We have to understand that it is part of a much larger scientific enquiry.
On Substack there are a few substacks writing about the geometry of the LLM space.
Actually, for me that is a lot of reading to keep up with and, as yet, I haven't managed.
I also found something else on Substack of immediate relevance both to understanding consciousness and understand where we sit on Substack as a social medium.
This is an interview by the author Gunnar Gronlid with Karl Friston in the substack H-Bar Journal from Nov 19th 2025.
GUNNAR: A term you’ve used a couple of times so far that I think is important is sparsity. I’ve heard you make the point elsewhere that one of the most aesthetically beautiful and functionally elegant aspects of the brain is its sparse connectivity. So, basically, despite the brain having billions of neurons, which form this holistic web out of trillions of connections, each neuron is actually only connected to a very small subset of the rest. Although we imagine the brain as one big bundle of connections, it really has this beautifully sparse structure where neurons are mostly connected to their neighbors, and these neighboring connections fan out in a very ordered manner into a broader structure that is hierarchically organized. And that is not necessarily an immediately intuitive idea, because people feel themselves to be of one mind, so to speak, so they imagine the brain to be more singularly unified in its connectivity. So why is sparsity such a good thing from the perspective of having a functional self-organizing structure?
KARL FRISTON: That’s an excellent question, which I think also would be really usefully unpacked in terms of notions of deglobalization. There’s a popular view that mass connectivity, in the Facebook sense, is a good thing. In my world, it’s really bad. Dense connectivity is the killer. It is death.
That is really just an inversion of the truism that for things to exist—by which I mean they persist in some characteristic space over time—you are explicitly saying that their Markov blanket persists. But we’ve just said the Markov blanket is defined in terms of sparse coupling; it’s defined in terms of connections that are not there as much as the connections that are there. So you immediately have a view of the world in which, if you don’t have sparse connectivity, you can’t have Markov blankets. If you can’t have Markov blankets, you’re just left with a soup. There would be nothing in that kind of universe."
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Substack publishes no serious investigation into Category Theory in this domain, although one of the authors who writes about LLMs is somewhat "category theoretic".
For instance I have found a recent note in relation to other writings about the "potential dialogue between tensor logic and topos theory? Both address the same fundamental problem—bridging different modes of representation while preserving structure—from different mathematical traditions."
That indicates the work has yet to be done, here in relation to the geometric approach and category theory.
For which I am using as my starting point the work of David Corfield, in particular his Modal Homotopy Type Theory (MHoTT) book.
I am not writing about this yet.
I do not understand it well enough.
A couple of my links that in turn have links to other authors.
Hi Adam, interesting thoughts and I'll checkout your links. Your point about sparsity is very relevant. If you haven't seen this paper that directly addresses this then I'd recommend it. https://dynamicaspects.org/papers/philosophy/agi2025.pdf
I'm reading your work with great interest.
We have to understand that it is part of a much larger scientific enquiry.
On Substack there are a few substacks writing about the geometry of the LLM space.
Actually, for me that is a lot of reading to keep up with and, as yet, I haven't managed.
I also found something else on Substack of immediate relevance both to understanding consciousness and understand where we sit on Substack as a social medium.
This is an interview by the author Gunnar Gronlid with Karl Friston in the substack H-Bar Journal from Nov 19th 2025.
https://hbarjournal.substack.com/p/karl-friston-functioning-brains-and
Let me quote:-
"Sparsity, And Soups
GUNNAR: A term you’ve used a couple of times so far that I think is important is sparsity. I’ve heard you make the point elsewhere that one of the most aesthetically beautiful and functionally elegant aspects of the brain is its sparse connectivity. So, basically, despite the brain having billions of neurons, which form this holistic web out of trillions of connections, each neuron is actually only connected to a very small subset of the rest. Although we imagine the brain as one big bundle of connections, it really has this beautifully sparse structure where neurons are mostly connected to their neighbors, and these neighboring connections fan out in a very ordered manner into a broader structure that is hierarchically organized. And that is not necessarily an immediately intuitive idea, because people feel themselves to be of one mind, so to speak, so they imagine the brain to be more singularly unified in its connectivity. So why is sparsity such a good thing from the perspective of having a functional self-organizing structure?
KARL FRISTON: That’s an excellent question, which I think also would be really usefully unpacked in terms of notions of deglobalization. There’s a popular view that mass connectivity, in the Facebook sense, is a good thing. In my world, it’s really bad. Dense connectivity is the killer. It is death.
That is really just an inversion of the truism that for things to exist—by which I mean they persist in some characteristic space over time—you are explicitly saying that their Markov blanket persists. But we’ve just said the Markov blanket is defined in terms of sparse coupling; it’s defined in terms of connections that are not there as much as the connections that are there. So you immediately have a view of the world in which, if you don’t have sparse connectivity, you can’t have Markov blankets. If you can’t have Markov blankets, you’re just left with a soup. There would be nothing in that kind of universe."
--
Substack publishes no serious investigation into Category Theory in this domain, although one of the authors who writes about LLMs is somewhat "category theoretic".
For instance I have found a recent note in relation to other writings about the "potential dialogue between tensor logic and topos theory? Both address the same fundamental problem—bridging different modes of representation while preserving structure—from different mathematical traditions."
That indicates the work has yet to be done, here in relation to the geometric approach and category theory.
For which I am using as my starting point the work of David Corfield, in particular his Modal Homotopy Type Theory (MHoTT) book.
I am not writing about this yet.
I do not understand it well enough.
A couple of my links that in turn have links to other authors.
https://substack.com/@saltiela/note/c-190077405?r=imxe&utm_source=notes-share-action&utm_medium=web
https://substack.com/@saltiela/note/c-187071937?r=imxe&utm_source=notes-share-action&utm_medium=web
Hi Adam, interesting thoughts and I'll checkout your links. Your point about sparsity is very relevant. If you haven't seen this paper that directly addresses this then I'd recommend it. https://dynamicaspects.org/papers/philosophy/agi2025.pdf