Structural guidance improves long-horizon reasoning in large language models
SAGE: Mitigating Long-Horizon Reasoning Biases via Topological Guidance
Artificial Intelligence
Summary
Long tasks where a computer has to think many steps ahead are hard for language models, especially when rewards are rare. The authors found that models often make mistakes by exploring too many unhelpful paths or by letting small errors add up over time. They designed a new method called SAGE that uses math ideas to guide the model’s thinking, helping it avoid these problems. Tests show that SAGE helps models solve tough reasoning problems more accurately.
What this means in practice
- •For ai system builders: Improve AI agents that perform multi-step reasoning tasks by incorporating structural guidance to reduce reasoning errors over long sequences.
- •For algorithm engineers: Develop enhanced methods for guiding search and exploration in complex decision spaces to better handle sparse reward feedback.
Authors
Xinyue Zeng, Jiawei Zhang, Yujun Yan, Dawei Zhou
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.