Belief-Space Perception Routing under Coupled Sensor Faults and Compute Contention

A robot that has to see and react on a fixed clock runs into two problems at once. Its cameras degrade in rain, mud, fog, and darkness. And the single onboard processor it runs on is shared with planning and control, so the compute left over for perception moves around from second to second. Most systems model the two separately. We present a perception router that tracks probabilistic estimates of sensor-fault state and compute- contention state, couples them with a noisy-OR term, and uses the coupled estimate to pick one of four detector configurations (YOLO11x/n at 1280 or 640 px) so that the frame finishes before its deadline. Where the two stressors co-occur, the coupled policy cuts the deadline-miss rate by 1.1 to 9.4 percentage points against a policy that treats them independently. The interval excludes zero in five of six conditions, the pooled effect over 10 sequences and 6 conditions has sign-test p = 0.001, and every uncoupled control and the fault-free trajectory sit at exactly 0.0 pp. Routing costs tens of microseconds per frame. We then asked whether the coupling the method exploits arises on its own. Across eight real RADIATE adverse-weather sequences and three workload proxies independent of the fault signal, after Benjamini-Hochberg correction and a replication run, none of 24 tests found it. We report that null and scope the routing result as a proof of mechanism. Whether such coupling occurs in the field is still open, and the released evaluation pipeline lets a deployment settle it on its own traces.

When Do Learned Diffusion Proposals Help Constraint Solving? A Controlled Study on Continuous Algebraic Systems

Solving a continuous algebraic constraint system requires two decisions: which values satisfy the constraints, and which structural augmentation renders an unsolvable system solvable. Classical solvers answer the first well and the second only by enumeration. On that discrete decision, a candidate-conditioned repair ranker choosing among K augmentations reaches the exhaustive-search ceiling at a fraction of the calls, outperforming random (0.997 vs 0.236 balanced nonlinear menu accuracy; p < 10^-70; 0.982 +/- 0.006 across seeds) and beating a budget-matched per-candidate probe on accuracy and cost. MARC turns such a system into a factor graph, over which a graph-neural diffusion denoiser proposes assignments, descent on an exact computer-algebra energy polishes them, and an exact symbolic checker certifies solutions. Evaluations of diffusion-based proposals rarely include one control: random multi-start under the same refinement budget. Applied to our system, it sharply curtails what the learned proposal contributes on the value decision. Does it beat random multi-start at choosing satisfying assignments? Only narrowly, in a predictable regime. Across trapped low-dimensional families it ties with random restart, but dominates in high dimension, where random search fails. Once variables couple, the advantage is gone. Since all methods share one polish and one checker, best-of-K random multi-start succeeds with probability exactly 1 - (1 - q(n))^K, where q(n) is single-start reachability; one measured constant, with no free parameters, reproduces the entire curve (mean absolute error 0.012). The favorable regime is not specific to our synthetic families: across eight real-world systems in robotics, positioning, optimization, and algebra, classical multi-start solved all eight, none in the learning-favorable regime. We map the regimes in which learned proposals improve solvers.