ATEMPO: Amortized Transfer Entropy Model Per-lag Over-Time

Emma Andrews, Konstantinos Kontras, Keane Ong, Maarten De Vos, Gianmarco Mengaldo

When one time series informs another, the delay at which that information arrives determines if models can utilize this relationship effectively. A source may be strongly predictive at one delay but uninformative at neighboring lags. Therefore, fixed input windows may obscure this structure by bundling informative and irrelevant history together. Transfer entropy (TE) can recover these delays by measuring how much a source's past tells us about a target beyond the target's own history. However, existing TE estimators require separate fits across source and conditioning depths, with further estimation on local windows to track delays over time. We introduce ATEMPO, a diffusion-based transfer entropy estimator amortized over lags and time. ATEMPO samples source and conditioning depths during training and conditions explicitly on temporal position, allowing a single score network to estimate the full TE surface without refitting. Differencing this surface recovers when information arrives. Across synthetic datasets with ground-truth TE, ATEMPO achieves the lowest mean relative error among baselines, and on datasets with known lags, ATEMPO achieves $0.98\pm0.04$ lag-detection…