#01Nov 7, 2026
math.OC
GEAR: A GPU-Accelerated Global Solver for Bounded Continuous Nonlinear Programs via Linear Bound Propagation
Duo Zhou, Hesun Chen, Xiangru Zhong and 2 more
We present a novel GPU-accelerated global solver for constrained nonlinear programming (NLP) inspired by the efficient linear bound propagation framework in neural network (NN) verification. Existing work on NN verification, a problem that can be cast as feasibility detection for a nonlinear objective, demonstrated orders-of-magnitude speedups with the linear bound propagation-based framework when compared to traditional solvers. Extending this paradigm to global nonlinear programming requires addressing many challenges: a global constrained NLP solver must effectively exploit all, possibly unstructured, nonlinear constraints to improve the objective, whereas NN verification typically handles simple input box constraints over a well-structured NN and does not directly optimize an objective function. We address these challenges by fully exploiting the linear bounds produced by bound propagation: these linear bounds can be viewed as relaxations of nonlinear constraints and used to provide lower bounds, check infeasibility, and guide the search for a primal solution. In addition, we propose tighter linear relaxations for bilinear, quotient, and other commonly used nonlinear functions in NLP problems, and a projected augmented Lagrangian method tightly coupled to our dual solving procedure to produce primal solutions. Our method solves 421 of 505 bounded and continuous NLP problems in the GAMS and MINLPLib benchmarks under a 180-second limit, more than each of the six global solvers we compare with, including Gurobi and BARON (commercial), and SCIP (open-source). Sixteen of these problems are certified by none of the six global solvers; all of them contain exponential, logarithmic, or trigonometric terms, which are often challenging for traditional approaches. Project webpage is at https://verified-intelligence.github.io/GEAR.
#02Nov 7, 2026
stat.ML
Group-Conditional Conformal Risk Control: Exact Guarantees, Limits, and Overlapping Extensions
Tareq Aldirawi, Wenge Guo
We study group-conditional conformal risk control (CRC) for disjoint and overlapping groups under bounded monotone losses. For disjoint groups, we establish exact finite-sample conditional risk control, two-sided bounds on the group-restricted risk, and fundamental limitations arising from local support and calibration-rank granularity. For overlapping groups, we study two exactly valid approaches: group-restricted calibration followed by union deployment, and direct calibration of the deployed prediction-set family. We characterize the union's limiting reconciliation gap, identify conditions for its disappearance, and establish sharp lower bounds for structured losses in specified product-form models. We also demonstrate a strict size advantage for direct calibration in an ordinal model. Experiments show that direct calibration can reduce prediction-set size, but its efficiency depends on group structure, loss type, and shape fitting. Results on historical diabetic-retinopathy scores further illustrate these tradeoffs. Overall, local support, reconciliation slack, and threshold heterogeneity determine efficiency, with neither approach uniformly dominating.
#03Nov 7, 2026
cs.AI
Decentralised Drone Swarm Formation under Silent Failures with ACO Pheromone Claims and PSO Tuning
Md. Abu Horaira
We study decentralised drone formation, without a central planner, under the conditions that make it hard: nobody knows how many drones are alive, failures are silent, radio is short-ranged and lossy, and actuation is noisy. In our controller, ant colony optimisation (ACO) allocates drones to picture positions through claims that behave as reinforced, evaporating pheromone and are gossiped between neighbours, so evaporation doubles as failure detection. A particle swarm optimisation (PSO) law flies the drones, a noise-buffered Voronoi filter keeps them apart, and PSO also tunes the controller offline. We prove that claims of destroyed drones vanish within bounded time, that conflicts between drones that exchange tables are resolved consistently, that survivors cover the picture to within a factor of two, and that drones cannot collide while their safety cells are feasible. On held-out seeds and with two tuned configurations, the controller formed the picture in 95-99% of runs in the hardest regime, restored it after a silent loss of half the swarm in 96-100% of runs at normal difficulty, transferred unchanged to eight unseen shapes and to 300 drones, and overlapped in 5 of 21,088 runs. A CBBA-style baseline that shares the evaporating claims but uses argmax without swaps was at least as reliable as ours once tuned with the same budget, and repaired faster, whereas ours generalised better to unseen shapes. The benefit thus comes from the pheromone dynamics and from tuning, not from ACO's stochastic construction or PSO's social terms. A centralised oracle is faster.
#04Nov 7, 2026
cs.LG
HexIt: Learning Hexahedral Block Decomposition with Expert Iteration on Combinatorial Maps
Arjun Narayanan, Per-Olof Persson
Decomposing a polyhedral solid into a few well-shaped hexahedral blocks is a long-standing open problem in mesh generation. We cast it as a sequential decision problem on a 3-dimensional generalised map: an agent splits edges, faces and volumes with three insert operations until every cell is a hexahedron and the mesh passes a quality threshold, and a policy that convolves over the map's involutions chooses each insert. A successful decomposition takes over a hundred decisions, and a uniformly random policy never finds one. We clone a policy from constructed decompositions and improve it by expert iteration. On held-out chamfered solids that share no boundary topology with the cloning data, the final policy solves an expected $94.4\%$ in $20$ samples, and expert iteration raises the best-of-20 solve rate on large chamfered solids from $0.203$ to $0.355$. At matched compute, PPO, GRPO and VinePPO updates all make the cloned policy worse.
#05Nov 7, 2026
cs.RO
EmbodiedIntentBench: Benchmarking Intent-Driven Runtime Adaptation for Mobile Robotic Missions
Rajat Bhattacharjya, Changwoon Lee, Hyeonjong Ju and 6 more
Mobile robotic sensing systems must adapt to operator requirements, limited resources, changing connectivity, and observation opportunities shaped by physical motion. Evaluating runtime strategies therefore requires assessing whether their decisions fulfill mission objectives, beyond isolated perception accuracy or execution efficiency. We present EmbodiedIntentBench, a benchmark for intent-driven runtime adaptation in mobile robotic missions. It represents mission intent through structured contracts for coverage, temporal evidence, reporting, urgency, and resources, and couples simulated unmanned aerial vehicle (UAV) workloads with causal, resource-accounted execution. Computation decisions affect mission time, resource use, and which observations can contribute evidence. We evaluate fixed and adaptive perception strategies in multi-phase missions and under changing urgency, connectivity, and battery conditions. In the multi-phase Depot study, a configuration with 87.5% full-bank target recall across visible target observations completes only 1 of 16 missions, whereas a lower-recall configuration completes 14. In an ablation, ignoring execution-induced observation loss increases aggregate mission success and reverses the ordering of two runtime strategies. Replays using Jetson AGX Orin CPU and GPU profiles change the relative success of local and remote strategies. In selected Jetson GPU-profile replays, intent-driven adaptation reduces modeled task energy by up to 28% with unchanged mission success. EmbodiedIntentBench provides an extensible framework for evaluating runtime decisions against mission fulfillment under physical and resource constraints.