Reactivating Test-Time Scaling for Plane Geometry Problem Solving

arXiv:2608.30156v1 Announce Type: new Abstract: Plane geometry problem (PGP) solving has become a critical benchmark for multimodal reasoning because it requires accurate visual perception and precise multi-step symbolic deduction. Although test-time scaling (TTS) has demonstrated remarkable success in general mathematical reasoning, it fails to scale effectively under the symbolic-program paradigm for plane geometry. We identify two key obstacles: limited reasoning diversity induced by rigid symbolic programs and insufficient explicit visual grounding before symbolic deduction. To address these issues, we propose Multi-Trace Synthesis (MTS), which converts each symbolic program into heterogeneous reasoning traces, including executable Python scripts and CoT-augmented variants. We further propose Perception-Augmented (PA) training, which parses diagrams into structured semantic clauses before deduction, and Consensus-Guided Multi-Trace Ensemble (CG-MTE) for efficient self-adaptive inference. Experiments on three geometry benchmarks show that our method consistently improves PGP-solving across model scales and achieves strong performance against both general-purpose MLLMs and specialized geometry solvers. Under test-time scaling, CG-MTE achieves comparable accuracy to high-budget self-consistency while reducing sampling cost by up to 8x. Code and data are publicly available at https://github.com/Jason8Kang/ReTTS-PGPS.

Related

• SPARC: Separating Perception And Reasoning Circuits for Test-time Scaling of VLMs
• DRAGON: A Benchmark for Evidence-Grounded Visual Reasoning over Diagrams
• Scaling Test-Time Compute to Achieve IOI Gold Medal with Open-Weight Models
• Doing More With Less: Revisiting the Effectiveness of LLM Pruning for Test-Time Scaling
• When to Trust Tools? Adaptive Tool Trust Calibration For Tool-Integrated Math Reasoning

Source: arXiv cs.CL | 2026-09-01