{"id":1186456,"date":"2025-02-18T00:00:00","date_gmt":"2025-02-18T08:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=1186456"},"modified":"2026-09-16T09:03:24","modified_gmt":"2026-09-16T16:03:24","slug":"computational-statistical-tradeoffs-at-the-next-token-prediction-barrier-autoregressive-and-imitation-learning-under-misspecification","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/computational-statistical-tradeoffs-at-the-next-token-prediction-barrier-autoregressive-and-imitation-learning-under-misspecification\/","title":{"rendered":"Computational-Statistical Tradeoffs at the Next-Token Prediction Barrier: Autoregressive and Imitation Learning under Misspecification"},"content":{"rendered":"\n\n\n<p class=\"wp-block-paragraph\">Next-token prediction with the logarithmic loss is a cornerstone of autoregressive sequence modeling, but, in practice, suffers from error amplification, where errors in the model compound and generation quality degrades as sequence length <math><mi>H<\/mi><\/math> increases. From a theoretical perspective, this phenomenon should not appear in well-specified settings, and, indeed, a growing body of empirical work hypothesizes that misspecification, where the learner is not sufficiently expressive to represent the target distribution, may be the root cause. Under misspecification &#8212; where the goal is to learn as well as the best-in-class model up to a multiplicative approximation factor <math><mrow><mi>C<\/mi><mo>\u2265<\/mo><mn>1<\/mn><\/mrow><\/math> &#8212; we confirm that <math><mi>C<\/mi><\/math> indeed grows with <math><mi>H<\/mi><\/math> for next-token prediction, lending theoretical support to this empirical hypothesis. We then ask whether this mode of error amplification is avoidable algorithmically, computationally, or information-theoretically, and uncover inherent computational-statistical tradeoffs. We show: (1) Information-theoretically, one can avoid error amplification and achieve <math><mrow><mi>C<\/mi><mo>=<\/mo><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/math>. (2) Next-token prediction can be made robust so as to achieve <math><semantics><mrow><mtext>C=tilde O(H)<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">C=tilde O(H)<\/annotation><\/semantics><\/math>, representing moderate error amplification, but this is an inherent barrier: any next-token prediction-style objective must suffer <math><mrow><mi>C<\/mi><mo>=<\/mo><mi>\u03a9<\/mi><mo stretchy=\"false\">(<\/mo><mi>H<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/math>. (3) For the natural testbed of autoregressive linear models, no computationally efficient algorithm can achieve sub-polynomial approximation factor <math><mrow><mi>C<\/mi><mo>=<\/mo><msup><mi>e<\/mi><mrow><mrow><mo stretchy=\"false\">(<\/mo><mo>log<\/mo><mi>H<\/mi><mo stretchy=\"false\">)<\/mo><mrow><mrow><mn>1<\/mn><mo>&#8211;<\/mo><mi>\u03a9<\/mi><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/mrow><\/mrow><\/mrow><\/msup><\/mrow><\/math>; however, at least for binary token spaces, one can smoothly trade compute for statistical power and improve on <math><mrow><mi>C<\/mi><mo>=<\/mo><mi>\u03a9<\/mi><mo stretchy=\"false\">(<\/mo><mi>H<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/math> in sub-exponential time. Our results have consequences in the more general setting of imitation learning, where the widely-used behavior cloning algorithm generalizes next-token prediction.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Next-token prediction with the logarithmic loss is a cornerstone of autoregressive sequence modeling, but, in practice, suffers from error amplification, where errors in the model compound and generation quality degrades as sequence length H increases. From a theoretical perspective, this phenomenon should not appear in well-specified settings, and, indeed, a growing body of empirical work [&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":"Dhruv Rohatgi","user_id":0},{"type":"user_nicename","value":"Adam Block","user_id":"43395"},{"type":"text","value":"Audrey Huang","user_id":0},{"type":"user_nicename","value":"Akshay Krishnamurthy","user_id":"30913"},{"type":"user_nicename","value":"Dylan 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