Geometry of the Mamba Output Representation y_t on Atmospheric CO₂ Time Series

This repository contains an exploratory analysis of the output representation (y_t) of a minimal Mamba model trained on atmospheric CO₂ time series. The analysis investigates whether the model output representation exhibits low-dimensional geometric structure aligned with the temporal dynamics of the signal. Key observations: - The representation energy coordinates (E1, E2) form a recurrent trajectory aligned with the seasonal cycle.- A simple phase coordinate can be derived from the energy coordinates.- When visualized in (phase, radius, year) space, the representation forms a recurrent trajectory with slow drift across years. The analysis focuses on the geometry of the model output representation rather than the internal hidden state.