Sensing Regime-Level Climate Instability via Hidden-State Dynamics of Mamba

Overview This repository explores representation dynamics of a Mamba-based time-series model.The analysis focuses on the model output representation y_t. Data Synthetic signals: sine, random Real signal: atmospheric CO₂ time series Model d_model = 128n_layers = 4d_state = 64 Example representation tensor: y_t shape = (16856, 128) Research Progress Season 1Representation energy analysis using ‖y_t‖. Season 2Comparison between representation energy and EWMA-smoothed signals. Season 3Quadrant-based representation analysis (Q1–Q4) derived from y_t dynamics. Season 4Comparison between Q4 events and ENSO variability (ONI). Season 5 Update — Flip-Based Analysis The quadrant approach was replaced with a sign-flip metric. For each timestep: delta_y_t = y_t - y_(t-1) Flip count: neg_cnt(t) =number of dimensions wheresign(delta_y_t) != sign(delta_y_(t-1)) This produces flip burst events representing rapid directional changes in representation space. Artifact Verification Flip bursts were compared with hidden-state energy (‖h_t‖). Result: flip bursts do not align with hidden-state energy changes This indicates the flip events are representation artifacts rather than genuine dynamical transitions. ENSO Comparison Flip bursts were compared with the Oceanic Niño Index (ONI) using: Spearman correlation lagged correlation Granger causality Result: no statistically significant relationship detected. Conclusion The Season 5 experiments show that sign-flip bursts in representation dynamics are artifacts of the representation layer (y_t) rather than indicators of hidden-state transitions or ENSO-related climate signals. Reproducibility Notebook: 260305_season5_fwd_bwd_train_ht_with_y_flip.ipynb Includes: forward/backward training hidden-state extraction flip metric computation artifact verification ENSO comparison ## Update (Season 5) The Season 5 analysis shows that the flip-based signal behaves as a representation artifact under the current setup. This update replaces the previous quadrant-based analysis of y_t with a sign-flip metric computed from representation differences. delta_y_t = y_t - y_(t-1) A flip count (neg_cnt) is defined as the number of dimensions where the sign of delta_y_t changes between consecutive steps. Flip bursts were also compared with hidden-state energy (||h_t||). The lack of alignment indicates that these flip patterns are artifacts of the representation dynamics rather than indicators of hidden-state transitions or ENSO-related climate signals. Update (Dataset) This dataset contains hidden-state (h_t) and output (y_t) representations extracted from a Mamba sequence model trained on daily atmospheric CO₂ concentration time series. The model uses a configuration with 2 heads, head dimension 64, and SSM state dimension (d_state) 128. Both forward and backward model passes are included. The original time series contained missing timestamps. These gaps were handled using forward-fill imputation to maintain a continuous daily sequence prior to model training. The dataset is intended for analyzing representation dynamics and regime-level transitions in climate-related time series. Contents:- ht_f : forward hidden states- yt_f : forward output representations- ht_b : backward hidden states- yt_b : backward output representations