Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learning

arXiv:2512.10534 · cs.AI · Submitted 2025-12-11 · Read on arXiv

cs.AI

Submitted: 2025-12-11

Updated: 2026-09-04

Terminology

• Reinforcement Learning — 47× in this paper · explained in 4 episodes
• Generalization — 7× in this paper · explained in 13 episodes
• Ablation — 5× in this paper · explained in 1 episode
• Benchmark — 3× in this paper · explained in 2 episodes
• Complexity-Boosting Reinforcement Learning — 3× in this paper
• Fine-Tuning — 3× in this paper · explained in 5 episodes
• International Mathematical Olympiad — 3× in this paper
• Large Language Model (LLM) — 3× in this paper · explained in 3 episodes
• Ablation Studies — 2× in this paper · explained in 1 episode
• Ablation study — 2× in this paper · explained in 1 episode
• Agentic Reasoning — 2× in this paper · explained in 1 episode
• Core — 2× in this paper · explained in 2 episodes
• GRPO — 2× in this paper · explained in 6 episodes
• Test-time Scaling — 2× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• GRPO Objective — 1× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• Model-Agnostic — 1× in this paper · explained in 2 episodes
• Open Reasoning — 1× in this paper
• Reinforcement Learning (RL) — 1× in this paper · explained in 25 episodes
• Shared Knowledge Ensemble of Search Trees — 1× in this paper
• Steering — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics
• Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving
• Self-Evolving Curriculum for LLM Reasoning
• Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2
• Synthetic Data Generation & Multi-Step RL for Reasoning & Tool Use
• Benchmarking the Spectrum of Agent Capabilities
• RL of Thoughts: Navigating LLM Reasoning with Inference-time Reinforcement Learning
• Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline
• START: Self-taught Reasoner with Tools
• ToRL: Scaling Tool-Integrated RL
• Agent RL Scaling Law: Agent RL with Spontaneous Code Execution for Mathematical Problem Solving
• Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoning
• Maximizing Confidence Alone Improves Reasoning
• WebRL: Training LLM Web Agents via Self-Evolving Online Curriculum Reinforcement Learning
• DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition
• rStar2-Agent: Agentic Reasoning Technical Report
• Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search
• Newclid: A User-Friendly Replacement for AlphaGeometry
• LADDER: Self-Improving LLMs Through Recursive Problem Decomposition
• Agentic Reasoning and Tool Integration for LLMs via Reinforcement Learning

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