CLASP: Cluster-Conditioned Latent Alignment with Shared Prototypes for Entity-Level Time-Series Forecasting

Forecasting across heterogeneous entities requires sharing statistical strength while preserving entity-specific variation. We introduce CLASP, Cluster-conditioned Latent Alignment with Shared Prototypes, a probabilistic latent partial-pooling mechanism. From an entity's observed history, CLASP constructs context-dependent latent distributions and aligns them with shared Gaussian prototype priors capturing population structure. Prototype-assignment weights, obtained from provided labels or learned from history and metadata, combine independent component draws, inducing an aggregate Gaussian posterior during training and a prototype-induced aggregate Gaussian prior at deployment. This partially pooled latent augments the observed history and conditions diverse forecasting backbones, with an optional validation-fitted readout. We characterize the latent train–deployment discrepancy by deriving its exact Gaussian KL divergence, proving a data-processing upper bound by component KL divergences, and showing that under one-hot assignments it equals the uncapped CLASP pooling penalty. Under additional bounded-loss, sampling, and sample-independence assumptions, we obtain PAC-Bayes guarantees for posterior-sampled risk under a fixed prediction map and a single entity-level latent law. We evaluate CLASP on held-out WEATHER-5K stations and eICU patients across forecasting horizons and provided and inferred population structure. Controlled ablations show substantial gains from prototype alignment and prior learning beyond the optional readout, with additional improvements from probabilistic and multi-prototype representations. Within-backbone comparisons show consistent gains from the complete CLASP pipeline across the evaluated probabilistic and deterministic forecasters.