Running list of ideas and notes

Fullstack categorical semantics

db / api / frontend

what are the morphisms?

let’s say you store user uploaded notes

instead of modeling domains model it as categories

functor somewhere

predicate isDeleted - same on

records are infinite tuples with finite non-zeros - keys are elements of a free monoid

projections remove fields

what are the types

what is the ambient category

Quantization

take a (feedforward) network

change the field \mathbb{R} to (ring) \mathbb{Z}

the weights are scalars (now \mathbb{Z}-module)

isomorphic to an abelian group?

anything interesting here?

each weight in the next layer is a linear combo

non linearity is in the way but clamps to \mathbb{Z}

other interesting (commutative) rings for an R-module?

Algebraic crap about neural networks

take a (feedforward) network, remove non linearity

linear maps

take (co)chain complex? can you? is there a point?

why?

take (projective) resolution? are the maps somehow related to the original maps?

how what does non-linearity do functorially? is there a generalization?

Spherical stable diffusion processes

what happens when the underlying manifold of a diffusion process changes

for example, can we perform diffusion process on a sphere

is this a simple reparametrization? any interesting invariants preserved?

wild curvature appears, linearity is local not global

does rotation invariance help with anything?