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.
By Luoning Zhang, Xu Zhuang, Tianhao Wang, Nathan Kaplan
arXiv:2601. 22211v2 Announce Type: replace Abstract: Reinforcement learning (RL) with combinatorial action spaces remains challenging because feasible action sets are exponentially large and governed by complex feasibility constraints, making direct policy parameterization impractical.
By Lingkai Kong, Anagha Satish, Hezi Jiang, Akseli Kangaslahti, Andrew Ma, Wenbo Chen, Mingxiao Song, Lily Xu, Milind Tambe
arXiv:2608.30162v1 Announce Type: new
Abstract: We present a reinforcement-learning agent that solves symbolic equations step by step, covering both nonlinear closed equations (radicals, exponentials...
By Kevin P O Keeffe
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 $1\leq p,q\leq \infty$. For $p<q$, we obtain error $\widetilde{O}_{p,q}(GR/T^{1/p-(1/q-1/2)_{+}})$ after $T$ oracle queries, efficiently realizing the nearly optimal rates of (MBG+26), thereby resolving the nonsmooth end of the COLT 2015 open problem (Guz15b).
arXiv:2606. 10806v1 Announce Type: new Abstract: Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures.
By Xiaoyang Chen, Xiang Jiang
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 $1\leq p,q\leq \infty$.
By David Mart\'inez-Rubio, Crist\'obal Guzm\'an
arXiv:2512. 18471v2 Announce Type: replace Abstract: Continual learning systems face a fundamental geometric obstacle: as experience accumulates on a fixed-capacity manifold, covering numbers grow linearly with time, eventually forcing representational overlap and catastrophic interference.
By Xin Li
The paper investigates the optimization landscape of reinforcement learning with verifiable rewards (RLVR) on algorithmic tasks such as iterated group and quasigroup multiplication. By mapping entropy‑regularized RLVR with myopic tabular policies to a spin‑glass energy model, the authors prove that for a broad class of models with uncorrelated inputs the landscape is benign—there are no local minima that can trap training. They identify practical obstacles like diffusive barriers and gradient‑estimation errors, show these can be mitigated by choosing an appropriate entropy regulator, and demonstrate that a transformer trained from scratch with only last‑token rewards can learn an algorithmic chain of thought for iterated non‑Abelian group multiplications.
By Noa Rubin, Zohar Ringel
arXiv:2609. 29881v1 Announce Type: cross Abstract: Choosing Shellsort gaps is a well-known open problem.
By Bo Liu
The paper announces a new lower bound of 0.8559 for the Steiner ratio, improving on the previous 0.824 bound for the Gilbert‑Pollak Conjecture. It introduces an AI system that uses large language models to generate rule‑constrained geometric lemmas, which are then turned into executable verification functions that certify the bound. The approach relies on only thousands of LLM calls, highlighting the feasibility of LLM‑based methods for advanced mathematical research.
By Yisi Ke, Tianyu Huang, Yankai Shu, Di He, Jingchu Gai, Liwei Wang
arXiv:2510. 11103v3 Announce Type: replace-cross Abstract: Many robotic control tasks require policies to act on orientations, yet the geometry of SO(3) makes this nontrivial.
By Martin Schuck, Sherif Samy, Angela P. Schoellig