CircuitTS: Discovering Functional Temporal Circuits in Time-Series Foundation Models

Time Series Foundation Models (TSFMs) achieve strong zero-shot forecasting, yet their internal temporal mechanisms remain poorly understood. Existing TSF interpretability mainly reveals what temporal information is encoded, while conventional circuit analysis identifies where a behavior is supported; neither jointly characterizes a temporal function by its causal support and internal state. We introduce **CircuitTS**, which defines a functional temporal circuit as a computational support together with its function-specific causal state. CircuitTS comprises two components. **Counterfactual Circuit Discovery** constructs controlled counterfactuals for Period**, Trend, and Copy, localizes candidate supports through intervention responsiveness, function selectivity, and behavioral alignment, and verifies them through sufficiency, necessity, and specificity. **Circuit Utilization** evaluates cross-dataset generalization and aligns causal states for cross-model transplantation. Experiments on three heterogeneous TSFMs and nine real-world benchmarks show that temporal functions can exhibit different anatomical realizations while retaining causal roles, generalize to unseen datasets, and transfer across independently pretrained models. CircuitTS thus moves TSFM interpretability from representation analysis toward function-centered causal mechanisms.