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NeurIPS 2022

STaR: Bootstrapping Reasoning With Reasoning

A 6B model writes its own reasoning data: keep rationales that reach the right answer, rationalize the misses, fine-tune, repeat. It nearly matched a 30x larger fine-tuned model on CommonsenseQA.

Breakdown by FDE Interviews · 12 min read · Updated

About the original · 2022
AUTHORS
Zelikman, Wu, Mu, Goodman
FROM
Stanford University, Google Research
PUBLISHED
Mar 2022 · NeurIPS 2022
CITED BY
1,246Semantic Scholar · Nov 2026
IN THIS BREAKDOWN · 10 SECTIONS

You can read 17% of this breakdown.

01

The paper in one minute

Models answer reasoning questions better when they write a rationale first, but teaching a model to do that by fine-tuning needs thousands of written rationales. Few-shot chain-of-thought prompting needs only a few, but for mid-sized models it is weak: GPT-J 6B scored 36.6% on CommonsenseQA with chain-of-thought examples, against 60.0% when fine-tuned to output answers directly.

STaR, the Self-Taught Reasoner, turns the few examples into a large training set. Prompted with about ten example rationales, the model writes a rationale and an answer for every question in a dataset that has answers but no rationales. Rationales that end in the correct answer are kept. The model is fine-tuned on them, and the improved model writes the next round of rationales. Each round restarts fine-tuning from the original pretrained model to avoid overfitting.

That loop stalls on questions the model never gets right, because they never enter the training set. The paper's second idea, rationalization, fixes this: for a missed question, the model is shown the correct answer as a hint and asked to write a rationale again. If it reaches that answer, the rationale is added to the training set as if the model had written it unaided. On CommonsenseQA, STaR with rationalization reached 72.5%, close to a GPT-3 175B fine-tuned on answers (73.0%). It also improved GSM8K and multi-digit addition. The authors note that the method needs a model with some few-shot reasoning ability to start and works poorly when answers can be guessed.

THE IDEA, VISUALLY
ONE OUTER LOOP (ALGORITHM 1) question x model writes r, y' y' = y ? yes keep (x, r, y) no rationalize: give y as a hint, write r again keep (x, r, y) if it reaches y, hint removed fine-tune the ORIGINAL model on everything kept repeat Filtering on the answer is the only check on the reasoning. On numeric answers a lucky guess is rare; on a yes/no task, a model that reasons correctly 30% of the time keeps 54% lucky rationales (our arithmetic). Rationalization trains on problems the model could not solve, which plain filtering never sees. COMMONSENSEQA DEV, GPT-J 6B (TABLE 1) few-shot, direct 20.9 few-shot, chain of thought 36.6 fine-tuned, direct (100% data) 60.0 STaR, no rationalization 68.8 69.7% of data kept STaR + rationalization 72.5 86.7% kept GPT-3 175B fine-tuned 73.0 30x larger chance is 20% on five options GSM8K TEST (TABLE 2) few-shot CoT 3.1, direct fine-tune 5.8, STaR 10.1, STaR + rationalization 10.7 (28.7% of data kept) arXiv 2203.14465, Stanford and Google, 2022
STaR's outer loop: the model writes a rationale and an answer for each training question, and only rationales that reach the correct answer are kept. For misses, it is shown the answer as a hint and tries again; successful rationalizations are kept with the hint removed. The original model is fine-tuned on everything kept and the loop repeats. On CommonsenseQA, GPT-J 6B went from 60.0% (fine-tuned on answers) to 72.5%.
Research notes: the problem, approach and results
72.5%

CommonsenseQA dev accuracy for GPT-J 6B with STaR and rationalization (Table 1)

+12.5

points over the same model fine-tuned to predict answers directly, 60.0% (Table 1)

86.7%

share of CommonsenseQA training questions that ended up with a kept rationale (Table 1)

THE PROBLEM

Training a model to write rationales before answering needs a dataset of rationales, which is expensive to write by hand. Few-shot chain of thought avoids the dataset but, for a 6B model, scored far below fine-tuning on answers alone.

THE IDEA

Use a handful of example rationales to make the model write rationales for a large question-answer dataset. Keep only rationales whose final answer is correct, fine-tune on them, and repeat. For questions it gets wrong, give the correct answer as a hint and keep the rationale if it reaches that answer (rationalization).

THE RESULT

GPT-J 6B reached 72.5% on CommonsenseQA dev, against 60.0% when fine-tuned to predict answers directly and 73.0% for a fine-tuned GPT-3 175B. On GSM8K it reached 10.7% against 5.8%; on 1-5 digit addition, 89.5% against 76.3%.

02

Why it matters to an FDE

STaR is an early template for many reasoning-data pipelines that followed, including the rejection-sampling fine-tuning stages in later reasoning models. Three ideas from it apply directly to customer work.

Answers you already have can become reasoning data. Many customers have years of labeled outcomes (approved claims, resolved tickets, reconciled invoices) and no written reasoning. A STaR-style loop asks the model to explain how to reach each known outcome and keeps the explanations that do.

The filter is only as good as the check. STaR keeps a rationale if the final answer matches. With numeric answers, a lucky match is rare. With five options or yes/no, many wrong rationales reach the right answer by chance and get kept. Know your check's false-pass rate before you trust the kept set.

Rationalized data needs review. A rationale written after seeing the answer can argue backwards. The authors warn that the method amplifies whatever reasoning reaches the labels, including biased shortcuts, so sample and read the rationalized examples before training on them.

THE FULL BREAKDOWN

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  • ◇1 architecture diagram
  • </>1 runnable code experiment
  • ▦2 results tables
  • ?5 interview questions with answers
  1. 03Key takeaways

    How the loop works, what rationalization adds, where the method stops and two misreadings

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  2. 04How it works

    Algorithm 1, the policy-gradient view, rationalization as a second distribution and the setup

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  3. 05The numbers that matter

    CommonsenseQA and GSM8K tables, arithmetic curves, human ratings and the few-shot ablation

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  4. 06Try it yourself

    Recheck the tables, count lucky rationales, check the GPT-J shape and run a toy of the loop

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  5. 07Where it breaks

    Weak starting models, guessable answers, faithfulness, bias amplification, cost and slips

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  6. 08Using it on a deployment

    Building reasoning data from a customer's labeled outcomes, checks, and review

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  7. 09Interview angles

    Five questions this paper prepares you for, with answer hints

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