{"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/how-many-and-which-training-points-would-need","title":"How Many and Which Training Points Would Need to be Removed to Flip this Prediction?","arxiv_id":"2302.02169","date":"2023-02-04","proceeding":null,"authors":["Jinghan Yang","Sarthak Jain","Byron C. Wallace"],"abstract":"We consider the problem of identifying a minimal subset of training data $\\mathcal{S}_t$ such that if the instances comprising $\\mathcal{S}_t$ had been removed prior to training, the categorization of a given test point $x_t$ would have been different. Identifying such a set may be of interest for a few reasons. First, the cardinality of $\\mathcal{S}_t$ provides a measure of robustness (if $|\\mathcal{S}_t|$ is small for $x_t$, we might be less confident in the corresponding prediction), which we show is correlated with but complementary to predicted probabilities. Second, interrogation of $\\mathcal{S}_t$ may provide a novel mechanism for contesting a particular model prediction: If one can make the case that the points in $\\mathcal{S}_t$ are wrongly labeled or irrelevant, this may argue for overturning the associated prediction. Identifying $\\mathcal{S}_t$ via brute-force is intractable. We propose comparatively fast approximation methods to find $\\mathcal{S}_t$ based on influence functions, and find that -- for simple convex text classification models -- these approaches can often successfully identify relatively small sets of training examples which, if removed, would flip the prediction.","url_abs":"https://arxiv.org/abs/2302.02169v2","url_pdf":"https://arxiv.org/pdf/2302.02169v2.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":"how-many-and-which-training-points-would-need","repo_url":"https://github.com/ecielyang/smallest_set","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"prediction","task_name":"Prediction"},{"task_slug":"text-classification","task_name":"Text Classification"},{"task_slug":"text-classification-1","task_name":"text-classification"}],"methods":[{"method_slug":"flip","method_name":"FLIP"},{"method_slug":"test","method_name":"Test"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2302.02169","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2302.02169"}},"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/ecielyang/smallest_set","reach":null}],"summary":{"ran_fixture":1,"ran_honours":1,"ran_draft_wrong":2,"unverified":2},"by_repo_kind":{"official":{"samples":6,"ran":4,"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":6,"samples":[{"code_sha256_prefix":"394ed4867d5740ce","entry":"Remove","repo":"ecielyang/smallest_set","repo_kind":"official","path":"Smallest_k.py","file_url":"https://github.com/ecielyang/smallest_set/blob/HEAD/Smallest_k.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"394ed4867d5740ce"}},{"code_sha256_prefix":"f0458fd6f37c6080","entry":"concatenate","repo":"ecielyang/smallest_set","repo_kind":"official","path":"recursive.py","file_url":"https://github.com/ecielyang/smallest_set/blob/HEAD/recursive.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f0458fd6f37c6080"}},{"code_sha256_prefix":"51f77e4457107d04","entry":"error","repo":"ecielyang/smallest_set","repo_kind":"official","path":"recursive.py","file_url":"https://github.com/ecielyang/smallest_set/blob/HEAD/recursive.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"51f77e4457107d04"}},{"code_sha256_prefix":"6154bee9b6ca26bd","entry":"prediction","repo":"ecielyang/smallest_set","repo_kind":"official","path":"recursive.py","file_url":"https://github.com/ecielyang/smallest_set/blob/HEAD/recursive.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"6154bee9b6ca26bd"}},{"code_sha256_prefix":"22cc94a64b762c8a","entry":"approximate_k","repo":"ecielyang/smallest_set","repo_kind":"official","path":"Smallest_k.py","file_url":"https://github.com/ecielyang/smallest_set/blob/HEAD/Smallest_k.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":"22cc94a64b762c8a"}},{"code_sha256_prefix":"412344879324027f","entry":"new_train","repo":"ecielyang/smallest_set","repo_kind":"official","path":"Smallest_k.py","file_url":"https://github.com/ecielyang/smallest_set/blob/HEAD/Smallest_k.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":"412344879324027f"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}