arxiv: 2112.00114 · v1 · submitted 2021-11-30 · 💻 cs.LG · cs.NE

Recognition: 3 theorem links

· Lean Theorem

Show Your Work: Scratchpads for Intermediate Computation with Language Models

Maxwell Nye , Anders Johan Andreassen , Guy Gur-Ari , Henryk Michalewski , Jacob Austin , David Bieber , David Dohan , Aitor Lewkowycz

show 4 more authors

Maarten Bosma David Luan Charles Sutton Augustus Odena

Authors on Pith no claims yet

Pith reviewed 2026-05-13 00:26 UTC · model grok-4.3

classification 💻 cs.LG cs.NE

keywords language modelsscratchpadsmulti-step computationtransformersfew-shot learningintermediate stepsprogram execution

0 comments

The pith

Language models solve multi-step tasks like long addition and program execution when trained to emit intermediate steps on a scratchpad.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Large pre-trained language models handle single-pass tasks well but fail at unbounded multi-step computations such as adding large integers or running programs. The paper demonstrates that the same models succeed when prompted or trained to generate step-by-step intermediate results before the final answer. This scratchpad approach works in the few-shot regime and scales across tasks of rising complexity. A reader would care because it provides a direct method to extend existing models to problems that previously required architectural changes or external tools.

Core claim

Transformers perform complex multi-step computations by emitting intermediate results into a scratchpad. On tasks ranging from long addition to execution of arbitrary programs, this produces correct final answers where direct generation fails, including when only a few examples are provided.

What carries the argument

The scratchpad is the sequence of explicit intermediate computation results that the model is trained or prompted to output before the final answer.

If this is right

Models compute accurate long sums by producing partial results at each digit position.
Program execution succeeds by simulating each instruction in order within the scratchpad.
Few-shot examples that include scratchpad steps enable new multi-step tasks without full retraining.
Accuracy remains high as task length and complexity increase because each step is handled separately.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same step-by-step emission pattern could apply to untested reasoning domains such as math word problems or logical deduction chains.
Pairing scratchpads with external checkers on intermediate results might reduce compounding errors further.
Scaling the approach to larger models or different sequence architectures remains an open test of generality.

Load-bearing premise

The model generates correct intermediate steps whose errors do not accumulate fatally before the final answer.

What would settle it

A controlled test supplying externally verified correct intermediate steps on multi-step problems and measuring whether the model still produces incorrect final answers.

read the original abstract

Large pre-trained language models perform remarkably well on tasks that can be done "in one pass", such as generating realistic text or synthesizing computer programs. However, they struggle with tasks that require unbounded multi-step computation, such as adding integers or executing programs. Surprisingly, we find that these same models are able to perform complex multi-step computations -- even in the few-shot regime -- when asked to perform the operation "step by step", showing the results of intermediate computations. In particular, we train transformers to perform multi-step computations by asking them to emit intermediate computation steps into a "scratchpad". On a series of increasingly complex tasks ranging from long addition to the execution of arbitrary programs, we show that scratchpads dramatically improve the ability of language models to perform multi-step computations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Scratchpads let models break multi-step tasks into explicit steps and lift final accuracy on addition, polynomials, and program execution, though without direct checks on intermediate correctness.

read the letter

The key takeaway is that training language models to emit intermediate scratchpad steps helps them handle tasks that need multiple computations, like long addition or running programs, where standard one-pass generation falls short. What stands out as new is the explicit use of scratchpads during both training and inference to break down these problems. The paper walks through a set of tasks that get harder, starting with addition and moving to polynomial evaluation and full program execution. They show that models can do this even with few examples, and the scratchpad version outperforms the baseline. The paper does a good job of making the method concrete and testing it on increasingly demanding examples. The results indicate real gains in accuracy for these multi-step cases. On the downside, the experiments focus on whether the final answer is correct, without a separate check on whether each scratchpad step is accurate. This matches the stress-test concern, and it means we can't rule out that the benefits come from extra supervision or output length rather than true intermediate computation. It's not a fatal issue for the claims, but it would strengthen the paper to add that analysis where possible, like for the addition task. The citation pattern looks fine, building on prior language model work without overclaiming. This paper is aimed at people in machine learning who work on reasoning and program synthesis with transformers. A reader looking for practical ways to extend model capabilities on computational tasks will get something out of the experiments and the simple idea. It deserves a serious referee because the empirical demonstration is clear enough to merit feedback, even if more controls would help. Recommendation: send it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper claims that pre-trained language models, which struggle with unbounded multi-step computations such as long addition or program execution, can be trained (or prompted) to emit intermediate computation results into a 'scratchpad' and thereby achieve dramatically better performance on these tasks, including in the few-shot regime.

