{"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/multi-dimensional-concept-discovery-mcd-a","title":"Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees","arxiv_id":"2301.11911","date":"2023-01-27","proceeding":null,"authors":["Johanna Vielhaben","Stefan Blücher","Nils Strodthoff"],"abstract":"The completeness axiom renders the explanation of a post-hoc XAI method only locally faithful to the model, i.e. for a single decision. For the trustworthy application of XAI, in particular for high-stake decisions, a more global model understanding is required. Recently, concept-based methods have been proposed, which are however not guaranteed to be bound to the actual model reasoning. To circumvent this problem, we propose Multi-dimensional Concept Discovery (MCD) as an extension of previous approaches that fulfills a completeness relation on the level of concepts. Our method starts from general linear subspaces as concepts and does neither require reinforcing concept interpretability nor re-training of model parts. We propose sparse subspace clustering to discover improved concepts and fully leverage the potential of multi-dimensional subspaces. MCD offers two complementary analysis tools for concepts in input space: (1) concept activation maps, that show where a concept is expressed within a sample, allowing for concept characterization through prototypical samples, and (2) concept relevance heatmaps, that decompose the model decision into concept contributions. Both tools together enable a detailed understanding of the model reasoning, which is guaranteed to relate to the model via a completeness relation. This paves the way towards more trustworthy concept-based XAI. We empirically demonstrate the superiority of MCD against more constrained concept definitions.","url_abs":"https://arxiv.org/abs/2301.11911v2","url_pdf":"https://arxiv.org/pdf/2301.11911v2.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":"multi-dimensional-concept-discovery-mcd-a","repo_url":"https://github.com/jvielhaben/mcd-xai","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"multi-dimensional-concept-discovery-mcd-a","repo_url":"https://github.com/grobruegge/hu-mcd","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"xai","task_name":"Explainable Artificial Intelligence (XAI)"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2301.11911","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2301.11911"}},"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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