Memory for Attention: Language-Conditioned Re-Perception with a Vision--Language--Motion Map
A robot carrying a persistent, behavior-annotated map faces two planning questions, and its memory answers only one well. The \emph{spatial-navigation} question -- how to walk around a room -- we address first and report a negative: building on Vision--Language--Motion Maps (VLMM), a behavior-aware planner cost cuts a planning-time objective by $\sim$35\% over 28 AI2-THOR scenes, but under closed-loop execution the real benefit nearly vanishes ($\sim$4\%) and an on-demand vision--language model (VLM) does as well. The \emph{resource-allocation} question differs: under a limited perception budget, what should the robot re-observe now to keep its map fresh? Framing re-perception as this attention decision, we show a persistent map's memory (change-history, or even just recency of last sighting) yields the best schedule (held-out), matching an oracle, while the memoryless VLM prior is poor. Because the schedule reallocates budget toward what matters, memory's benefit concentrates on the important objects ($\sim$1.6$\times$ the mean), and a downstream fetch task confirms fewer wasted trips; the gain grows with per-instance heterogeneity exactly as a Cauchy--Schwarz bound predicts -- it equals $\mathrm{Var}(\sqrt\lambda)$, the variance of root-volatility. With a real CLIP prior on rendered objects the advantage is $+21$--$26\%$. The map's distinctive value appears when the task is \emph{language-conditioned}: told what to track, VLMM grounds the relevant objects (open-vocabulary) and tracks their change (memory), beating even a strong relevance-weighted recency baseline ($+2.5\%$) -- so its motion channel adds value beyond a last-seen timestamp -- and an on-demand VLM ($+8.9\%$); neither language nor dynamics alone suffices. The map earns its keep not by telling the robot how to walk around a room, but by telling it what to pay attention to.