Prediction Limits and Koopman Closure of Geometry-Induced Soft State Abstractions

arXiv:2609.32652 · cs.AI, cs.LG, math.DS · Submitted 2026-09-26 · Read on arXiv

cs.AI, cs.LG, math.DS

Submitted: 2026-09-26

Updated: 2026-09-26

Code: https://github.com/MohitKumarRostock/Kernel_Affine_Hull_Koopman_Mac

Terminology

• Abstraction — 80× in this paper · explained in 1 episode
• Benchmark — 12× in this paper · explained in 2 episodes
• Ablation — 11× in this paper · explained in 1 episode
• Accuracy — 10× in this paper · explained in 1 episode
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Regularization — 7× in this paper · explained in 3 episodes
• Aggregation — 6× in this paper · explained in 1 episode
• Post-Selection — 6× in this paper · explained in 2 episodes
• Provenance — 5× in this paper · explained in 4 episodes
• Robustness — 5× in this paper · explained in 5 episodes
• Reconstruction Error — 4× in this paper · explained in 2 episodes
• Reinforcement Learning — 4× in this paper · explained in 4 episodes
• Clustering — 3× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Kernel Affine Hull Machine — 3× in this paper
• Consistency — 2× in this paper · explained in 3 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Kernel Affine Hull Koopman Machine — 2× in this paper
• Redundancy — 2× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 2× in this paper · explained in 3 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Admissibility — 1× in this paper · explained in 2 episodes
• Angular Error — 1× in this paper · explained in 1 episode
• Deep Reinforcement Learning — 1× in this paper · explained in 2 episodes
• Differentially Private — 1× in this paper · explained in 3 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Error Decomposition — 1× in this paper · explained in 3 episodes
• Federated Learning — 1× in this paper · explained in 14 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces
• Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems
• Operator-Theoretic Framework for Gradient-Free Federated Learning
• Kernel Affine Hull Machines as Compute-Efficient Encoders for Frozen Semantic Spaces
• Gymnasium: A Standard Interface for Reinforcement Learning Environments
• Spectral State Compression of Markov Processes

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