| title | SAGE: Mitigating Long-Horizon Reasoning Biases via Topological Guidance |
|---|---|
| authors | Xinyue Zeng, Jiawei Zhang, Yujun Yan, Dawei Zhou |
| date | 2026-09-24 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2609.30192 |
| upvotes | 8 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf code |
| abstract | Long-horizon reasoning remains a central challenge for large language models (LLMs) under sparse-reward regimes. We argue that this brittleness arises from two biases induced by complex reasoning spaces: an exploration bias, where models are drawn toward locally plausible but structurally unstable branches, and a compounding bias, where small local deviations accumulate across depth and suppress rare rewards. We introduce Symbolic Closure Analysis (SCA) as a theoretical lens characterizing how branching structures and sparse rewards induce these biases in long-horizon reasoning with local admissibility, and as a design principle for structural priors in less formal reasoning tasks. Motivated by this analysis, we propose SAGE (Structural Admissibility-Guided Exploration), a unified framework that injects structural guidance to alleviate exploration bias and compounding bias in long-horizon reasoning. SAGE combines two complementary structural guidance: algebraic sparsification, which projects locally admissible candidates onto operator-indexed algebraic subspaces to suppress spurious branching and mitigate exploration bias, and hyperbolic structural guidance, which embeds reasoning states into a negatively curved space to provide dense depth-wise signals and mitigate compounding bias. Across 12 benchmarks and 7 model families, SAGE outperforms competitive baselines. In particular, SAGE achieves up to an 8-fold improvement on the Andrews-Curtis problem, an open real-world long-horizon task. Code is available at: https://github.com/Susan571/SAGE-NeurIPS2026. |
cite
@misc{zeng2026sage,
title={SAGE: Mitigating Long-Horizon Reasoning Biases via Topological Guidance},
author={Xinyue Zeng and Jiawei Zhang and Yujun Yan and Dawei Zhou},
year={2026},
eprint={2609.30192},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2609.30192}
}