AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems
Eugenio Cainelli, Lorenzo Luccioli, Alessandro Iraci, Giovanni Paolini
Abstract
We introduce qtBench, a benchmark of 29 open problems in algebraic combinatorics. These problems ask for a simple combinatorial algorithm that explains given polynomial coefficients or identities. To help AI agents search for such algorithms, we provide a scaffold for playing with combinatorial objects, countering cheating attempts, and testing candidate solutions. To explore how far frontier AI systems can go on these problems, we collaborated with OpenAI, whose researchers obtained proposed solutions to several of them. This highlights bigger meta-problems: is AI discovery at scale ethical? How should these results be released? How should proof digestion be organized? We discuss these questions and give our views.
Create a lesson
Related papers
Double-Rollout Reinforcement Learning with Sampling-based Reward Estimation
Haifeng Qian, David Mosallanezhad, Christian Munley et al.
G2WAM: World Action Models for Efficient and Geometry Grounded Image-Goal Navigation
Ke Gui, Chenghao Shi, Ziyue Wang et al.
Making Language the Low-Rate Code of Vision: Successive Refinement from Words to Pixels
Ruilin Gong, Hao Gong
Overtaught, Underlearned: Learner-Centered Distillation from Multi-Agent Discussion
Mengtao Zhou, Jianxiao Wang, Xiupeng Chen et al.
Does the Explanation Drift Before the Guarantee? Label-Free Early Warning on Evolving Graphs
Tomasz Szandała, Damian Raczkowski
EAU: Environment-Agent-User Co-evolution for Training User-Centric Agents
Min Cai, Dan Zhang, Gao Xing et al.