@inproceedings{zheng-etal-2026-reward,
title = "When Reward-Free Signals Are Not Directions: A Gradient-Level Diagnostic for Test-Time Reasoning Optimization",
author = "Zheng, Shijie and
Dai, Yinxing and
Pu, Zhiqiang",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.1166/",
doi = "10.18653/2026.findings-emnlp.1166",
pages = "24687--24703",
ISBN = "979-8-89176-462-0",
abstract = "First-order test-time optimization (TTO) updates continuous variables such as logits or latent states for a single input. Successful methods usually rely on external reward models or verifiers to supply a semantic gradient. We ask whether reward-free signals from model distributions or prompted self-verification can supply comparable update directions for reasoning tasks. In logit-space TTO, we compare each reward-free gradient with an operational reward-model reference direction, instantiated as the reward-model gradient on the same logits. Across Qwen2.5-7B-Instruct, Qwen3-14B, and Llama-3.1-8B-Instruct, confidence gradients remain nearly orthogonal to the reference, entropy-slope gradients have vanishing scale near greedy rollouts, and terminal answer certainty is sparse and reference-sensitive. Prompted-verifier gradients are more reference-dependent: in a tokenizer-matched Llama diagnostic, four variants attain moderate RM-relative alignment and measurable local RM-score gains. Nevertheless, in end-to-end TTO on Qwen2.5-7B-Instruct and Llama-3.1-8B-Instruct, the selected reward-free signals produce no wrong-to-correct flips on MATH-500, AIME-2024, AIME-2025, or GSM8K, while a separate reward-model-guided TTO reproduction provides an external positive control with measurable gains."
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<abstract>First-order test-time optimization (TTO) updates continuous variables such as logits or latent states for a single input. Successful methods usually rely on external reward models or verifiers to supply a semantic gradient. We ask whether reward-free signals from model distributions or prompted self-verification can supply comparable update directions for reasoning tasks. In logit-space TTO, we compare each reward-free gradient with an operational reward-model reference direction, instantiated as the reward-model gradient on the same logits. Across Qwen2.5-7B-Instruct, Qwen3-14B, and Llama-3.1-8B-Instruct, confidence gradients remain nearly orthogonal to the reference, entropy-slope gradients have vanishing scale near greedy rollouts, and terminal answer certainty is sparse and reference-sensitive. Prompted-verifier gradients are more reference-dependent: in a tokenizer-matched Llama diagnostic, four variants attain moderate RM-relative alignment and measurable local RM-score gains. Nevertheless, in end-to-end TTO on Qwen2.5-7B-Instruct and Llama-3.1-8B-Instruct, the selected reward-free signals produce no wrong-to-correct flips on MATH-500, AIME-2024, AIME-2025, or GSM8K, while a separate reward-model-guided TTO reproduction provides an external positive control with measurable gains.</abstract>
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%0 Conference Proceedings
%T When Reward-Free Signals Are Not Directions: A Gradient-Level Diagnostic for Test-Time Reasoning Optimization
%A Zheng, Shijie
%A Dai, Yinxing
%A Pu, Zhiqiang
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F zheng-etal-2026-reward
%X First-order test-time optimization (TTO) updates continuous variables such as logits or latent states for a single input. Successful methods usually rely on external reward models or verifiers to supply a semantic gradient. We ask whether reward-free signals from model distributions or prompted self-verification can supply comparable update directions for reasoning tasks. In logit-space TTO, we compare each reward-free gradient with an operational reward-model reference direction, instantiated as the reward-model gradient on the same logits. Across Qwen2.5-7B-Instruct, Qwen3-14B, and Llama-3.1-8B-Instruct, confidence gradients remain nearly orthogonal to the reference, entropy-slope gradients have vanishing scale near greedy rollouts, and terminal answer certainty is sparse and reference-sensitive. Prompted-verifier gradients are more reference-dependent: in a tokenizer-matched Llama diagnostic, four variants attain moderate RM-relative alignment and measurable local RM-score gains. Nevertheless, in end-to-end TTO on Qwen2.5-7B-Instruct and Llama-3.1-8B-Instruct, the selected reward-free signals produce no wrong-to-correct flips on MATH-500, AIME-2024, AIME-2025, or GSM8K, while a separate reward-model-guided TTO reproduction provides an external positive control with measurable gains.
%R 10.18653/2026.findings-emnlp.1166
%U https://aclanthology.org/2026.findings-emnlp.1166/
%U https://doi.org/10.18653/2026.findings-emnlp.1166
%P 24687-24703
Markdown (Informal)
[When Reward-Free Signals Are Not Directions: A Gradient-Level Diagnostic for Test-Time Reasoning Optimization](https://aclanthology.org/2026.findings-emnlp.1166/) (Zheng et al., Findings 2026)
ACL