AI 中文总结
该研究提出潜在记忆表作为纵向数据分析单元，通过记忆算子生成，经含复合质量指数Q的六属性验证，在SoccerMon案例中表现优于经典基线，可复用且能区分真实记忆与对照。
AI 中文摘要
我们为纵向数据提出了一种新的分析单元：潜在记忆表（Latent Memory Table）。科学贡献并非编码器，而是该表——其作为可复用的统计对象，与主成分得分矩阵、估计随机效应表或预测概率表处于同等地位。我们估计了一张统计表，用于汇总近期纵向历史，旨在整个统计工作流程中被存储、查询、分析和复用。记忆算子将每个带掩码的窗口历史映射为有限维状态；收集这些带不确定性的状态，便得到潜在记忆表。验证围绕六个属性展开：可恢复性、个性化、时间一致性、可解释性、稳定性和可复用性，由复合质量指数\textit{Q}汇总；Transformer、SoccerMon案例研究和模拟实验旨在论证该表值得获得这一地位。经典指数加权移动平均及相关短、长程标量汇总，是同一算子类别的受限、通常为单变量的特例。一项具有已知记忆机制的模拟研究表明，\textit{Q}和旋转不变恢复评分可区分真实多变量或个性化记忆与阴性对照及误设窗口，而仅政权分类准确率无法做到。SoccerMon作为实证案例研究：构建的潜在记忆表取得\textit{Q}\textasciitilde0.73，而经典方法和滞后主成分基线约为0.40，对部分健康目标具有增量保留价值，且存在用于行级可靠性的Procrustes集成。
英文摘要
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.
