We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints. Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits.
arXiv:2606. 26399v1 Announce Type: new Abstract: We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints.
arXiv:2606. 09278v1 Announce Type: cross Abstract: Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints.
arXiv:2609.38863v1 Announce Type: cross Abstract: The two-dimensional irregular knapsack problem in a fixed circular container is an important combinatorial optimization problem for maximizing materi...
arXiv:2607. 05359v1 Announce Type: new Abstract: Planning under uncertainty in continuous domains is essential for autonomous systems, yet computationally demanding.
Planning under uncertainty in continuous domains is essential for autonomous systems, yet computationally demanding. Tree-based search methods such as Monte Carlo Tree Search (MCTS) remain popular, but their branching structure can require sampling budgets that grow exponentially with lookahead depth in the worst case.
arXiv:2609. 29881v1 Announce Type: cross Abstract: Choosing Shellsort gaps is a well-known open problem.
GeoPAR is a geometry-guided parallel autoregressive reinforcement learning framework designed for large-scale multi-agent combinatorial optimization. It introduces a projection-window sparse geometry mechanism, sparse edge-biased attention, and cache-guided conflict-aware assignment to better model local geometric structures and reduce duplicate task selections. Experiments on heterogeneous vehicle routing and multi-depot pickup-and-delivery problems demonstrate improved zero-shot generalization, fewer rollout steps, and efficient inference.
arXiv:2607. 27169v1 Announce Type: new Abstract: Solving a continuous algebraic constraint system requires two decisions: which values satisfy the constraints, and which structural augmentation renders an unsolvable system solvable.
arXiv:2609.37356v1 Announce Type: new Abstract: Generating optimization instances that are both feasible and computationally challenging is crucial for benchmarking solvers and training learning-base...
arXiv:2607. 23785v1 Announce Type: cross Abstract: The Simple Temporal Problem (STP) is a core framework for quantitative temporal constraints.
arXiv:2609. 20701v1 Announce Type: cross Abstract: We study efficient algorithms for realizing the first-order oracle complexity of optimization of $G$-Lipschitz convex functions with respect to the $\ell_{q}$-norm over an $\ell_{p}$-ball of radius $R$, where $1\leq p,q\leq \infty$.
arXiv:2505. 15201v5 Announce Type: replace-cross Abstract: Reinforcement Learning (RL) algorithms sample multiple n>1 solution attempts for each problem and reward them independently.