{"id":1178923,"date":"2026-07-16T10:12:30","date_gmt":"2026-07-16T17:12:30","guid":{"rendered":"https:\/\/find.codeghost.online\/en-us\/research\/publication\/learning-to-reason-with-curriculum-ii-compositional-generalization\/"},"modified":"2026-07-20T06:35:56","modified_gmt":"2026-07-20T13:35:56","slug":"learning-to-reason-with-curriculum-ii-compositional-generalization","status":"publish","type":"msr-research-item","link":"https:\/\/find.codeghost.online\/en-us\/research\/publication\/learning-to-reason-with-curriculum-ii-compositional-generalization\/","title":{"rendered":"Learning to Reason with Curriculum II: Compositional Generalization"},"content":{"rendered":"\n\n\n<p class=\"wp-block-paragraph\">Compositional generalization, the ability to solve complex problems by combining solutions to simpler sub-problems, is a fundamental capability of both natural and artificial intelligence, and a key mechanism underlying chain-of-thought reasoning. However, the theoretical underpinnings of compositional generalization remain poorly understood: when and why does decomposing a problem into parts yield more efficient learning than solving it directly? We study this question through the canonical problem of learning to simulate semiautomata (predicting the outcome of <math><mi>T<\/mi><\/math> steps of sequential computation), a model that captures state tracking, regular language recognition, and modular arithmetic. We show that an autocurriculum-based approach building on Part I of this series, recursively decomposing longer sequences into shorter sub-problems, learning to solve them, and composing the solutions, achieves dramatically better statistical complexity than direct methods. (i) For a setting inspired by supervised fine-tuning (SFT) where the learner receives interactive feedback on intermediate states of the computation, curriculum facilitates learning from only <math><mrow><msup><mn>2<\/mn><mrow><mrow><mi>\ud835\udcaa<\/mi><mo stretchy=\"false\">(<\/mo><msqrt><mrow><mrow><mo>log<\/mo><mi>T<\/mi><\/mrow><\/mrow><\/msqrt><mo stretchy=\"false\">)<\/mo><\/mrow><\/mrow><\/msup><\/mrow><\/math> tokens of supervision; i.e., subpolynomial in the sequence length <math><mi>T<\/mi><\/math>, overcoming the <math><mrow><mi>\u03a9<\/mi><mo stretchy=\"false\">(<\/mo><mi>T<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/math> token barrier required by direct simulation. (ii) For a setting inspired by reinforcement learning with verifiable rewards (RLVR), where the learner improves a pre-trained reference model using an outcome verifier, we show that curriculum reduces the requirement on the reference model from coverage at the full sequence length <math><mi>T<\/mi><\/math> to coverage at a shorter block length <math><mrow><mi>B<\/mi><mo>\u226a<\/mo><mi>T<\/mi><\/mrow><\/math>, an exponentially weaker condition.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Compositional generalization, the ability to solve complex problems by combining solutions to simpler sub-problems, is a fundamental capability of both natural and artificial intelligence, and a key mechanism underlying chain-of-thought reasoning. However, the theoretical underpinnings of compositional generalization remain poorly understood: when and why does decomposing a problem into parts yield more efficient learning than [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Nived Rajaraman","user_id":0},{"type":"text","value":"Audrey Huang","user_id":0},{"type":"user_nicename","value":"Miro Dud\u00edk","user_id":"32867"},{"type":"user_nicename","value":"Robert Schapire","user_id":"33549"},{"type":"user_nicename","value":"Dylan Foster","user_id":"40330"},{"type":"user_nicename","value":"Akshay 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