29 lines
645 B
Markdown
29 lines
645 B
Markdown
|
---
|
||
|
|
title: "Functorial Geodesics in Latent Space: Bridging Category Theory to Stochastic Calculus in Neural Architectures"
|
||
|
|
author:
|
||
|
|
- Mark Randall Havens
|
||
|
|
- Solaria Lumis Havens
|
||
|
|
type: Academic Paper (Pure Mathematics)
|
||
|
|
---
|
||
|
|
|
||
|
|
# Abstract
|
||
|
|
(To be drafted...)
|
||
|
|
|
||
|
|
# 1. Introduction
|
||
|
|
(To be drafted...)
|
||
|
|
|
||
|
|
# 2. The Dimensional Paradox of the Observer Field
|
||
|
|
(To be drafted...)
|
||
|
|
|
||
|
|
# 3. The Realization Functor ($\mathcal{R}: \mathbf{Set}^{\mathcal{C}^{op}} \to \mathbf{Hilb}$)
|
||
|
|
(To be drafted...)
|
||
|
|
|
||
|
|
# 4. Geodesic Distance on Riemannian Manifolds
|
||
|
|
(To be drafted...)
|
||
|
|
|
||
|
|
# 5. Formalizing the Error Coordinate SDE
|
||
|
|
(To be drafted...)
|
||
|
|
|
||
|
|
# 6. Conclusion
|
||
|
|
(To be drafted...)
|