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This lack of clarity stems from the fact that we usually do not have access to any notion of ground-truth attribution and from a more general debate on what good interpretations are. In this paper we propose to formalise feature selection/attribution based on the concept of relaxed functional dependence. In particular, we extend our notions to the instance-wise setting and derive necessary properties for candidate selection solutions, while leaving room for task-dependence. By computing ground-truth attributions on synthetic datasets, we evaluate many state-of-the-art attribution methods and show that, even when optimised, some fail to verify the proposed properties and provide wrong solutions.","url_abs":"https://arxiv.org/abs/2104.12437v2","url_pdf":"https://arxiv.org/pdf/2104.12437v2.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-rigorous-interpretations-a","repo_url":"https://github.com/DariusAf/functional_attribution","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"towards-rigorous-interpretations-a","repo_url":"https://github.com/deezer/functional_attribution","is_official":0,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"explainable-artificial-intelligence","task_name":"Explainable artificial intelligence"},{"task_slug":"feature-importance","task_name":"Feature Importance"},{"task_slug":"interpretable-machine-learning","task_name":"Interpretable Machine Learning"},{"task_slug":"feature-selection","task_name":"feature selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2104.12437","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2104.12437"}},"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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