GridProbe: Posterior-Probing for Adaptive Test-Time Compute in Long-Video VLMs

Long-video understanding in VLMs is bottlenecked by a single monolithic forward pass over thousands of frames at quadratic attention cost. A common mitigation is to first $select$ a small subset of informative frames before the forward pass; common for training-free selectors via auxiliary encoder-space similarities. Such signals are capped by contrastive pretraining, which usually fails on reasoning-heavy queries (negation, cross-frame counting, holistic summarization). We propose $\textbf{GridProbe}$, an efficient training-free posterior-probing inference paradigm that scores evidence in $\textbf{answer space}$ using a frozen VLM's own reasoning and then selects question-relevant frames $\textbf{adaptively}$, resulting in sub-quadratic attention cost with little to no accuracy loss. We arrange frames on a $K{\times}K$ grid and run lightweight row $R$ and column $C$ probes, where each probe reads its peak posterior as a query-conditioned confidence. The outer product of $R$ and $C$ yields an interpretable $\textbf{importance map}$ whose skewness and kurtosis drive $\textbf{Shape-Adaptive Selection}$, a closed-form rule that reliably replaces the fixed frame budget $M$ with a per-question $M_{\mathrm{eff}}$. We show empirically that $M_{\mathrm{eff}}$, surprisingly, tracks intrinsic question difficulty without ever seeing the answer, a sign of test-time adaptive compute. On Video-MME-v2, $\textbf{GridProbe}$ matches the monolithic baseline within $1.6$ pp Avg Acc at $3.36\times$ TFLOPs reduction, while on LongVideoBench it Pareto-dominates the baseline ($+0.9$ pp at $0.35\times$ compute). Because the selector and QA models can be decoupled, pairing a small 2B selector with a stronger 4B or 8B QA is strictly Pareto-dominant over the 2B monolithic baseline (up to $+4.0$ pp at $0.52\times$ compute, on average), with no retraining. Finally, the interpretability of the importance maps opens future avenues for behavioral diagnostics, grounding, and frame-selection distillation.