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    <abstract>Reasoning-oriented language model training relies on traces that expose learnable dependencies, yet existing data-selection criteria use length, perplexity, difficulty, or judge-assigned quality. We argue that useful reasoning traces should also be sensitive to dependency order: intermediate steps are easier to encode in their natural premise-to-conclusion order but less predictable when dependency-revealing order is perturbed.\par We introduce Local-DeltaAvg, a training-free data-selection metric. For each reasoning trace, we construct a semantically reversed counterpart that preserves problem content while perturbing dependency-revealing order. A fixed probe model scores both trajectories, and Local-DeltaAvg computes a paired local negative log-likelihood gap between the original and reversed contexts. The resulting probe-dependent score estimates the conditional encoding cost induced by order perturbation and identifies where this sensitivity is concentrated.\par We evaluate Local-DeltaAvg as a relative ranking signal for reasoning-oriented continued-pretraining data selection, followed by an identical downstream SFT protocol. Under matched token budgets, it consistently outperforms length-, perplexity-, difficulty-, and judge-based selection across diverse reasoning benchmarks. Control analyses show that semantic reversal is essential and that high-gap regions align with annotated critical reasoning steps. These results suggest that dependency-order sensitivity is a lightweight and effective proxy for reasoning-data utility.</abstract>
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%0 Conference Proceedings
%T Directional Structurality: A Lightweight Proxy for Reasoning Data Quality
%A Chen, Ze
%A Liu, Kaixuan
%A Zhang, Haomai
%A Zou, Jiaxuan
%A Chen, Zhuo
%A Tan, Xiaotian
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F chen-etal-2026-directional
%X Reasoning-oriented language model training relies on traces that expose learnable dependencies, yet existing data-selection criteria use length, perplexity, difficulty, or judge-assigned quality. We argue that useful reasoning traces should also be sensitive to dependency order: intermediate steps are easier to encode in their natural premise-to-conclusion order but less predictable when dependency-revealing order is perturbed.\par We introduce Local-DeltaAvg, a training-free data-selection metric. For each reasoning trace, we construct a semantically reversed counterpart that preserves problem content while perturbing dependency-revealing order. A fixed probe model scores both trajectories, and Local-DeltaAvg computes a paired local negative log-likelihood gap between the original and reversed contexts. The resulting probe-dependent score estimates the conditional encoding cost induced by order perturbation and identifies where this sensitivity is concentrated.\par We evaluate Local-DeltaAvg as a relative ranking signal for reasoning-oriented continued-pretraining data selection, followed by an identical downstream SFT protocol. Under matched token budgets, it consistently outperforms length-, perplexity-, difficulty-, and judge-based selection across diverse reasoning benchmarks. Control analyses show that semantic reversal is essential and that high-gap regions align with annotated critical reasoning steps. These results suggest that dependency-order sensitivity is a lightweight and effective proxy for reasoning-data utility.
%U https://aclanthology.org/2026.emnlp-main.345/
%P 7936-7957

Markdown (Informal)

[Directional Structurality: A Lightweight Proxy for Reasoning Data Quality](https://aclanthology.org/2026.emnlp-main.345/) (Chen et al., EMNLP 2026)

• Directional Structurality: A Lightweight Proxy for Reasoning Data Quality (Chen et al., EMNLP 2026)

ACL

• Ze Chen, Kaixuan Liu, Haomai Zhang, Jiaxuan Zou, Zhuo Chen, and Xiaotian Tan. 2026. Directional Structurality: A Lightweight Proxy for Reasoning Data Quality. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 7936–7957, Budapest, Hungary. Association for Computational Linguistics.