# The Coupling Tax: How Shared Token Budgets Undermine Visible Chain-of-Thought Under Fixed Output Limits

Source: [The Coupling Tax: How Shared Token Budgets Undermine Visible Chain-of-Thought Under Fixed Output Limits](<https://www.sota2.com/research/paper/6a0162b8dbc836b87d8232fd>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-12T05:00:12.036Z

Authors: Wenhua Nie, Junlin Liu, Jianan Wu, Zijie Meng, Yilong Fan, Zhang Zijian, Haoran Zheng, Jyh-Shing Roger Jang

Published: 2026-05-08T12:54:53.000Z

## Abstract

Chain-of-thought reasoning is often treated as a monotone way to improve language-model accuracy by letting a model think longer. We identify a countervailing effect, the coupling tax: when reasoning traces and final answers share one output-token budget, long traces can crowd out the answer they are meant to support. Across GSM8K, MATH-500, and five BIG-Bench Hard tasks with Qwen3 models at three scales, non-thinking mode matches or outperforms thinking mode on GSM8K and MATH-500 at every budget up to 2048 tokens, while harder tasks shift the crossover to larger budgets. We derive a truncation-waste decomposition, $\\mathrm{Acc}\_{\\mathrm{think}}(b)=\\alpha\_c F\_L(b)+\\alpha\_t(1-F\_L(b))$, that predicts this crossover from chain-length and accuracy statistics and explains inverse scaling within the Qwen family. A DeepSeek-R1-Distill-Llama-8B replication shows the same pattern under a different thinking interface. As a mitigation, split-budget generation decouples reasoning and answer budgets; on full MATH-500, IRIS reaches 74.0% accuracy, a strengthened extraction variant reaches 78.8%, and a fixed non-oracle SC+IRIS gate reaches 83.6%. The results show that test-time reasoning should be evaluated as a budget-allocation problem, not only as a question of whether longer traces are available.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Mathematical Reasoning on MATH 500 (Accuracy, Total Tokens)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math-500-accuracy-total-tokens.md>): Mathematical Reasoning; MATH 500; Accuracy: 83.6.

- [Reasoning on BIG-Bench Hard (5 subtasks full)](<https://www.sota2.com/research/sota/reasoning-on-big-bench-hard-5-subtasks-full.md>): Reasoning; BIG-Bench Hard 5 subtasks (full); Accuracy: 86.

- [Mathematical Reasoning on GSM8K n=200 (pilot)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-gsm8k-n-200-pilot.md>): Mathematical Reasoning; GSM8K n=200 (pilot); Accuracy: 94.

- [Mathematical Reasoning on GSM8K (full set)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-gsm8k-full-set.md>): Mathematical Reasoning; GSM8K n=1,319 (full set); Accuracy: 91.43.

- [Mathematical Reasoning on MATH-500 n=200 (pilot)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math-500-n-200-pilot.md>): Mathematical Reasoning; MATH-500 n=200 (pilot); Accuracy (%): 61.

- [Mathematical Reasoning on MATH-500 (Accuracy, Delta, Token Length, Ratio)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math-500-accuracy-delta-token-length-ratio.md>): Mathematical Reasoning; MATH 500; Accuracy: 80.5.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2605.07686>)

[PDF](<https://arxiv.org/pdf/2605.07686.pdf>)