Uniform Aggregation of Mamba Output Channels and Correlation with Original Signals

This record provides a reproducible experiment package for analyzing the relationship between the output channels (y_hat) of a Mamba autoencoder and the original input signals. The central question explored is whether a simple uniform aggregation of output channels preserves meaningful information about the original time series. A Mamba-based autoencoder is trained using reconstruction loss only, without supervision or forecasting objectives. For each time step t, the model produces output channels y_hat(t). These channels are aggregated uniformly as s(t) = sum_i y_hat(t, i). The aggregated signal is compared directly with the original input signal x(t). For each signal, two metrics are reported: raw correlation between x(t) and s(t), and affine-calibrated correlation using x(t) ≈ a · s(t) + b. Calibration parameters are fitted on a training split only and evaluated on the full series. Latent states in sequence models are high-dimensional, non-identifiable, and highly dependent on architectural and parameter choices. Their interpretation often requires additional projections or heuristics. In contrast, the model output y_hat is directly observable and directly comparable to the original input signal. This approach minimizes assumptions and treats the model as a signal transformer rather than a latent feature extractor. This work is exploratory and diagnostic in nature. No claim is made that uniform aggregation is optimal, and correlation results do not imply causality or predictive utility. The experiment is intended as a minimal baseline and sanity check for analyzing Mamba output representations. Acknowledgements This work benefited from iterative discussions and drafting assistance provided by ChatGPT (OpenAI), which was used as a tool for clarification, structuring, and refinement of ideas. The responsibility for the content, interpretation, and conclusions remains solely with the author. --- notes This record is intended as an exploratory and diagnostic baseline.It does not claim optimal aggregation, latent interpretability, or predictive performance.