aiqbench analysis
This research establishes that for certain serial reasoning tasks, the "chain of thought" in transformers performs essential computational work rather than serving as mere decoration. By modeling transformers as shallow circuits, the study proves that erasing or shuffling these chains causes accuracy to collapse to a theoretical limit known as the task ceiling. These findings clarify the fundamental necessity of iterative reasoning steps for solving complex problems like finite group word problems and advanced math benchmarks.
Ceiling of a Task: When Can a Transformer Succeed Without Its Chain of Thought?
arXiv:2609.33134v1 Announce Type: new Abstract: Reasoning models generate long chains of thought before they answer, yet it is debated whether the content of these chains does real computational work or is largely decorative. We study this question by viewing a transformer as a shallow circuit. One forward pass through a fixed number of layers has constant depth, so any procedure that runs the model a constant number of times is a shallow circuit. We call the best accuracy that a shallow circuit can reach on a task the ceiling of the task, and a task is serial if its ceiling lies below one. We prove three results on serial tasks that hold for every transformer, no matter how it was trained. Necessity: replacing the chain by anything that does not depend on its content, such as filler tokens or a restatement of the question, drives the accuracy down to the ceiling, and on a maximally serial task down to chance. Depth: no shallow computation can write the chain of a model whose accuracy exceeds the ceiling, not even approximately. Locality: the answer is one shallow pass away from the finished chain, so all of the serial reasoning happens in the chain. On word problems of finite groups, whose ceilings are known, small transformers trained from scratch, with or without reinforcement learning, attain the predicted numbers: chain-trained models solve every input length and fall to chance when the chain is erased, chainless models collapse to the ceiling as the input length grows, and open-weight reasoning models given the same problem in words return to the baseline without their chain. On MATH-500 and AIME, erasing the chain costs open reasoning models 0.52 to 0.82 accuracy, a sentence shuffle is harmless, and a token shuffle is as harmful as erasing; the same holds for checkpoints trained by GRPO with a correct or a random reward. The ceiling of a task therefore answers when a transformer can succeed without its chain of thought.
Title:Ceiling of a Task: When Can a Transformer Succeed Without Its Chain of Thought?
Abstract:Reasoning models generate long chains of thought before they answer, yet it is debated whether the content of these chains does real computational work or is largely decorative. We study this question by viewing a transformer as a shallow circuit. One forward pass through a fixed number of layers has constant depth, so any procedure that runs the model a constant number of times is a shallow circuit. We call the best accuracy that a shallow circuit can reach on a task the ceiling of the task, and a task is serial if its ceiling lies below one. We prove three results on serial tasks that hold for every transformer, no matter how it was trained. Necessity: replacing the chain by anything that does not depend on its content, such as filler tokens or a restatement of the question, drives the accuracy down to the ceiling, and on a maximally serial task down to chance. Depth: no shallow computation can write the chain of a model whose accuracy exceeds the ceiling, not even approximately. Locality: the answer is one shallow pass away from the finished chain, so all of the serial reasoning happens in the chain. On word problems of finite groups, whose ceilings are known, small transformers trained from scratch, with or without reinforcement learning, attain the predicted numbers: chain-trained models solve every input length and fall to chance when the chain is erased, chainless models collapse to the ceiling as the input length grows, and open-weight reasoning models given the same problem in words return to the baseline without their chain. On MATH-500 and AIME, erasing the chain costs open reasoning models 0.52 to 0.82 accuracy, a sentence shuffle is harmless, and a token shuffle is as harmful as erasing; the same holds for checkpoints trained by GRPO with a correct or a random reward. The ceiling of a task therefore answers when a transformer can succeed without its chain of thought.
Artificial Intelligence (cs.AI)
arXiv:2609.33134 [cs.AI]
(or arXiv:2609.33134v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.33134 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 432 words
