SurF: Learning A Time-Rescaling Map for Event-Stream Forecasting Across Datasets

Irregularly sampled multivariate event streams are hard to model with forecasters built for regularly sampled series: inter-event intervals span orders of magnitude, and time units differ from one corpus to the next. We propose Survival Flows or SurF, an event forecasting model built on the fact that the Time Rescaling Theorem (TRT) maps every point process to the same i.i.d. unit-rate exponential target. SurF learns the cumulative intensity that realizes this map; its output is unit-free comprising a single set of weights, with no per-dataset parameters, can be learned across heterogeneous event-stream datasets. We build a Transformer encoder to represent three monotone parameterizations of the cumulative intensity function that require no Monte Carlo integration to evaluate the likelihood (two closed-form, one a deterministic per-interval quadrature rule) enabling fast and accurate gradient estimation to learn the map. On six real-world benchmarks, SurF attains the best next-event time RMSE on $5/6$ and closely tails the best on Taxi. Under a leave-one-out protocol, in which the target corpus is excluded from training and model selection, SurF-GLQ attains lower time RMSE than these baselines trained the same way on $5/6$ datasets and lower held-out NLL than DTPP on all six; on Amazon, Earthquake and Taobao it even matches or beats the baselines trained on the target corpus.