Cuckoo filters are a widely adopted approximate membership query (AMQ) data structure that supports insertions, lookups, and deletions with low memory overhead. At high load factors, however, insertion performance degrades sharply due to the random-walk eviction process, which may require a large number of element relocations. Recent work on bucketized cuckoo hash tables has shown that \emph{fresh-priority eviction}, which preferentially evicts elements whose alternate bucket location has not yet been used, achieves $O(\ell m)$ total expected evictions for bucket size~$\ell$, an improvement over the standard random walk. In this paper, we show that this technique transfers to \emph{cuckoo filters} despite their use of XOR-based partial-key hashing. The key insight is that a fresh element's fingerprint, although stored in the table, is not examined by the eviction policy, so when the fingerprint length satisfies $k = Ω(\log m)$, the alternate bucket hash remains a near-uniform random variable, a property we call \emph{latent randomness}. We prove that under this condition the corruption graph remains subcritical and the total number of evictions is $O(\ell m \log m)$; we conjecture the tighter $O(\ell m)$ bound holds via the full amortized analysis of Bell and Kuszmaul. We further propose encoding the fresh/kicked state implicitly by the element's position within its bucket, requiring no additional per-element metadata. Experimental results on a filter with $2^{22}$ slots and $8$-bit fingerprints demonstrate $1.2\times$ to $2.4\times$ fewer evictions at load factors between $94\%$ and $99\%$ for bucket size $\ell = 8$, and a $1.73\times$ reduction in cumulative evictions to full capacity.
World action models (WAMs) predict the visual consequences of the actions they generate, which makes test-time selection a natural way to improve a fixed policy: imagine the futures of candidate actions and execute the best one. The benefit of selection is bounded by the selectable headroom, how much better the best candidate truly is, but the standard estimate, which executes each candidate once and keeps the best outcome, conflates candidate quality with the randomness of everything that follows. We introduce a denoised counterfactual protocol, based on bitwise-reproducible branching, repeated continuations, held-out oracles, and common random numbers, that measures the headroom a selector can realize, and use its measurements to build a fail-gated selector. Across four WAMs, two benchmarks, over 100,000 branched rollouts, and pre-registered tests, we find that (i) the standard estimate overstates the selectable headroom of native samples: bounds from 17 continuations per candidate place its selectable share between 24% and 66% for three WAMs; (ii) structured action perturbations create up to 16 points of selectable headroom; and (iii) in both WAMs with action-conditioned imagination, imagined futures carry candidate-outcome information with no detectable loss relative to real futures, information that the value head of Cosmos Policy leaves unused. Deviating from the policy chunk only when a readout of the WAM predicts failure, the selector raises closed-loop task success from 76.9% to 81.6% on held-out episodes of training tasks, with the largest gain where the policy fails most often, and from 62.6% to 69.8% on unseen tasks.
Long-horizon embodied navigation may be interrupted by a higher-priority instruction before the current task sequence is complete. The agent must finish its current atomic task, execute the inserted task, and resume the remaining sequence from the updated environment state, where its viewpoint and available navigation candidates may have changed. To evaluate this capability, we introduce PIFR benchmark, a novel task for runtime task preemption and resumption in embodied navigation. PIFR includes single, repeated, and nested interruption settings,with stage-specific metrics for inserted-task completion, resumption of the original task, and completion of the full sequence. Evaluations show that recovery performance varies across interruption conditions, while aggregate success can obscure differences in interruption handling and resumption. We further propose a lightweight candidate-ranking baseline to improve target re-grounding after interruption. Together, PIFR and the baseline provide a systematic framework for studying interruption handling and task recovery in long-horizon embodied navigation.