Foundation vs. Specialized Models: Evaluating Catastrophic Forgetting in Continual Time Series Forecasting

Time Series Foundation Models (TSFMs) have demonstrated notable success in general-purpose forecasting tasks; however, their adaptation to specialized classification problems remains constrained by the computational bottleneck of standard attention and the systematic omission of classical statistical knowledge. This technical report introduces KairosHope, a next-generation TSFM designed to reconcile massive generalization with analytical precision in classification tasks. The core of the proposal is the HOPE block, an architecture that replaces quadratic attention with a dual-memory system: Titans modules for dynamic short-term retention and a Continuum Memory System (CMS) for the abstraction of long-term historical context. To enrich the inductive bias, a Hybrid Decision Head is introduced, which fuses deep latent representations with deterministic statistical features extracted via tsfeatures package. KairosHope undergoes self-supervised pre-training on the massive Monash archive, combining Masked Time Series Modeling (MTSM) and contrastive learning (InfoNCE). Its subsequent adaptation to the UCR benchmark datasets is conducted through a rigorous Linear Probing and Full Fine-Tuning (LP-FT) protocol to prevent catastrophic forgetting. Empirical results demonstrate superior performance in domains characterized by strict temporal causality such as HAR or Sensor data. Consequently, KairosHope establishes a robust and efficient framework for the adaptation of foundation models to time series analysis.

Time Series Foundation Models (TSFMs) have borrowed the long context paradigm from natural language processing under the premise that feeding more history into the model improves forecast quality. But in stochastic domains, distant history is often just high-frequency noise, not signal. Hence, the proposed work tests whether this premise actually holds by running continuous context architectures (PatchTST included) through the ETTh1 benchmark. The obtained results contradict the premise: an inverse scaling law shows up clearly, with forecasting error rising as context gets longer. A 3,000-step window causes performance to drop by over 68%, evidence that attention mechanisms are poor at ignoring irrelevant historical volatility. Retrieval-Augmented Forecasting (RAFT) is evaluated as an alternative. RAFT achieves a mean squared error (MSE) of 0.379 with a fixed 720-step window and selective retrieval, outperforming both long-context configurations and zero-shot foundation models (Chronos, Moirai) despite requiring far less computation. In addition, the retrieval step injects only the most relevant historical segments as dynamic exogenous variables, which gives the model a context-informed inductive bias it cannot build on its own from raw sequences. Therefore, foundation models going forward need to shift architecturally toward selective retrieval.

Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.