PENCIL: Long Thoughts with Short Memory

Chenxiao Yang, Nathan Srebro, David Mcallester, Zhiyuan Li
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:71092-71156, 2025.

Abstract

While state-of-the-art LLMs have demonstrated great promise of using long Chains-of-Thought (CoT) to boost reasoning, scaling it up to more challenging problems is fundamentally limited by suboptimal memory usage — intermediate computations accumulate indefinitely in context even no longer needed for future thoughts. We introduce PENCIL, which incorporates a novel reduction mechanism into the autoregressive generation process that recursively clean up intermediate thoughts based on patterns learned from training. By alternately generating and erasing, PENCIL can think deeper to solve harder problems using shorter context and less computes. Empirically, for example, we demonstrate PENCIL with a small 25M-parameter transformer and 2048 context length solves Einstein’s puzzle — a task that challenges much larger models like GPT-4. Theoretically, we prove PENCIL can perform universal efficient computation by simulating any Turing machines with optimal time and space complexity, and thus can solve arbitrary computable tasks that are otherwise intractable for vanilla CoT.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-yang25ac, title = {{PENCIL}: Long Thoughts with Short Memory}, author = {Yang, Chenxiao and Srebro, Nathan and Mcallester, David and Li, Zhiyuan}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {71092--71156}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/yang25ac/yang25ac.pdf}, url = {https://proceedings.mlr.press/v267/yang25ac.html}, abstract = {While state-of-the-art LLMs have demonstrated great promise of using long Chains-of-Thought (CoT) to boost reasoning, scaling it up to more challenging problems is fundamentally limited by suboptimal memory usage — intermediate computations accumulate indefinitely in context even no longer needed for future thoughts. We introduce PENCIL, which incorporates a novel reduction mechanism into the autoregressive generation process that recursively clean up intermediate thoughts based on patterns learned from training. By alternately generating and erasing, PENCIL can think deeper to solve harder problems using shorter context and less computes. Empirically, for example, we demonstrate PENCIL with a small 25M-parameter transformer and 2048 context length solves Einstein’s puzzle — a task that challenges much larger models like GPT-4. Theoretically, we prove PENCIL can perform universal efficient computation by simulating any Turing machines with optimal time and space complexity, and thus can solve arbitrary computable tasks that are otherwise intractable for vanilla CoT.} }
Endnote
%0 Conference Paper %T PENCIL: Long Thoughts with Short Memory %A Chenxiao Yang %A Nathan Srebro %A David Mcallester %A Zhiyuan Li %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-yang25ac %I PMLR %P 71092--71156 %U https://proceedings.mlr.press/v267/yang25ac.html %V 267 %X While state-of-the-art LLMs have demonstrated great promise of using long Chains-of-Thought (CoT) to boost reasoning, scaling it up to more challenging problems is fundamentally limited by suboptimal memory usage — intermediate computations accumulate indefinitely in context even no longer needed for future thoughts. We introduce PENCIL, which incorporates a novel reduction mechanism into the autoregressive generation process that recursively clean up intermediate thoughts based on patterns learned from training. By alternately generating and erasing, PENCIL can think deeper to solve harder problems using shorter context and less computes. Empirically, for example, we demonstrate PENCIL with a small 25M-parameter transformer and 2048 context length solves Einstein’s puzzle — a task that challenges much larger models like GPT-4. Theoretically, we prove PENCIL can perform universal efficient computation by simulating any Turing machines with optimal time and space complexity, and thus can solve arbitrary computable tasks that are otherwise intractable for vanilla CoT.
APA
Yang, C., Srebro, N., Mcallester, D. & Li, Z.. (2025). PENCIL: Long Thoughts with Short Memory. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:71092-71156 Available from https://proceedings.mlr.press/v267/yang25ac.html.

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