DXSP: gesture-only temporal localization of decisive moments in dyadic persuasion.

Persuasive systems must detect user engagement in real time in order to adapt their strategy. Existing methods rely primarily on facial expressions or voice signals. Both raise privacy concerns and degrade under low video quality, motion blur, and ambient noise. Body gestures offer a privacy-preserving alternative, since skeleton representations do not encode identifiable facial features. What is missing is a method that localizes the specific moments at which gesture matters, rather than averaging behavior across the whole interaction. We introduce Dyadic Cross-Sparse Pooling (DXSP), a gesture-only neural architecture that localizes sparse decisive moments in dyadic persuasion without using face, voice, or verbal content. DXSP models both participants through cross-attention, weights candidate moments by interpersonal synchrony through a concordance gate, and selects exactly k = 3 windows per dyad through a hard top-k mechanism. We evaluate DXSP on 46 Japanese dyadic persuasion dialogues using upper-body pose data from the Sapiens Goliath foundation model. First, decisive moments are distributed across the full interaction rather than concentrated in any single phase. A three-component mixture fits the selected positions, but random selection of the same number of windows reproduces this evidence at every value of k from 1 to 10. Second, the relative concentration of decisive moments across phases differs between successful and failed outcomes. Successful dyads place 49.1% of their peaks in the opening phase. Failed dyads place 42.0% in the middle phase. Three tests converge on this contrast, including a permutation test that accounts for within-dyad clustering. Only the opening-phase comparison survives correction, and the association is not stable across values of k. Third, joint-level differences did not reach significance after correction across the seven joints, and the joint ranking is exploratory. The study contributes a mechanism that returns explicit decisive positions, evidence that mixture-based clustering claims require calibration against a matched null, and a preliminary phase-level link between decisive-moment placement and outcome. Gesture-only sensing therefore relates to persuasion at the level of phase distribution rather than detecting three-phase structure. This offers preliminary guidance for phase-aware intervention timing.