Beyond the Readout: Reservoir State Statistics for Model-Space Learning under Sparse Observations

Multivariate time series often arrive with non-uniform timestamps and asynchronous per-channel observations, violating regular-grid assumptions of standard sequence models, while scarce labels and limited training resources make learning tasks more challenging. Model-space learning offers a lightweight alternative by fitting a dynamical model to each sequence and performing downstream analysis in the resulting model space. However, under irregular sampling, channels with very few observations weakly constrain the per-channel regression, leaving the fitted readout an unreliable summary. In this paper, we propose Reservoir State Statistics (RSS), a readout-complementary representation that augments the readout with three inversion-free trajectory summaries: centroid, spread, and terminal state. RSS is computed on the trajectory of the Global Decay Reservoir Network (GDRN), a continuous-time reservoir with per-channel time decay, cross-channel global pooling, and event-driven masked updates for asynchronous multivariate observations. Across multiple datasets, GDRN-RSS achieves competitive few-shot accuracy with CPU runtimes of seconds.