselling it a bit, it's also Finsler, and RoPE adds additional structure to that manifold (and when we get to RoPE it wouldn't surprise me if the neocortex and LLMs do diverge significantly in how they compute, but does the structure change? dunno yet).

Basically, I'm fairly confident in what I say about machine learning models that understand natural language; for non-NL machine learning, maybe the same structure emerges with enough complexity, but I haven't really pondered that.

[ainch]

Thank you for expanding! I come from more of an ML background so still learning a lot on these topics:

Agreed that the neocortex uses fewer layers because of looping - I also suspect it's partly because neurons are more complex than the neurons used in ANNs, so in principle they should be capable of more sophisticated computation in a single forward pass (especially considering that handling multiple neurotransmitters could mean superposed functions).

The point about there being one correct way to model something does seem backed up by the Platonic Representation hypothesis (https://arxiv.org/pdf/2405.07987). I've even seem some work that shows you can find a bijective map between the latent spaces of different transformers (https://arxiv.org/pdf/2505.12540).

Your point about Finsler spaces is fascinating - I hadn't come across the term before. It'd be interesting to see if there's work that specifically allows latents to exhibit that kind of directional metric behaviour, and whether that improves generalisation or something.

On the entire brain being dedicated to prediction, that's more of a high-level comment. I was thinking of work like Andy Clark on predictive processing, which suggests that even regions of the brain which we think of as receptive (eg. the visual cortex) may be implementing a generative/predictive model which is corrected by sensory input.

[koverstreet]

I'm not sure if the complexity is at the neuron level. It's clearly possible; we see some pretty complex behavior from single celled organisms - Stentors - and there were the experiments (starting in the 70s, I believe) that conditioned flatworms, ground them up and fed them to new flatworms and showed that the new flatworms had the same conditioning. Those experiments were replicated but never explained, but they hint at something like maybe memories being encoded in RNA.

It'd be wild if our brains used a mechanism like that somewhere, but I doubt it's in the neocortex because those would be slow processes compared to what the neocortex has to do.

I think the sophistication in the neocortex just comes from it using something more sophisticated with transformers. Most of the looped LLM research I've scanned through, they seemed to be training the model to "know" when it should loop more and think harder, and I don't think that approach will ever work - you're solving for paths on a manifold, so the looping needs to happen at the abstraction layer below the manifold, looping more if it's still converging. And architectures with more recurrence are just harder for us humans to reason about and comparatively easier for dumb evolution to find clever solutions, so my money is that that's where the neocortex has LLMs beat.

And I'd say the manifold hypothesis is quite a bit more than a hypothesis at this point. There's been work on production LLMs to use manifold analysis to optimize them - there was a paper in Nature on it back in January. Baby stuff compared to what could be done, but the geometric approach keeps popping up in mechanistic interpretability and seems to be showing the most insights.