Dynamical Parameters: An Interpretability Framework for Time-Series Foundation Models

This work studies a central gap in interpreting time-series foundation models (TSFMs): a dynamical property may be accessible in a hidden state even when the forecast fails to respond correctly as that property changes. We formalize these properties as Dynamical Parameters, including trend slope, oscillation frequency, and autoregressive dependence. We compare their representation accessibility, measured by recovery from hidden states, with their forecast response, measured by agreement with the expected forecast change. Across nine frozen TSFMs and thirteen laws, 42 of 63 model-parameter cells achieve accessibility above 0.95, whereas their median reference-aligned response relative to the conditional reference is only 0.46. To explain this gap, causal geometry compares the hidden-state change required to produce the reference response with the change induced by the parameter intervention. Directly modifying the hidden state recovers the reference response, but the parameter intervention often moves the state in a different direction. These results show that accessible parameter information need not be expressed in forecasts when input changes miss the required hidden-state direction.