Towards Solving the Gilbert-Pollak Conjecture via Large Language Models

arXiv:2601.22365 · cs.DM, cs.LG · Submitted 2026-01-29 · Read on arXiv

cs.DM, cs.LG

Submitted: 2026-01-29

Updated: 2026-09-02

Code: https://github.com/keyisi2006/Steine

Terminology

• Verification — 163× in this paper · explained in 2 episodes
• Steiner Minimal Tree — 33× in this paper
• Minimum Spanning Tree — 16× in this paper
• Core — 6× in this paper · explained in 2 episodes
• Pruning — 6× in this paper · explained in 4 episodes
• Verifier — 6× in this paper · explained in 2 episodes
• Cylindrical Algebraic Decomposition — 5× in this paper
• Reinforcement Learning — 4× in this paper · explained in 4 episodes
• Combinatorial Optimization — 3× in this paper · explained in 2 episodes
• Hallucination — 3× in this paper · explained in 3 episodes
• Structured Reasoning — 3× in this paper · explained in 3 episodes
• Ablation — 2× in this paper · explained in 1 episode
• Accuracy — 2× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Generative AI — 2× in this paper · explained in 2 episodes
• Iterative Refinement — 2× in this paper · explained in 3 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Abstraction — 1× in this paper · explained in 1 episode
• Computational Tractability — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Reinforcement Learning (RL) — 1× in this paper · explained in 25 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Very Large Scale Integration — 1× in this paper

Sources

• Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery
• OpenAI o1 System Card
• OpenAI GPT-5 System Card
• DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data
• The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search
• InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning

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