Understanding Latent-Dimension Scaling in Dynamical-System Learning through Spectral Reliability
We analyze the learned time evolution through the eigenstructure of Koopman operators, using relative residuals to detect spurious eigenpairs arising even as one-step error falls.
ProofPaper ↗
Key points
- In deep learning, approximation theory motivates increasing representation size.
- We ask whether this benefit extends to dynamics learning through autoregressive prediction.
- For bounded Koopman operators, we show that minimal residuals over learned dictionary spaces converge pointwise to their full-space counterparts as these spaces approximate the observable space in $L^2$.
- We compare two models of a shared Koopman autoencoder trained alternately for reconstruction and latent evolution, using latent-prediction loss (one-step prediction errors in latent coordinates) or spectral-residual loss (relative residuals of candidate eigenpairs).
Sources (1)
- [1]Understanding Latent-Dimension Scaling in Dynamical-System Learning through Spectral ReliabilityarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 12:42 PM
We analyze the learned time evolution through the eigenstructure of Koopman operators, using relative residuals to detect spurious eigenpairs arising even as one-step error falls.
In deep learning, approximation theory motivates increasing representation size.
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