# Rethinking Dense Sequential Chains: Reasoning Language Models Can Extract Answers from Sparse, Order-Shuffling Chain-of-Thoughts

arXiv: https://arxiv.org/abs/2605.07307 · HTML: https://mlsanity.com/paper/2605.07307/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 8 of its 13 references that are in the map.
- First posted on arXiv 8 May 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 8 of 8)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [Text and Patterns: For Effective Chain of Thought, It Takes Two to Tango](https://mlsanity.com/paper/2209.07686/) (2022)
- [CodeElo: Benchmarking Competition-level Code Generation of LLMs with Human-comparable Elo Ratings](https://mlsanity.com/paper/2501.01257/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Readout Shortcut: Positional Number Copying Dominates Arithmetic CoT Readout in Small Language Models](https://mlsanity.com/paper/2605.22870/) (2026)

## Abstract (arXiv)

Modern reasoning language models generate dense, sequential chain-of-thought traces implicitly assuming that every token contributes and that steps must be consumed in order. We challenge both assumptions through a systematic intervention pipeline--removal, masking, shuffling, and noise injection--applied to model-generated reasoning chains across three models and three benchmarks. Our findings are counterintuitive on three dimensions. Order: Does the sequential order of a reasoning chain matter for answer extraction? No--line-level shuffling reduces accuracy by less than 0.5 pp; word-level shuffling retains 62%-89% accuracy; only token-level shuffling collapses to near zero. Pretrained-only and instruction-tuned variants exhibit near-identical tolerance (78.67% vs. 78.00% under line shuffling), indicating order-independence originates from pretraining rather than reasoning-specific fine-tuning. Dense: Is all the information in a reasoning chain important for answer extraction? No--masking numeric digits collapses accuracy to exactly 0%, while masking alphabetic prose improves accuracy by 4.7 pp. Robustness: Is a reasoning chain that is both order-shuffling and non-dense still robust? Yes--the most aggressively reduced representation (all natural language removed, lines arbitrarily shuffled) still achieves 83% accuracy, and injecting false answers at 3x true-answer frequency leaves accuracy unchanged (83.3%->83.3%), falsifying a frequency-based extraction account. These results establish that answer extraction operates on a sparse, order-insensitive, and structurally robust informational substrate, opening paths toward parallelized and token-efficient reasoning generation.