@inproceedings{cheng-etal-2026-topoeval,
title = "{T}opo{E}val: A Comprehensive Benchmark for Topological Reasoning in Foundation Models",
author = "Cheng, Yinzhu and
Meng, Yihan and
Xie, Haihua and
Sun, Mingming",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.1475/",
doi = "10.18653/2026.findings-emnlp.1475",
pages = "31391--31421",
ISBN = "979-8-89176-462-0",
abstract = "Topological reasoning{---}the ability to identify structural invariants under continuous deformations{---}is a cornerstone of human visual cognition, yet it remains under-explored in modern AI systems. Existing benchmarks provide limited coverage of mathematical topology as a discipline and rarely probe the depth of topological reasoning. To bridge this gap, we introduce TopoEval, an 800-item benchmark suite for topological reasoning. TopoEval centers on a 400-item answer-based Core track and includes a 400-item Proof track for reference-grounded informal proof assessment. The suite spans four major topology branches, twelve fine-grained subfields, and three difficulty levels. On Core, we investigate model scaling, reasoning depth, prompt strategies, image dependency, and academic tiers. The strongest Core configuration reaches 73.0{\%} overall and 54.1{\%} on all 85 K12 items. For context, topology-trained graduate-student solvers reach 96.3{\%} under the audited protocol in Appendix B.2. On Proof, pass-plus-borderline rates are low across the selected conditions, indicating difficulty in producing reference-aligned natural-language topology proofs. TopoEval profiles these capabilities across academic level, image dependency, and proof quality."
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<abstract>Topological reasoning—the ability to identify structural invariants under continuous deformations—is a cornerstone of human visual cognition, yet it remains under-explored in modern AI systems. Existing benchmarks provide limited coverage of mathematical topology as a discipline and rarely probe the depth of topological reasoning. To bridge this gap, we introduce TopoEval, an 800-item benchmark suite for topological reasoning. TopoEval centers on a 400-item answer-based Core track and includes a 400-item Proof track for reference-grounded informal proof assessment. The suite spans four major topology branches, twelve fine-grained subfields, and three difficulty levels. On Core, we investigate model scaling, reasoning depth, prompt strategies, image dependency, and academic tiers. The strongest Core configuration reaches 73.0% overall and 54.1% on all 85 K12 items. For context, topology-trained graduate-student solvers reach 96.3% under the audited protocol in Appendix B.2. On Proof, pass-plus-borderline rates are low across the selected conditions, indicating difficulty in producing reference-aligned natural-language topology proofs. TopoEval profiles these capabilities across academic level, image dependency, and proof quality.</abstract>
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%0 Conference Proceedings
%T TopoEval: A Comprehensive Benchmark for Topological Reasoning in Foundation Models
%A Cheng, Yinzhu
%A Meng, Yihan
%A Xie, Haihua
%A Sun, Mingming
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F cheng-etal-2026-topoeval
%X Topological reasoning—the ability to identify structural invariants under continuous deformations—is a cornerstone of human visual cognition, yet it remains under-explored in modern AI systems. Existing benchmarks provide limited coverage of mathematical topology as a discipline and rarely probe the depth of topological reasoning. To bridge this gap, we introduce TopoEval, an 800-item benchmark suite for topological reasoning. TopoEval centers on a 400-item answer-based Core track and includes a 400-item Proof track for reference-grounded informal proof assessment. The suite spans four major topology branches, twelve fine-grained subfields, and three difficulty levels. On Core, we investigate model scaling, reasoning depth, prompt strategies, image dependency, and academic tiers. The strongest Core configuration reaches 73.0% overall and 54.1% on all 85 K12 items. For context, topology-trained graduate-student solvers reach 96.3% under the audited protocol in Appendix B.2. On Proof, pass-plus-borderline rates are low across the selected conditions, indicating difficulty in producing reference-aligned natural-language topology proofs. TopoEval profiles these capabilities across academic level, image dependency, and proof quality.
%R 10.18653/2026.findings-emnlp.1475
%U https://aclanthology.org/2026.findings-emnlp.1475/
%U https://doi.org/10.18653/2026.findings-emnlp.1475
%P 31391-31421
Markdown (Informal)
[TopoEval: A Comprehensive Benchmark for Topological Reasoning in Foundation Models](https://aclanthology.org/2026.findings-emnlp.1475/) (Cheng et al., Findings 2026)
ACL