{"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/improved-representation-of-asymmetrical","title":"Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddings","arxiv_id":"2211.15120","date":"2022-11-28","proceeding":null,"authors":["Tongzhou Wang","Phillip Isola"],"abstract":"Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives and are gaining more attention in machine learning applications. Imposing such quasimetric structures in model representations has been shown to improve many tasks, including reinforcement learning (RL) and causal relation learning. In this work, we present four desirable properties in such quasimetric models, and show how prior works fail at them. We propose Interval Quasimetric Embedding (IQE), which is designed to satisfy all four criteria. On three quasimetric learning experiments, IQEs show strong approximation and generalization abilities, leading to better performance and improved efficiency over prior methods. Project Page: https://www.tongzhouwang.info/interval_quasimetric_embedding Quasimetric Learning Code Package: https://www.github.com/quasimetric-learning/torch-quasimetric","url_abs":"https://arxiv.org/abs/2211.15120v2","url_pdf":"https://arxiv.org/pdf/2211.15120v2.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":"improved-representation-of-asymmetrical","repo_url":"https://github.com/quasimetric-learning/torch-quasimetric","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[{"method_slug":"fail","method_name":"fail"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2211.15120","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2211.15120"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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/quasimetric-learning/torch-quasimetric","reach":null}],"summary":{"ran_fixture":1,"unverified":1},"by_repo_kind":{"official":{"samples":2,"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":0,"samples":[{"code_sha256_prefix":"3dae47d0a3c9fa73","entry":"iqe","repo":"quasimetric-learning/torch-quasimetric","repo_kind":"official","path":"torchqmet/iqe.py","file_url":"https://github.com/quasimetric-learning/torch-quasimetric/blob/HEAD/torchqmet/iqe.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"3dae47d0a3c9fa73"}},{"code_sha256_prefix":"3b7e20e89fd6bce5","entry":"check_env_flag","repo":"quasimetric-learning/torch-quasimetric","repo_kind":"official","path":"torchqmet/pqe/cdf_ops/load_ext.py","file_url":"https://github.com/quasimetric-learning/torch-quasimetric/blob/HEAD/torchqmet/pqe/cdf_ops/load_ext.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":"MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"3b7e20e89fd6bce5"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}