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:
Continuous Manifold Evolution: Utilizing ODE-based latent states to replace discrete attention-triggered state jumps.
Curvature-Constrained Regularization: Defining logical coherence through Geodesic Flows rather than static vector proximity.
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)
