Interaction Coordinate Distillation for Multimodal Sentiment Analysis

Multimodal sentiment analysis relies not only on modality-specific evidence but also on how linguistic, acoustic, and visual cues interact. Knowledge distillation can transfer the capabilities of a high-capacity multimodal teacher to a compact student, yet existing approaches primarily define supervision over final predictions, latent representations, or relational structures, leaving predictive interactions across modality combinations largely implicit. We propose Interaction Coordinate Distillation (ICD), which treats teacher and student predictions over the seven non-empty modality subsets as set functions and applies an anchored Möbius decomposition to obtain aligned first-, second-, and third-order interaction coordinates. The invertible transform reorganizes the same teacher subset responses into interaction coordinates, where coordinate-wise matching couples errors across related modality subsets through Möbius contrasts. This allows ICD to change the structure of the distillation constraint without changing the underlying teacher information. ICD jointly optimizes interaction-coordinate matching, task supervision, and full-modality distillation. Experiments on CMU-MOSEI and CMU-MOSI, together with controlled comparisons over raw subset supervision, interaction orders, and random orthogonal reparameterization, show that ICD effectively reconstructs teacher-defined interaction coordinates while achieving strong downstream performance. The additional subset computation required by ICD is absent at inference, introducing no inference-time overhead.