[2511.10833] SURFACEBENCH: A Geometry-Aware Benchmark for Symbolic Surface Discovery

Computer Science > Machine Learning arXiv:2511.10833 (cs) [Submitted on 13 Nov 2025 (v1), last revised 2 Mar 2026 (this version, v2)] Title:SURFACEBENCH: A Geometry-Aware Benchmark for Symbolic Surface Discovery Authors:Sanchit Kabra, Shobhnik Kriplani, Parshin Shojaee, Chandan K. Reddy View a PDF of the paper titled SURFACEBENCH: A Geometry-Aware Benchmark for Symbolic Surface Discovery, by Sanchit Kabra and 3 other authors View PDF HTML (experimental) Abstract:Equation discovery from data is a central challenge in machine learning for science, which requires the recovery of concise symbolic expressions that govern complex physical and geometric phenomena. Recent large language model (LLM) approaches have shown promise in symbolic regression, yet existing benchmarks predominantly evaluate low-dimensional scalar functions and rely on string-level or regression-based metrics that fail to capture structural and geometric equivalence. We introduce SURFACEBENCH, the first geometry-aware benchmark for symbolic discovery of three-dimensional surfaces. Unlike scalar curve-fitting tasks, SURFACEBENCH targets surface-level reasoning, where multi-variable coupling, coordinate transformations, and geometric structure must be inferred directly from data. The benchmark comprises 183 analytically constructed, science-inspired surface equations across 15 categories and three representation paradigms: explicit, implicit, and parametric forms. Each task includes variable semantics and synt...