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: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: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:2607. 23785v1 Announce Type: cross Abstract: The Simple Temporal Problem (STP) is a core framework for quantitative temporal constraints.
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.
The Simple Temporal Problem (STP) is a core framework for quantitative temporal constraints. As STP data can be inconsistent, we study MAXSTP: compute a maximum-cardinality consistent subset of constraints.
arXiv:2607. 27670v2 Announce Type: replace-cross Abstract: Jigsaw puzzle solving requires jointly reasoning about visual content and geometric constraints, yet existing benchmarks use rectangular cuts that create ambiguous ground truth in texture-repeated regions.
arXiv:2607. 23602v1 Announce Type: cross Abstract: Controllers based on sampling and latent world models assign a predicted terminal cost to each candidate action sequence, choose the minimum, execute its first action block, and replan.
arXiv:2607. 02491v1 Announce Type: new Abstract: In this work, we focus on SE-RRMs, a symbol-equivariant instantiation of RRMs that exhibits improved extrapolation to larger problem sizes.
arXiv:2511. 13391v4 Announce Type: replace-cross Abstract: Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a defining challenge in discrete geometry.