{"paper":{"title":"On the Generalization of Knowledge Distillation: An Information-Theoretic View","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Knowledge distillation generalization is bounded by the KL divergence between teacher and student training kernels.","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Bingying Li, Haiyun He","submitted_at":"2026-05-13T08:10:05Z","abstract_excerpt":"Knowledge distillation is widely used to improve generalization in practice, yet its theoretical understanding remains elusive. In the standard distillation setting, a teacher model provides soft predictions to guide the training of a student model. We model teacher and student training as coupled stochastic processes and introduce a distillation divergence, defined as the Kullback-Leibler divergence between these two stochastic kernels. Within this framework, we derive two generalization bounds for the student model relative to the teacher's generalization gap: an upper bound under a sub-Gaus"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive two generalization bounds for the student model relative to the teacher's generalization gap: an upper bound under a sub-Gaussian assumption via algorithmic stability, and a lower bound under a central condition with sharper dependence on the distillation divergence. We further develop a loss-sharpness-aware bound with an explicit tightness regime, showing that the teacher's local flatness can strictly tighten the bound.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The modeling of teacher and student training as coupled stochastic processes whose kernels admit a well-defined KL divergence; the sub-Gaussian assumption required for the stability upper bound; and the central condition required for the lower bound.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Knowledge distillation generalization bounds are derived via a new distillation divergence measuring teacher-student kernel difference, with tighter bounds from teacher loss flatness.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Knowledge distillation generalization is bounded by the KL divergence between teacher and student training kernels.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"465d037b85ef728b0b3a698cc4a1fa9bcc54f8866c8876828c6bcf47afab11ed"},"source":{"id":"2605.13143","kind":"arxiv","version":1},"verdict":{"id":"9a1a90dd-91fd-4198-ab52-778d0780dd9a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:17:32.574187Z","strongest_claim":"We derive two generalization bounds for the student model relative to the teacher's generalization gap: an upper bound under a sub-Gaussian assumption via algorithmic stability, and a lower bound under a central condition with sharper dependence on the distillation divergence. We further develop a loss-sharpness-aware bound with an explicit tightness regime, showing that the teacher's local flatness can strictly tighten the bound.","one_line_summary":"Knowledge distillation generalization bounds are derived via a new distillation divergence measuring teacher-student kernel difference, with tighter bounds from teacher loss flatness.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The modeling of teacher and student training as coupled stochastic processes whose kernels admit a well-defined KL divergence; the sub-Gaussian assumption required for the stability upper bound; and the central condition required for the lower bound.","pith_extraction_headline":"Knowledge distillation generalization is bounded by the KL divergence between teacher and student training kernels."},"references":{"count":27,"sample":[{"doi":"","year":2015,"title":"Distilling the Knowledge in a Neural Network","work_id":"d927ab1f-17b8-4002-9d09-c3d55764fbad","ref_index":1,"cited_arxiv_id":"1503.02531","is_internal_anchor":true},{"doi":"","year":2018,"title":"Y . Zhang, T. Xiang, T. M. Hospedales, and H. Lu, “Deep mutual learning,” inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2018","work_id":"dc2acf6a-0b71-49b1-afcb-66e6af5f3cfa","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3097983","year":2017,"title":"In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining","work_id":"549e2be2-2a91-45cb-975d-7e91ebca64c1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Towards understanding knowledge distillation,","work_id":"4b8048df-7596-42b7-bbf8-ca6b43789c73","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Do deep nets really need to be deep?","work_id":"e6d1e85f-e2c2-4839-ae24-a62aa2c387d0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":27,"snapshot_sha256":"eb41b6dfbea3ce4f0030c1ba790fd7c6768ce31f429689eb196e394bb2c26912","internal_anchors":2},"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"}