# Temporal Lifting as Latent-Space Regularization for Continuous-Time Flow Models in AI Systems

arXiv: https://arxiv.org/abs/2510.09805 · HTML: https://mlsanity.com/paper/2510.09805/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 11 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 1 of 1)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)

## Abstract (arXiv)

We present a latent-space formulation of adaptive temporal lifting for continuous-time dynamical systems. The method introduces a smooth monotone mapping t mapsto τ(t) that regularizes near-singular behavior of the underlying flow while preserving its conservation laws. In the lifted coordinate, trajectories such as those of the incompressible Navier-Stokes equations on the torus mathbbT3 become globally smooth. From the standpoint of machine-learning dynamics, temporal lifting acts as a continuous-time normalization operator that can stabilize physics-informed neural networks and other latent-flow architectures used in AI systems. The framework links analytic regularity theory with representation-learning methods for stiff or turbulent processes.