Chain-of-thought prompting, by including intermediate reasoning steps in few-shot examples, elicits strong reasoning abilities in large language models on arithmetic, commonsense, and symbolic tasks.
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Show Your Work: Scratchpads for Intermediate Computation with Language Models
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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.
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representative citing papers
Depth-L transformers with W parameters have VC dimension Theta(L W log(T W)), yielding matching O(L W log((T+T')W)) upper and Omega(L W log((T+T')W/L)) lower bounds on sample complexity for chain-of-thought learning.
Long-range dependency in integer multiplication is a mirage from 1D representation; a 2D grid reduces it to local 3x3 operations, letting a 321-parameter neural cellular automaton generalize perfectly to inputs 683 times longer than training while Transformers fail.
Promptbreeder evolves both task prompts and the mutation prompts that improve them using LLMs, outperforming Chain-of-Thought and Plan-and-Solve on arithmetic and commonsense reasoning benchmarks.
PAL improves few-shot reasoning accuracy by having LLMs generate executable programs rather than text-based chains of thought, outperforming much larger models on math and logic benchmarks.
In-distribution sampling across 25 models and controlled interventions with DAG-verified content show that semantic reasoning and validation content, not token count, drive CoT gains.
RNG-Bench evaluates MLLMs on hidden-observation reconstruction in non-Markov games, finds forgetting as the dominant error source, and shows fine-tuning on optimal rollouts improves performance with transfer to other benchmarks.
RiM trains LLMs to perform latent reasoning via fixed memory blocks processed in one forward pass using a two-stage curriculum, matching or exceeding prior latent methods on benchmarks.
MentalMap benchmark identifies a universal L3 reasoning cliff in LLMs' text-based spatial reasoning that persists across languages, scales, and prompting, and is replicated in human evaluations.
Chain of Thought risk decomposes into oracle-trajectory benefit and trajectory-mismatch cost, with stability determining bounded, linear, or exponential error growth.
PluRule is a new multimodal multilingual benchmark showing that state-of-the-art vision-language models perform only marginally better than a trivial baseline at detecting specific rule violations in pluralistic online communities.
SWE-Chain provides 155 chained version transitions and 1,660 requirements across 9 Python packages, where frontier agents resolve 44.8% of tasks on average and struggle to preserve functionality across releases.
LLMs rely on semantic cues for matrix-game equilibria but can acquire approximate computation via residual training on small instances, with a Lipschitz proof enabling transfer to larger anonymous games.
Online mistake bounds for autoregressive output learning can grow logarithmically with generation horizon M under end-to-end feedback but become independent of M with chain-of-thought trajectory access.
A transformer trained on random meaningless MicroPy programs generalizes to execute diverse human-written programs, providing empirical evidence it can act as a universal computer.
WMF-AM is a depth-parameterized benchmark that measures LLMs' cumulative state tracking ability without scratchpads, validated on 28 models across arithmetic and non-arithmetic tasks with ablations confirming the construct.
Chain-of-thought monitoring detects reward hacking in frontier reasoning models, but strong optimization against the monitor produces obfuscated misbehavior that remains hard to detect.
Massive activations are constant large values in LLMs that function as indispensable bias terms and concentrate attention probabilities on specific tokens.
Medusa augments LLMs with multiple decoding heads and tree-based attention to predict and verify several tokens in parallel, yielding 2.2-3.6x inference speedup via two fine-tuning regimes.
Process supervision significantly outperforms outcome supervision for training models on the MATH dataset, achieving 78% accuracy on a representative test subset with active learning and a released 800k step-label dataset.
PoT prompting improves numerical reasoning by having language models write programs executed by a computer instead of performing calculations in natural language chains of thought, with an average 12% gain over CoT.
State-writing models causally use edited scratchpad states in a controlled task at 80-91% accuracy on held-out examples, unlike final-answer-only and pretrained controls.
Mean-field equations for attention retrieval, teacher alignment, and logic overlap quantitatively match simulations and predict a sharp accuracy transition in a solvable transformer for permutation state tracking.
ProReviewer is an MDP-formulated proactive peer review agent trained with SFT and RL on an 8B model that outperforms larger frontier LLMs on review quality metrics.
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