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Distance functions supported on these asymmetrical structures are called quasimetrics. Despite their common appearance, little research has been done on the learning of quasimetrics. Our theoretical analysis reveals that a common class of learning algorithms, including unconstrained multilayer perceptrons (MLPs), provably fails to learn a quasimetric consistent with training data. In contrast, our proposed Poisson Quasimetric Embedding (PQE) is the first quasimetric learning formulation that both is learnable with gradient-based optimization and enjoys strong performance guarantees. Experiments on random graphs, social graphs, and offline Q-learning demonstrate its effectiveness over many common baselines.","url_abs":"https://arxiv.org/abs/2206.15478v4","url_pdf":"https://arxiv.org/pdf/2206.15478v4.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":"on-the-learning-and-learnablity-of","repo_url":"https://github.com/ssnl/poisson_quasimetric_embedding","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"paper_slug":"on-the-learning-and-learnablity-of","repo_url":"https://github.com/quasimetric-learning/torch-quasimetric","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"q-learning","task_name":"Q-Learning"},{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"}],"methods":[{"method_slug":"gravity","method_name":"Gravity"},{"method_slug":"q-learning","method_name":"Q-Learning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.15478","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.15478"}},"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. 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