Learning Latent Memory States from Longitudinal Athlete Monitoring Data

We propose a new unit of analysis for longitudinal data: the Latent Memory Table. The scientific contribution is not the encoder. It is that table, treated as a reusable statistical object on the same footing as a matrix of principal-component scores, a table of estimated random effects, or a table of predicted probabilities. We estimate a statistical table that summarizes recent longitudinal history and is intended to be stored, queried, analysed and reused throughout the statistical workflow. A memory operator maps each masked windowed history to a finite-dimensional state; collecting those states with uncertainty yields the Latent Memory Table. Validation is organized around six properties---recoverability, personalization, temporal coherence, interpretability, stability and reusability---summarized by a composite quality index (Q); the Transformer, the SoccerMon case study and the simulations exist to argue that this table deserves that status. Classical exponentially weighted moving averages and related short- and long-horizon scalar summaries arise as restricted, typically univariate special cases of the same operator class. A simulation study with known memory mechanisms shows that (Q) and rotation-invariant recovery scores discriminate genuine multivariate or personalized memory from negative controls and from misspecified windows, whereas regime classification accuracy alone does not. SoccerMon serves as an empirical case study: a constructed Latent Memory Table attains (Q≈ 0.73) versus about (0.40) for classical and lagged principal-component baselines, with incremental held-out value for some wellness targets and Procrustes ensembles for row-wise reliability.