Reactivating Test-Time Scaling for Plane Geometry Problem Solving

arXiv:2608.30156 · cs.CL · Submitted 2026-08-31 · Read on arXiv

cs.CL

Submitted: 2026-08-31

Updated: 2026-08-31

Code: https://github.com/Jason8Kang/ReTTS-PGPS

Terminology

• Trace — 119× in this paper · explained in 2 episodes
• Accuracy — 40× in this paper · explained in 1 episode
• Test-time Scaling — 21× in this paper · explained in 2 episodes
• Benchmark — 20× in this paper · explained in 2 episodes
• Consistency — 19× in this paper · explained in 3 episodes
• Self-consistency — 19× in this paper · explained in 2 episodes
• Reasoning Traces — 17× in this paper · explained in 3 episodes
• Verification — 13× in this paper · explained in 2 episodes
• Multi-Trace Ensemble — 7× in this paper
• Multi-Trace Synthesis — 6× in this paper
• Ablation — 4× in this paper · explained in 1 episode
• Fine-Tuning — 4× in this paper · explained in 5 episodes
• Grounding — 3× in this paper · explained in 3 episodes
• Multimodal Reasoning — 3× in this paper · explained in 5 episodes
• Adaptive Inference Strategy — 2× in this paper · explained in 1 episode
• Alignment — 2× in this paper · explained in 1 episode
• Distribution Shift — 2× in this paper · explained in 5 episodes
• Program-Aided Language — 2× in this paper
• Reinforcement Learning — 2× in this paper · explained in 4 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Scaling Laws — 2× in this paper · explained in 4 episodes
• Test-Time Scaling (TTS) — 2× in this paper · explained in 2 episodes
• Visual Grounding — 2× in this paper · explained in 2 episodes
• Ablation Studies — 1× in this paper · explained in 1 episode
• Ablation study — 1× in this paper · explained in 1 episode
• Adaptive Strategy — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Axioms — 1× in this paper · explained in 2 episodes
• CVF International Conference on Computer Vision — 1× in this paper
• Calibration — 1× in this paper · explained in 7 episodes
• Chain-of-Thought (CoT) — 1× in this paper · explained in 4 episodes
• Core — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hallucination — 1× in this paper · explained in 3 episodes
• Redundancy — 1× in this paper · explained in 2 episodes

Sources

• Qwen2.5-VL Technical Report
• Milestones over Outcome: Unlocking Geometric Reasoning with Sub-Goal Verifiable Reward
• Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities
• GPT-4 Technical Report
• GeoThought: A Dataset for Enhancing Mathematical Geometry Reasoning in Vision-Language Models
• Bridging Formal Language with Chain-of-Thought Reasoning to Geometry Problem Solving
• Fuse, Reason and Verify: Geometry Problem Solving with Parsed Clauses from Diagram
• FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solving
• GeoFM: Enhancing Geometric Reasoning of MLLMs via Synthetic Data Generation through Formal Language

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