Learning Latent Memory States from Longitudinal Athlete Monitoring Data

2026-08-06

AI Summary

This study addresses the challenge of modeling and reusing recent historical information in longitudinal athlete monitoring by introducing the “latent memory table” as a novel analytical unit. The approach employs a Transformer-based memory operator to map masked temporal windows into finite-dimensional states, which are aggregated into a statistical table amenable to storage, querying, and reuse. This framework unifies and generalizes classical techniques such as moving averages and principal component analysis, while emphasizing six key quality attributes—including restorability, personalization, and temporal consistency—and incorporates uncertainty quantification, Procrustes-based row reliability ensembles, and a composite quality index Q for evaluation. In the SoccerMon case study, the latent memory table achieves a quality index of 0.73, substantially outperforming conventional methods (approximately 0.40) and demonstrating incremental predictive value for certain health indicators.

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.

Problem

• Latent Memory
• Longitudinal Data
• Statistical Representation
• Temporal Memory
• Reusable Summary

Innovation

• Latent Memory Table
• memory operator
• longitudinal data
• reusable statistical object
• composite quality index