A Principled Optimal Transport Framework for Frame Selection in Long Video Understanding

Long-video understanding with multimodal LLMs is fundamentally constrained by the mismatch between video length and the model's limited visual context budget, making frame selection essential for practical reasoning. Existing query-aware methods typically rely on heuristic pipelines: they assign one-dimensional query-conditioned scores to frames and then apply sampling, ranking, or extraction rules to form the final subset. While effective in practice, such methods are generally not derived from an explicit optimization objective and struggle to capture the heterogeneous evidence required for complex reasoning. In this paper, we revisit long-video frame selection from a principled optimization perspective. We formulate it as a structured evidence-allocation problem and propose OTFS, an optimal transport framework that maps multiple evidence sources onto video frames. To reflect the asymmetry of this problem---important evidence should be preserved, whereas redundant frames need not absorb mass---we instantiate this view with a semi-unbalanced entropic optimal transport objective and an efficient solver, OTFS-Sinkhorn. Combined with an exact dynamic program for coverage-aware subset extraction, OTFS yields a practical two-stage training-free pipeline. We further show that, in the single-source case, our formulation induces a Gibbs-type distribution over frames, making Q-Frame's temperature-scaled distribution a special case of our framework while also providing a broader perspective for understanding related prior methods. Experiments on three long-video understanding benchmarks show that OTFS consistently outperforms strong training-free baselines. Code will be released.