Curves, Not Points: Structured Curve Approximation for Engagement Dynamics in Short-Form Video and Interactive Live Streaming

Audience engagement with video is inherently a trajectory, yet it is commonly reduced to scalar quantities such as watch time or completion rate. We instead model engagement as a structured function of time using low-dimensional parametric curve approximators. We first study live-stream engagement in KuaiLive-M3, where viewers may enter and leave throughout a room. We model occupancy as \(O=J-X\), using structured approximators for cumulative joins and exits, with a causal GRU predicting compact exit-curve parameters from evolving room representations. The resulting model achieves \(55.9%\) \(I_5\), where \(I_5\) is the fraction of rooms whose whole-trajectory occupancy IAE is at most \(5%\), compared with \(49.0%\) for the strongest independent pointwise neural baseline. We then study cross-audience retention transfer on KuaiRec-small and KuaiRec-big, which contain the same videos viewed by disjoint populations. We factor the retention representation into a video-specific parameter and behavioral watch-style parameters shared across videos. The resulting model achieves \(75.3%\) \(C_5\), where \(C_5\) is the fraction of test videos whose retention curve has sup-norm error at most \(5%\), compared with \(68.3%\) for the strongest neural baseline. Together, these results show that structured engagement curves provide compact functional representations that support accurate prediction, composition, and cross-audience transfer across distinct video-engagement regimes.