Echoes as Anchors: Probabilistic Costs and Attention Refocusing in LLM Reasoning
Zhuoyuan Hao, Zhuo Li, Wu Li, Fangming Liu, Min Zhang, Jing Li
Recent work improves reasoning in large reasoning models (LRMs) by test-time scaling through self-consistency and parallel thinking, adding generic "thinking tokens", or presenting the question twice, as in re-reading (RE2). However, 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 long chain-of-thought (CoT). In this work, we analyze and harness the model's tendency to restate the question, dubbed Echo of Prompt (EOP), as a front-loaded, compute-shaping mechanism, which can be viewed as self-generated prompt repetition inside the reasoning trace rather than in the input. Specifically, we formalize its probabilistic cost by casting echo removal as rejection-based conditioning, and define the Echo Likelihood Gap $Δ\mathcal{L}$ as a computable proxy linking early repetition to likelihood gains and downstream accuracy. We find that (1) in a causal intervention, reinserting an echo into failed GSM8K traces raises exact match by 7.9-10.4 points for two reasoning models but not for a non-reasoning base model; and (2) in length- and suffix-controlled likelihood analyses and layer-wise attention studies conducted to show that EOP's benefits go beyond verbosity, EOP increases answer to answer-prefix attention in middle layers, consistent with an attention refocusing mechanism. Building on these findings, we develop Echo-Distilled SFT (ED-SFT) to instill an "echo-then-reason" pattern through supervised finetuning, and training-free Echoic Prompting (EP) to re-ground the model mid-trace. We evaluate on GSM8K, MathQA, Hendrycks-MATH, AIME24, and MATH-500 under identical decoding settings and budgets, and find consistent gains over baselines, including thinking-token insertion. Our code is publicly released at https://github.com/hhh2210/echoes-as-anchors.
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