ProtoRoute: Dual-Timescale Persistent Evidence Learning for Medical Time-Series Classification

Existing medical time-series classification (MedTSC) methods primarily encode class knowledge in network parameters or prototypes optimized on the same gradient timescale as the encoder. We argue that transient $\text{within-sample}$ structure and persistent $\text{cross-sample}$ class evidence have different statistical scopes and should therefore be modeled and updated separately. Based on this perspective, we propose $\text{ProtoRoute}$, a dual-timescale framework that couples a $\text{fast}$ parametric encoder with a $\text{slow}$-evolving non-parametric class-evidence dictionary. The encoder-agnostic fast pathway captures transient representations of the current sample, while the persistent pathway maintains reusable class evidence across training observations. To read from this persistent state, we introduce hierarchical Token–Class–Prototype Slot routing, where Top-$r$ prototype aggregation preserves heterogeneous within-class evidence modes and Top-$q$ token aggregation suppresses dilution from weak background evidence. To evolve the persistent state, we further introduce Loss-Adaptive Prototype Evolution, an explicit epoch-level state transition that selectively incorporates reliable and complementary evidence while adapting class-wise replacement to training dynamics. Experiments on 8 datasets demonstrate the strong superiority of ProtoRoute.