Some Capital

@arithmoquine @1thousandfaces_ Hopfield Algebra and Geometric Learning. Those pique my interest too. We can do synthetic tests, no need to test on wet-ware.

i think i just need to be a bit more verbose we take like 500 neurons, and track when they spike. the spike-rates for all the neurons gives us a point in 500 dimensional space. this point moves around this space as the brain changes state, but since there's *some* underlying structure / compressability to the information, it's only going to be moving along a lower-dimensional manifold embedded in that 500 dimensional space. with enough data, we can use a dimensionality reduction algorithm like UMAP to find the most information-preserving mapping of the 500-dimensional paths to 2D space. and, the really fucking cool thing is that the resulting manifold has the same topology as the physical space explored by the rat while the data was collected. the structure of the maze is represented in this high-dimensional space, and the rat's brain-state moves along this internal representation of the maze to track the actual position. obv there's tons of other interesting stuff in that space, but the most salient feature is this maze-manifold

every time i remember we can do this i get a rush of excitement to be alive. literally just do dimensionality reduction w/ UMAP on neuronal spike data and you can recover topology from mental models of physical space

@MatthewBerman @AnthropicAI @ChatGPTapp @sama

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