The Markovian Thinker: Architecture-Agnostic Linear Scaling of Reasoning

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Main Authors: Aghajohari, Milad, Chitsaz, Kamran, Kazemnejad, Amirhossein, Chandar, Sarath, Sordoni, Alessandro, Courville, Aaron, Reddy, Siva
Format: Preprint
Published: 2025
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author Aghajohari, Milad
Chitsaz, Kamran
Kazemnejad, Amirhossein
Chandar, Sarath
Sordoni, Alessandro
Courville, Aaron
Reddy, Siva
author_facet Aghajohari, Milad
Chitsaz, Kamran
Kazemnejad, Amirhossein
Chandar, Sarath
Sordoni, Alessandro
Courville, Aaron
Reddy, Siva
contents Reinforcement learning (RL) has recently become a strong recipe for training reasoning LLMs that produce long chains of thought (LongCoT). Yet the standard RL "thinking environment", where the state is the prompt plus all prior reasoning tokens, makes the state unbounded and forces attention-based policies to pay quadratic compute as thoughts lengthen. We revisit the environment itself. We propose Markovian Thinking, a paradigm in which the policy advances reasoning while conditioning on a constant-size state, decoupling thinking length from context size. As an immediate consequence this yields linear compute with constant memory. We instantiate this idea with Delethink, an RL environment that structures reasoning into fixed-size chunks. Within each chunk, the model thinks as usual; at the boundary, the environment resets the context and reinitializes the prompt with a short carryover. Through RL, the policy learns to write a textual state near the end of each chunk sufficient for seamless continuation of reasoning after reset. Trained in this environment, an R1-Distill 1.5B model reasons in 8K-token chunks yet thinks up to 24K tokens, matching or surpassing LongCoT-RL trained with a 24K budget. With test-time scaling, Delethink continues to improve where LongCoT plateaus. The effect of linear compute is substantial: we empirically estimate at 96K average thinking length LongCoT-RL costs 27 H100-months vs. 7 for Delethink. Analysis at RL initialization shows off-the-shelf reasoning models (1.5B-120B) often sample Markovian traces zero-shot across diverse benchmarks, providing positive samples that make RL effective at scale. Our results show that redesigning the thinking environment is a powerful lever: it enables very long reasoning without quadratic overhead and opens a path toward efficient, scalable reasoning LLMs.
format Preprint
id arxiv_https___arxiv_org_abs_2510_06557
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Markovian Thinker: Architecture-Agnostic Linear Scaling of Reasoning
Aghajohari, Milad
Chitsaz, Kamran
Kazemnejad, Amirhossein
Chandar, Sarath
Sordoni, Alessandro
Courville, Aaron
Reddy, Siva
Machine Learning
Artificial Intelligence
Computation and Language
Reinforcement learning (RL) has recently become a strong recipe for training reasoning LLMs that produce long chains of thought (LongCoT). Yet the standard RL "thinking environment", where the state is the prompt plus all prior reasoning tokens, makes the state unbounded and forces attention-based policies to pay quadratic compute as thoughts lengthen. We revisit the environment itself. We propose Markovian Thinking, a paradigm in which the policy advances reasoning while conditioning on a constant-size state, decoupling thinking length from context size. As an immediate consequence this yields linear compute with constant memory. We instantiate this idea with Delethink, an RL environment that structures reasoning into fixed-size chunks. Within each chunk, the model thinks as usual; at the boundary, the environment resets the context and reinitializes the prompt with a short carryover. Through RL, the policy learns to write a textual state near the end of each chunk sufficient for seamless continuation of reasoning after reset. Trained in this environment, an R1-Distill 1.5B model reasons in 8K-token chunks yet thinks up to 24K tokens, matching or surpassing LongCoT-RL trained with a 24K budget. With test-time scaling, Delethink continues to improve where LongCoT plateaus. The effect of linear compute is substantial: we empirically estimate at 96K average thinking length LongCoT-RL costs 27 H100-months vs. 7 for Delethink. Analysis at RL initialization shows off-the-shelf reasoning models (1.5B-120B) often sample Markovian traces zero-shot across diverse benchmarks, providing positive samples that make RL effective at scale. Our results show that redesigning the thinking environment is a powerful lever: it enables very long reasoning without quadratic overhead and opens a path toward efficient, scalable reasoning LLMs.
title The Markovian Thinker: Architecture-Agnostic Linear Scaling of Reasoning
topic Machine Learning
Artificial Intelligence
Computation and Language
url https://arxiv.org/abs/2510.06557