Adaptation as Memory: Learning to Correct Time Series Foundation Models

Time series foundation models (TSFMs) generalize across domains, but adapting them to target-domain dynamics remains challenging. Existing adaptation methods use diverse mechanisms, yet lack a unified framework for understanding how target-domain knowledge is retained, accessed, updated, and applied. We address this gap by viewing TSFM adaptation as a memory process of construction, writing, reading, and execution. We instantiate this view with TS-CorM, a structured fast–slow corrective memory for frozen TSFMs. TS-CorM represents forecast corrections with compact coefficients, addresses them using joint history–forecast states, and retains their associations in explicit memory matrices. Slow Memory consolidates offline knowledge, while Fast Memory incorporates delayed feedback through recursive online updates without backpropagation. Across eight datasets and five TSFM backbones, TS-CorM improves forecasting in all 40 backbone–dataset pairs, with MSE reductions of up to 22.28%; compared with the best adaptation baseline, it reduces average MSE by 3.78% with 98.32% fewer parameters and 10.23% lower inference latency.