Sample Complexity and Mistake Bounds of Autoregressive Reasoning: CoT vs. EtE

Sample Complexity and Mistake Bounds of Autoregressive Reasoning: CoT vs. EtE

by Idan Mehalel

Formal & Physical Sciences AI — Models & Research UYQArtificial intelligence (AI)UYQMMachine learning
🎙 Idan Mehalel 👥 385 📅 May 14, 2026 ⏱ 61 min 👁 71 📄 original study 🧭 2026-08-16
Available in: English (current) Français

Keywords

autoregressivechain-of-thoughtsample complexitymistake boundsPAC learning

Summary

The talk presents a theoretical framework for studying the learnability of autoregressive models, which generate text token by token. The model is a next-token generator that, given a binary string, outputs a single bit, and is applied iteratively for T steps to produce a chain of thought and a final output. The learning task is to learn the input-output mapping induced by this process, with supervision either as end-to-end (only final output) or chain-of-thought (full chain). The talk addresses two questions: how sample complexity and mistake bounds scale with T, and how much chain-of-thought supervision helps. The results show that for end-to-end learning, the learning rates can vary widely, ranging from constant to linear in T for PAC learning, and up to Littlestone dimension times log T for online learning. In contrast, with chain-of-thought supervision, the learning rates collapse to constants depending only on the class, eliminating the dependence on T. The talk is based on two ongoing works, one with Steve Hanneke and Shay Moran, and another with Ilan Doron-Arad and Elchanan Mossel.

174 words

Critical Evaluation

Value of the Information & Strength of the Argument

The talk provides a rigorous theoretical analysis of a timely topic, offering novel insights into the benefits of chain-of-thought supervision. The argumentation is clear and well-structured, starting with motivation from LLMs, formal definitions, and then presenting results. The speaker effectively uses examples to illustrate concepts and addresses audience questions, strengthening the argument. The results are significant as they provide a theoretical justification for the empirical success of chain-of-thought prompting.

Scientific Rigor, Source Quality, Title Accuracy

The talk is scientifically rigorous, with clear definitions and proofs. The speaker cites relevant prior work, including Joshi et al. (COLT 2025) and the chain-of-thought prompting paper, and mentions ongoing collaborations. The title accurately reflects the content. The talk is based on ongoing research, so the results are not yet peer-reviewed, but the methodology appears sound. The speaker also acknowledges limitations of the model, such as its simplicity compared to real LLMs.

156 words

Title / Content Match

The title accurately reflects the content, focusing on sample complexity and mistake bounds for autoregressive reasoning, comparing chain-of-thought and end-to-end supervision.

Quality & Reliability

8/10

The talk presents original theoretical results, based on two ongoing works, with rigorous definitions and proofs. The speaker is a postdoc at MIT, and the work is joint with known researchers. The presentation is clear and technically sound, though the results are not yet peer-reviewed.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

  • Joshi et al. (COLT 2025) - PAC learning framework for next-token generators — Introduced the PAC-learning framework for next-token generators, which is the basis of this work.
  • Chain-of-Thought Prompting Elicits Reasoning in Large Language Models — Empirical work showing the benefit of chain-of-thought prompting, motivating the theoretical study.

Concurring Sources

  • Joshi et al. (COLT 2025) - PAC learning framework for next-token generators — Provides the formal framework used in this talk.

Contribution & Novelties

The talk presents original theoretical results on the sample complexity and mistake bounds of autoregressive reasoning, showing that chain-of-thought supervision can eliminate the dependence on generation length. This provides a formal justification for the empirical benefits of chain-of-thought. The results are based on two ongoing works, indicating active research.

Pour aller plus loin :

  • PAC learning — Foundational framework for statistical learning.
  • VC dimension — Key combinatorial measure for PAC learning.
  • Littlestone dimension — Analogous measure for online learning.
  • Chain-of-thought prompting — Empirical technique for improving reasoning in LLMs.

89 words

Radar Profile

The radar profile shows high scores in technical level and information quality, with slightly lower but still strong scores in quantity and reliability. This indicates a technically dense and reliable presentation, suitable for an expert audience.

Reliability 8/10