Exploring Tiny Recursive Models for Time- Series Regression: Battery State-of-Health Prediction

Abstract

Battery state-of-health (SoH) prediction is difficult because degradation depends on long, noisy histories of voltage, current, and temperature, while embedded battery-management systems impose tight memory budgets. This thesis adapts the Tiny Recursive Model (TRM), originally proposed for symbolic reasoning, into a compact continuous regressor for multivariate battery time series. The model is evaluated on 368 cells from six public aging datasets under an 8MB model-size constraint. Two tasks are studied: early-cycle forecasting from the first ten cycles to a full length-normalized SoH trajectory, and online point estimation from the most recent ten cycles to current SoH. The regression TRM is compared with a size-constrained LSTM, and a frequency-based Hierarchical Recursive Regression Model (HRRM) is introduced to test whether hierarchical recursive updates improve forecasting. For early-cycle forecasting, the regression TRM achieves a held-out MAE of 0.0068 and R2 = 0.9683, versus 0.0103 and R2 = 0.9276 for the LSTM, a 34% MAE reduction with significant gains across all reported metrics (p < 0.001). For online point estimation, the adaptive-computation TRM and LSTM are statistically indistinguishable, with MAE 0.0067 and 0.0066 (p > 0.60). The HRRM gives the strongest forecasting result, reaching MAE 0.0058 and R2 = 0.9768, a 14.8% MAE reduction over the regression TRM (p = 0.003). Refinement analyses show that the model visibly adjusts its prediction during the first few recursive steps before stabilizing, suggesting that TRM-style recursive refinement transfers from symbolic reasoning to regression.