Stable Takens' Embedding Theorem for Non-Uniformly-Sampled Linear Systems
arXiv:2608.14001
2026
Dynamics
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper offers a transferable stability mechanism for delay-coordinate representations under irregular sampling. For a linear system, the delay map is an observability matrix whose smallest singular value controls state-reconstruction sensitivity to measurement noise, while its condition number quantifies numerical instability. In a neural state-space encoder, this suggests selecting or learning irregular delay times using a differentiable observability-margin objective. The mechanism makes a falsifiable prediction: rollout or reconstruction error should increase as the smallest singular value approaches zero, with noise amplification bounded by the inverse of that singular value.
Ideas from this paper
✗ Failed on benchmark
2026
Replace uniformly spaced history taps in a neural state-space encoder with a fixed or learned set of non-uniform delays. Regularize the resulting delay-observation matrix to have a large smallest singular value, which makes latent-state reconstruction less sensitive to irregular timestamps and observation noise. This is directly applicable to event-based data, missing timestamps, and systems with multiple time scales.
Useful8/10
Difficulty6/10
Novelty7/10
△ Mechanism confirmed, baseline not beaten
2026
Use the observability margin to choose which delay taps to retain under a fixed memory or computation budget. Add a candidate delay only when it substantially increases the smallest singular value of the delay map, converting the paper's large-delay asymptotic result into an adaptive receptive-field construction for sequence models.
Useful7/10
Difficulty5/10
Novelty8/10