Pengxiang Cai, Wanchen Lian, Chenyang Liu +4cs.AI cs.LG
Interval prediction aims to achieve a target coverage level while producing intervals that are as short as possible. Many conformal regression pipelines first predict an uncertainty surrogate and then convert it into an interval through calibration or selection. This separation supports coverage calibration, but post hoc rules largely determine the final interval and do not fully use the learned output distribution. We observe that the resulting intervals have inherently hierarchical geometry: an interval can be recursively refined into nested subintervals, and binary trees naturally represent this structure. We formulate this hierarchy as next-interval prediction and propose PATH, which learns how probability mass flows from each interval to its next nested subintervals. PATH predicts a base leaf distribution and uses an autoregressive decoder to refine branch probabilities. Matching the distribution to the interval hierarchy aligns learning with extraction: PATH accumulates probability over adjacent output intervals and returns the shortest contiguous range reaching a selected mass. We compare PATH with 24 baselines for interval prediction on PATHBench, comprising 56 OpenML regression datasets. PATH substantially shortens the resulting intervals, achieving the lowest mean normalized length, 0.1473, while maintaining mean coverage of 0.9144. These results establish hierarchical output modeling as an effective approach for compact interval prediction on tabular data. Code is publicly available at https://github.com/pxcai/PATH.
Video temporal grounding (VTG) aims to localize the continuous video interval described by a natural-language query. However, current VLM-based methods typically produce this interval indirectly through two endpoint outputs, represented either as discrete timestamp tokens or continuous boundary coordinates. These formulations differ in how endpoints are encoded, but not in what is predicted: the event interval remains a derived object, while interval validity, duration, and interval-level similarity are handled only implicitly. We propose TimePLE, which reformulates VTG from endpoint prediction to interval-native grounding by predicting a single joint distribution over valid temporal intervals. TimePLE maps each interval to a point in a canonical position-duration square, where every support point corresponds to a valid span and neighboring points represent geometrically similar intervals. Given a video and query, the VLM generates a single latent <|TIMESPAN|> token whose hidden state is decoded into a joint interval distribution, refined through duration-aware coordinate correction, and converted into continuous boundaries. The same interval representation is used to encode input temporal anchors, aligning video-side temporal evidence with output-side span prediction. To reliably align the latent span representation with complete event intervals, we curate 90K-scale grounded samples and human-verify 3K-scale benchmark annotations. Experiments across four VTG benchmarks show that TimePLE consistently outperforms endpoint prediction baselines, achieving an average mIoU of 58.9, with clear gains on short-duration and medium-duration events.