In kernel DMD and Koopman analysis, many extracted modes are not features of the dynamics but artifacts of finite-rank projection. Increasing model capacity often amplifies spectral pollution rather than revealing structure.
A conceptual map of generation: subword tokenization → learned embeddings → attention-based next-token prediction. Concrete diagrams show what each stage buys you and what it assumes.
Normalizing flows turn density estimation into calculus: invertible transforms + Jacobians give exact log-likelihoods. This post builds the change-of-variables view and why architectures like RealNVP make it tractable.
In non-normal problems, eigenvalues are not stable summaries: tiny perturbations can move them drastically. Pseudospectra replace point eigenvalues with uncertainty-aware regions—crucial for DMD/Koopman-style analysis.
GARCH-style volatility can look calibrated—until the data regime changes. This post shows why coverage breaks under structural shifts and how Adaptive Conformal Inference re-calibrates online without distributional assumptions.