Routing by Hurst: Matching Decomposed Modes to Inductive Biases for Time-Series Learning

Abstract—Real-world time series superimpose persistent trends and transient flfluctuations whose statistical characters differ markedly. Systems neuroscience documents that the primate cortex handles such multi-scale input through a hierarchy of intrinsic temporal windows — early sensory areas integrate fast transients over short windows, while higher association areas integrate slow context over long ones. Most deep timeseries models, in contrast, force every component through a single homogeneous pathway, and decomposition-based methods split the signal but then share one post-decomposition network, leaving the architecture–component mismatch unresolved. We propose HRMN (Hurst-Routed Mode Network), a computational analogue of the cortical two-pathway organisation: Ensemble Empirical Mode Decomposition (EEMD) extracts intrinsic mode functions (IMFs), each is summarized by its Hurst exponent, and the components are dispatched to the architecture best matched to their statistical character — transient modes (H ≤ 0.6) to a Temporal Convolutional Network (TCN) branch with localised receptive fifields, persistent modes (H > 0.6) to a Transformer branch modelling long-range dependence — with branch outputs fused by an attention-weighted aggregation shared across classifification, regression, and anomaly detection. We confifirm empirically that real-world signals exhibit a bimodal persistence structure on either side of the chosen threshold, supporting the discrete two-pathway design over a continuous routing spectrum. On 12 benchmark datasets spanning the three tasks, HRMN consistently outperforms TimesNet (2023): 2.5–5.6 percentagepoint accuracy gains on classifification, 8.0–10.2% relative MSE reductions on regression, and 1.8–2.3 percentage-point AUC gains on anomaly detection, while using 0.95M parameters against 2.18M for TimesNet. A routing-criterion ablation, a 2×2 directional verifification, and bootstrap-stability analyses isolate the contribution of persistence-based matching from model capacity and routing-rule confounders.