Multimodal large language models (MLLMs) have enabled long-form video understanding at a scale that was not previously possible. However, the density of relevant content decreases sharply as video sequence length increases, and exposing the model to more irrelevant content measurably reduces its accuracy. In this paper, we address the problem of maximizing query-relevant information in a frame subset selected at inference time, without training. FORGE (Frame Orthogonality in Relevance Geometry) is a model-agnostic method that induces a query-conditioned geometry on a pretrained multimodal embedding space, unifying relevance and diversity into a single objective. In this space, frames that cover independent query-relevant directions are far apart, and selecting the subset of maximum information captures diverse query-relevant content within the budget. Experiments on Video-MME and LongVideoBench at budgets of 16, 32, and 64 frames show that FORGE improves the unified keyframe selection score by 11.0-15.3 points over the strongest training-free baseline and up to doubles keyframe recall (0.415 vs. 0.204 at K=64 on Video-MME). The gains extend to question answering, where accuracy improves in every evaluated setting across eight open-source MLLMs spanning 4B to 32B parameters, by up to 8.7 points over uniform sampling and 5.2 points over the strongest baseline. Our findings suggest that aligning the embedding space with the query's high-dimensional structure is a promising direction for inference-time video understanding.
BoN improves model outputs by sampling several candidates and selecting one with a proxy score, but it assumes that complete candidates can be evaluated reliably. Many vision-language tasks instead provide only partial verification: a finding, span, value, region, or relation may be checkable even when no dependable whole-response verifier exists. Moreover, the same claim may recur across candidates with opposing stances, allowing one observation to support part of the pool and contradict another. We introduce Best-of-Evidence (BoE), an inference-time selection framework that keeps the BoN candidate pool fixed, represents reusable claims with a signed candidate--factor graph, and allocates a limited budget to evidence actions that can change the final choice. BoE formalizes selection under partial verification and provides a practical score-based controller, with the zero-budget case recovering the underlying BoN decision. Theoretically, we show that residual evidence capacity limits any evidence-driven improvement and that shared factor queries can achieve an O(log K) versus Θ(K) query separation in a factor-code model. Common-ledger experiments on four medical VQA settings show that BoE can improve fixed-pool selection and rescue some BoN failures when evidence is reliable, contrastive, and decision-relevant, while also revealing the channel-quality and candidate-generation limits that prevent universal gains.