{"paper":{"title":"Teaching and Learning under Deductive Errors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Teachers can find small example sets that still guide learners making deductive errors to approximately correct hypotheses with high probability.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Brigt H{\\aa}vardstun, Jan Arne Telle, Jose Hernandez-Orallo","submitted_at":"2026-05-13T11:43:01Z","abstract_excerpt":"Most models of machine teaching and learning assume the learner makes no errors in its internal deductive inference. However, humans and large language models in few-shot learning regimes are two important examples of learners where this does not hold. They fail on some consistency checks, and they can fail stochastically. In this paper we introduce a teaching and learning framework that takes these deductive errors into account. We specifically study the case of machine teaching, as different characterizations of the teacher can account for both machine teaching and learning. In an overhauled"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For some estimated error level, the teacher must find a PAC teaching set that with high probability will lead the learner to guess a hypothesis that is approximately correct.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the learner's deductive error rate can be estimated in advance and remains consistent enough for the PAC guarantee to apply across different hypotheses.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends PAC machine teaching to handle deductive errors by requiring teachers to select sets that lead to approximately correct hypotheses with high probability despite learner mistakes, with complexity results and LLM experiments.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Teachers can find small example sets that still guide learners making deductive errors to approximately correct hypotheses with high probability.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d2041bff6d36d4c393e36b84c2acaa746ff1e21d800bf1a1dbfbb0f0282caeb6"},"source":{"id":"2605.13384","kind":"arxiv","version":1},"verdict":{"id":"415956ce-a527-4dfd-8161-8ae434fcb14a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:24:35.372634Z","strongest_claim":"For some estimated error level, the teacher must find a PAC teaching set that with high probability will lead the learner to guess a hypothesis that is approximately correct.","one_line_summary":"Extends PAC machine teaching to handle deductive errors by requiring teachers to select sets that lead to approximately correct hypotheses with high probability despite learner mistakes, with complexity results and LLM experiments.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the learner's deductive error rate can be estimated in advance and remains consistent enough for the PAC guarantee to apply across different hypotheses.","pith_extraction_headline":"Teachers can find small example sets that still guide learners making deductive errors to approximately correct hypotheses with high probability."},"references":{"count":300,"sample":[{"doi":"","year":2026,"title":"Machine Learning , volume=","work_id":"e3c5ecac-3d92-4781-959e-9222cb709f5f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Probably approximately correct: nature's algorithms for learning and prospering in a complex world , author=. 2013 , publisher=","work_id":"d40a8f99-b684-4dc7-86e2-2c0ee2f46c71","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"International Workshop on Parameterized and Exact Computation , pages=","work_id":"3184dc32-e03e-4dd7-8e2e-5d3a49066d53","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/2925416","year":2016,"title":"On Problems as Hard as","work_id":"6656f0e6-b19c-40ef-b945-bad5bd2ddd31","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Journal of Machine Learning Research , volume =","work_id":"6211251c-449d-4478-b8cd-43fe27b1b73f","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":300,"snapshot_sha256":"46a4e1bf0adf67234f26e5a0ba26554523bbce00dfe99460dc9af35153fce849","internal_anchors":8},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}