Significance. If the central empirical claim holds after verification of intermediate-step accuracy, the scratchpad technique would constitute a lightweight, architecture-agnostic method for extending transformer capabilities to reliable sequential reasoning, with potential value for symbolic computation, code execution, and related domains.

major comments (2)

[Experiments and Results] Experiments and Results sections: final-answer accuracy is reported with versus without scratchpads on addition, polynomial evaluation, and program execution, but no separate metric (e.g., token-level or step-level accuracy) is supplied for the correctness of the emitted scratchpad intermediates themselves. Without this, it remains possible that observed gains arise from longer output supervision, different loss weighting, or partial memorization rather than faithful step-by-step execution.
[Results] Task-specific results (program execution and long addition): the manuscript does not quantify the rate at which errors in intermediate scratchpad steps propagate to incorrect final answers, which directly tests the weakest assumption that intermediates remain reliable enough to prevent fatal compounding.

minor comments (2)

[Abstract] Abstract: the phrase 'dramatically improve' is used without any numerical illustration; adding one concrete accuracy delta (with baseline) would improve readability.
[Method] Method description: the precise formatting rules, length limits, and tokenization of the scratchpad are not fully specified for the few-shot prompting case, making exact reproduction harder.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback, which identifies key areas where additional analysis would strengthen the presentation of our results. We address each major comment below and will revise the manuscript to incorporate the suggested metrics and analyses.

read point-by-point responses

Referee: Experiments and Results sections: final-answer accuracy is reported with versus without scratchpads on addition, polynomial evaluation, and program execution, but no separate metric (e.g., token-level or step-level accuracy) is supplied for the correctness of the emitted scratchpad intermediates themselves. Without this, it remains possible that observed gains arise from longer output supervision, different loss weighting, or partial memorization rather than faithful step-by-step execution.

Authors: We agree that reporting only final-answer accuracy leaves room for alternative explanations of the observed gains. In the revised manuscript we will add step-level and token-level accuracy metrics for the scratchpad intermediates on the addition and program execution tasks (where ground-truth steps are available). These will be computed by comparing generated intermediates against the expected computation steps, which should help confirm that performance improvements arise from faithful step-by-step execution rather than supervision length or memorization artifacts. revision: yes
Referee: Task-specific results (program execution and long addition): the manuscript does not quantify the rate at which errors in intermediate scratchpad steps propagate to incorrect final answers, which directly tests the weakest assumption that intermediates remain reliable enough to prevent fatal compounding.

Authors: We acknowledge the value of quantifying error propagation to validate the reliability of the scratchpad approach. The revised version will include an analysis of this for the program execution and long addition tasks, for example by reporting final-answer accuracy conditioned on the correctness of the preceding scratchpad steps or by measuring the frequency with which intermediate errors lead to final mistakes. This will directly address the concern about compounding errors. revision: yes

Circularity Check

0 steps flagged

No significant circularity in empirical evaluation

full rationale

The paper is an empirical study reporting performance gains from training language models to emit intermediate steps into a scratchpad on tasks such as addition and program execution. No mathematical derivation chain exists that reduces any claimed result to a self-definition, fitted parameter renamed as prediction, or self-citation load-bearing uniqueness theorem. Experimental comparisons of final-answer accuracy with versus without scratchpads are independent measurements, not tautological by construction, and the paper does not invoke prior self-authored results to forbid alternatives or smuggle in ansatzes. The evaluation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the empirical observation that scratchpads help, but the training process inherits all standard transformer hyperparameters plus the choice of scratchpad format and length; no independent evidence is given that the intermediate steps are verifiably correct beyond the final-answer accuracy.

free parameters (1)

scratchpad format and length
Specific formatting and maximum length of the intermediate computation area are chosen to make the method succeed on the tested tasks.

axioms (1)

domain assumption Language models can learn to emit correct intermediate steps from few-shot examples or fine-tuning
The method assumes the model will generate accurate step-by-step traces rather than hallucinated ones.

pith-pipeline@v0.9.0 · 5464 in / 1271 out tokens · 51559 ms · 2026-05-13T00:26:39.518587+00:00 · methodology

discussion (0)

Forward citations

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