Atmospheric CO₂ Daily Volatility Time Series

Atmospheric CO₂ Seasonality Emerges as a Latent Limit Cycle in a Mamba State-Space Model This project investigates the internal representation learned by a Mamba state-space model trained on daily atmospheric CO₂ concentration data. Although modern sequence models achieve strong predictive performance, their internal latent dynamics are often difficult to interpret. In this work we analyze the latent vectors produced by the model and reveal that the learned representation organizes the CO₂ signal as a low-dimensional dynamical system. Specifically, the latent space exhibits: a seasonal asymmetric limit-cycle oscillator phase synchronization between latent and physical seasonal phase nonlinear phase warping emphasizing seasonal transition regimes a slowly expanding spiral manifold reflecting long-term CO₂ growth The latent seasonal phase is extracted from the model representation and compared with the physical CO₂ seasonal phase obtained via the Hilbert transform. The two phases exhibit strong synchronization, while the nonlinear phase mapping highlights biologically active seasonal transitions. These results demonstrate that modern state-space sequence models can learn interpretable dynamical coordinates that correspond to real physical processes. Repository Contents paper.md – manuscript describing the method and results analysis_clean.ipynb – notebook used to compute the latent representation and generate the figures figure files illustrating the latent dynamical structure processed datasets used in the analysis Data The atmospheric CO₂ data originates from the NOAA ESRL dataset: https://gml.noaa.gov/ccgg/trends/ For reproducibility, processed versions of the dataset are included in the repository: co2_daily.parquet df_y.parquet Reproducibility Running the provided notebook reproduces the figures presented in the manuscript. Keywords Mamba State Space Model Climate Time Series Latent Dynamics Limit Cycle CO₂ Seasonality