{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/towards-a-holistic-understanding-of","title":"Towards a Holistic Understanding of Mathematical Questions with Contrastive Pre-training","arxiv_id":"2301.07558","date":"2023-01-18","proceeding":null,"authors":["Yuting Ning","Zhenya Huang","Xin Lin","Enhong Chen","Shiwei Tong","Zheng Gong","Shijin Wang"],"abstract":"Understanding mathematical questions effectively is a crucial task, which can benefit many applications, such as difficulty estimation. Researchers have drawn much attention to designing pre-training models for question representations due to the scarcity of human annotations (e.g., labeling difficulty). However, unlike general free-format texts (e.g., user comments), mathematical questions are generally designed with explicit purposes and mathematical logic, and usually consist of more complex content, such as formulas, and related mathematical knowledge (e.g., Function). Therefore, the problem of holistically representing mathematical questions remains underexplored. To this end, in this paper, we propose a novel contrastive pre-training approach for mathematical question representations, namely QuesCo, which attempts to bring questions with more similar purposes closer. Specifically, we first design two-level question augmentations, including content-level and structure-level, which generate literally diverse question pairs with similar purposes. Then, to fully exploit hierarchical information of knowledge concepts, we propose a knowledge hierarchy-aware rank strategy (KHAR), which ranks the similarities between questions in a fine-grained manner. Next, we adopt a ranking contrastive learning task to optimize our model based on the augmented and ranked questions. We conduct extensive experiments on two real-world mathematical datasets. The experimental results demonstrate the effectiveness of our model.","url_abs":"https://arxiv.org/abs/2301.07558v1","url_pdf":"https://arxiv.org/pdf/2301.07558v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"towards-a-holistic-understanding-of","repo_url":"https://github.com/bigdata-ustc/quesco","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"contrastive-learning","task_name":"Contrastive Learning"}],"methods":[{"method_slug":"contrastive-learning","method_name":"Contrastive Learning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2301.07558","atlas_url":"https://app.syntology.ai/?focus=2301.07558","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2301.07558"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/bigdata-ustc/quesco","reach":null}],"summary":{"ran":1,"unverified":2},"by_repo_kind":{"official":{"samples":3,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":3,"samples":[{"code_sha256_prefix":"8498e3068a59af4b","entry":"QuesEncoder","repo":"bigdata-ustc/quesco","repo_kind":"official","path":"src/model.py","file_url":"https://github.com/bigdata-ustc/quesco/blob/HEAD/src/model.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"8498e3068a59af4b"}},{"code_sha256_prefix":"5eb3666c4072c5dc","entry":"MoCoTemplate","repo":"bigdata-ustc/quesco","repo_kind":"official","path":"src/model.py","file_url":"https://github.com/bigdata-ustc/quesco/blob/HEAD/src/model.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"5eb3666c4072c5dc"}},{"code_sha256_prefix":"e01c87aa1907b769","entry":"QuesMoCo","repo":"bigdata-ustc/quesco","repo_kind":"official","path":"src/model.py","file_url":"https://github.com/bigdata-ustc/quesco/blob/HEAD/src/model.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e01c87aa1907b769"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}