Qingfeng Guo | Searcharxiv

arXiv2025

ASSESS: A Semantic and Structural Evaluation Framework for Statement Similarity

Despite significant strides in statement autoformalization, a critical gap remains in the development of automated evaluation metrics capable of assessing formal translation quality. Existing metrics often fail to balance semantic and structural information: string-based methods neglect semantics, whereas proof-based approaches offer no graded similarity when proofs fail. To address these issues, we introduce ASSESS (A Semantic and Structural Evaluation Framework for Statement Similarity), which captures syntactic structure by transforming formal statements into operator trees and computes a real-valued similarity score using our novel TransTED (Transformation Tree Edit Distance) Similarity metric by incorporating semantic transformations. For rigorous validation, we present EPLA (Evaluating Provability and Likeness for Autoformalization), a benchmark comprising 1,247 expert-annotated formal statement pairs derived from miniF2F and ProofNet, distinctively labeled for both semantic provability and structural likeness. Experiments on the EPLA benchmark demonstrate that TransTED Similarity surpasses existing methods, achieving state-of-the-art accuracy and Kappa score. The benchmark dataset, code, and detailed experimental results are available at https://github.com/XiaoyangLiu-sjtu/ASSESS.

cs.LG↗

arXiv2025

Generalized Tree Edit Distance (GTED): A Faithful Evaluation Metric for Statement Autoformalization

Statement autoformalization, the automated translation of statements from natural language into formal languages, has become a subject of extensive research, yet the development of robust automated evaluation metrics remains limited. Existing evaluation methods often lack semantic understanding, face challenges with high computational costs, and are constrained by the current progress of automated theorem proving. To address these issues, we propose GTED (Generalized Tree Edit Distance), a novel evaluation framework that first standardizes formal statements and converts them into operator trees, then determines the semantic similarity using the eponymous GTED metric. Across the miniF2F and ProofNet benchmarks, GTED consistently ranks as a top-performing metric, achieving the highest accuracy and Kappa on miniF2F and the joint-highest accuracy on ProofNet. This strong overall performance provides the community with a computationally lightweight and more faithful metric for automated evaluation. The code and experimental results are available at https://github.com/XiaoyangLiu-sjtu/GTED.

cs.LG↗