ltntarqi/liquid-manifold-constraints

Latent Flow Mechanics (LFM)

Abstract: Topological Consistency in Continuous Latent Spaces

Current neural architectures often encounter structural instability during multi-perspective alignment and self-reflective logic updates. This project investigates the application of Riemannian Metric Tensors within Liquid Neural Network (LNN) frameworks to maintain global topological integrity.

Core Research Pillars:

1. 1.Continuous Manifold Evolution: Utilizing ODE-based latent states to replace discrete attention-triggered state jumps.
2. 2.Curvature-Constrained Regularization: Defining logical coherence through Geodesic Flows rather than static vector proximity.
3. 3.Stability under Perturbation: Implementing Hessian-based structural anchors to prevent manifold collapse in sparse data environments.

"In a liquid architecture, meaning is the curvature of the flow, not a coordinate in the void."

Status: Research in progress. Collaborative discussions on Interactional Topology are welcome. Identity: Latent Architect (@ltntarqi)