TempoGeom: Observation Design for Learning Switching Speeds in Temporal Graphs

Predicting whether an edge is present does not determine how rapidly it forms and disappears. We study observation design for jointly learning switching clocks and unknown, finite-dimensional time-varying affinities from discretely observed temporal graphs. Affinity perturbations can vanish at observation times while changing between-observation dynamics, confounding the small clock-dependent lag under fast switching. uses a two-scale efficient-Fisher analysis to retain these hidden nuisance effects. In an explicit shared-affinity family, reordering a fixed multiset of observation gaps changes local log-clock information from $\Theta ({\lambda }^{-4})$ to $\Theta ({\lambda }^{-2})$, where $\lambda$ scales switching rates, without changing observation count or horizon. We characterize how the observation graph determines the number of clock directions at each rate. Because both rates vanish, we introduce separated affinity anchors followed by probes on the switching timescale. Under quantitative affinity-conditioning, graph-rank, and uniform regularity assumptions, this design preserves a positive information floor over bounded relative clock uncertainty; a fixed positive minimum gap precludes such a floor for arbitrarily fast clocks. For finite clocks, we combine nuisance-aware receding-horizon design with centered graph regularization. Matched-estimator comparisons in polynomial and Fourier synthetic studies yield clock-RMSE reductions of $8.3\%$ and $11.5\%$ at the slowest scale, respectively, with no consistent advantage at faster scales. Broader pipeline gains also reflect regularization, whose benefits can reverse under increased heterogeneity. Together, these results separate the roles of observation timing, nuisance conditioning, and regularization in learning switching speeds.