Fixed-Size Event Records for Event-Time Gradient Reconstruction under Delayed Selective Labels

Historical-gradient reconstruction becomes a distinct learning problem when raw events are ephemeral, labels arrive selectively and after delay, and the target is the gradient at event time rather than at label arrival. We formulate a fixed-size event-record interface in an r-dimensional update subspace: logged logits and the corresponding event-time output Jacobian exactly reconstruct the per-example gradient in those coordinates. Doubly robust correction addresses selective label observation, while optional transport addresses coordinate drift between event and arrival; the two corrections have separate identifying assumptions. On a CIFAR-100 chronological stream with median delay 10, EVENTGRAD reaches 0.84 gradient cosine, 0.28 normalized bias, 10.9 regret, and 68.2% accuracy; doubly robust selection without transport reaches 0.75, 0.42, 13.8, and 65.1%. These results establish a precise event-record interface for delayed selective supervision and separate reconstruction, selection, and transport as distinct mechanisms.