Learning Latent Memory States from Longitudinal Athlete Monitoring Data

• URL: http://arxiv.org/abs/2608.06290v1
• Date: Thu, 06 Aug 2026 17:14:54 GMT
• Title: Learning Latent Memory States from Longitudinal Athlete Monitoring Data
• Abstract summary: We propose a new unit of analysis for longitudinal data: the Latent Memory Table.<n>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.
• Score: 0.5729101515196012
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 \(Q\approx 0.73\) 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.

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