# Echoes as Anchors: Probabilistic Costs and Attention Refocusing in LLM Reasoning

arXiv: https://arxiv.org/abs/2602.06600 · HTML: https://mlsanity.com/paper/2602.06600/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 16 of its 18 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 16 of 16)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Focusing Attention: Towards Accurate Text Recognition in Natural Images](https://mlsanity.com/paper/1709.02054/) (2017)
- [Found in the Middle: Calibrating Positional Attention Bias Improves Long Context Utilization](https://mlsanity.com/paper/2406.16008/) (2024)
- [Look Twice Before You Answer: Memory-Space Visual Retracing for Hallucination Mitigation in Multimodal Large Language Models](https://mlsanity.com/paper/2410.03577/) (2024)
- [Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning](https://mlsanity.com/paper/2506.02867/) (2025)
- [1.4 Million Open-Source Distilled Reasoning Dataset to Empower Large Language Model Training](https://mlsanity.com/paper/2503.19633/) (2025)
- [Re-Reading Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2309.06275/) (2023)
- [Understanding the Repeat Curse in Large Language Models from a Feature Perspective](https://mlsanity.com/paper/2504.14218/) (2025)
- [EchoPrompt: Instructing the Model to Rephrase Queries for Improved In-context Learning](https://mlsanity.com/paper/2309.10687/) (2023)
- [LLMSteer: Improving Long-Context LLM Inference by Steering Attention on Reused Contexts](https://mlsanity.com/paper/2411.13009/) (2024)

## Built on by (most cited first, 2 of 2)

- [LASER: A Corrective Lens for LVLMs via Visual Attention Preservation and Sink Suppression](https://mlsanity.com/paper/2607.01707/) (2026)
- [Mirror, Mirror on the Wall: Prompt Echoing in Small Instruct Language Models](https://mlsanity.com/paper/2609.15045/) (2026)

## Abstract (arXiv)

Test-time compute allocation in large reasoning models (LRMs) is widely used and has applications in mathematical problem solving, code synthesis, and planning. Recent work has addressed this problem by scaling self-consistency and parallel thinking, adding generic ``thinking tokens'' and prompting models to re-read the question before answering. Unfortunately, these approaches either inject task-agnostic tokens or mandate heuristics that do not explain -- and often ignore -- the spontaneous repetition that many LRMs exhibit at the head of their internal chains. In contrast, we analyze and harness the model's tendency to restate the question, which we term the Echo of Prompt (EOP), as a front-loaded, compute-shaping mechanism. We formalize its probabilistic cost by casting echo removal as rejection-based conditioning and defining the Echo Likelihood Gap DeltaL as a computable proxy. This provides the missing theoretical link that links early repetition to likelihood gains and downstream accuracy. However, it does not by itself specify how to exploit EOP. Consequently, we develop Echo-Distilled SFT (ED-SFT) to instill an ``echo-then-reason'' pattern through supervised finetuning, and Echoic Prompting (EP) to re-ground the model mid-trace without training. While promising, quantifying benefits beyond verbosity is non-trivial. Therefore, we conduct length and suffix-controlled likelihood analyses together with layer-wise attention studies, showing that EOP increases answer to answer-prefix attention in middle layers, consistent with an attention refocusing mechanism. We evaluate on GSM8K, MathQA, Hendrycks-MATH, AIME24, and MATH-500 under identical decoding settings and budgets, and find consistent gains over baselines. Code is available at https://github.com/hhh2210/echoes-as-anchors.