Temporal Functional Circuits: Explaining KAN Forecasts
A novel framework named Temporal Functional Circuits converts the edge functions of the Kolmogorov-Arnold Network (KAN) into reliable, time-based explanations for forecasting time series. This system utilizes a gated residual KAN that separates predictions into a linear foundation and a sparsely activated KAN adjustment. It associates each edge with input lags through output-aware attribution, ranks edges based on their learned activation range, and confirms faithfulness through edge-level interventions like zeroing and spline removal. The elimination of the learned B-spline while keeping the base SiLU term diminishes forecast accuracy, highlighting the predictive significance of the spline shape. The methodology is evaluated across four synthetic regimes of escalating complexity. The research is accessible on arXiv (2605.05685v1).
Key facts
- Temporal Functional Circuits is a framework for explaining KAN forecasts.
- KANs expose explicit learnable edge functions on every connection.
- The framework transforms KAN edge functions into temporally grounded explanations.
- It uses a gated residual KAN that decomposes forecasts into linear base and KAN correction.
- Edges are mapped to input lags via output-aware attribution.
- Edges are ranked by learned activation range.
- Faithfulness is validated through edge-level interventions like zeroing and spline removal.
- Removing the B-spline component degrades forecasts, showing spline shape carries predictive value.
Entities
Institutions
- arXiv