Hidden Dynamics as Sensors: Quadrant-Based Shock–Severity–Recovery (Notebook)

This notebook records an exploratory study on using Mamba hidden-state dynamics as “sensors” to summarize shock–severity–recovery structures in time series. Instead of modeling raw signals directly, two dynamics measures are derived from hidden states: (i) energy change (EWMA of |Δh|) and (ii) direction change (EWMA of 1 − cosine similarity). These measures define quadrant regimes (Q1–Q4) and three sensor summaries:(A) Q4 entry frequency, (B) strong Q4 tail ratio (top 95%), and (C) recovery path categories (Fast/Slow/Loop/NR). The same sensor frame is demonstrated on publicly available USD/KRW exchange-rate data (FRED), illustrating how shock frequency, tail severity, and recovery structure vary across periods. This work is not intended as a formal method proposal. The goal is to document exploratory experiments and visualizations that may inform further analysis. Notes & limitations: parameters (EWMA τ, quantile q) are design choices; severity is a relative tail metric (not absolute risk); quadrant uses absolute magnitudes (sign can be analyzed separately). AcknowledgementThanks to open-source tools and public data (FRED) that made this exploration possible.Assistance from AI tools was used for code refactoring and documentation.