SAGE: Mitigating Long-Horizon Reasoning Biases via Topological Guidance

Problem

Long-horizon reasoning biases in large language models (LLMs) present significant challenges, particularly in sparse-reward environments. This paper addresses these biases, which can lead to suboptimal decision-making and exploration inefficiencies. The work is presented as a preprint and has not undergone peer review.

Method

The authors propose a novel framework called SAGE (Structural Admissibility-Guided Exploration) to alleviate exploration and compounding biases in long-horizon reasoning tasks. The framework is underpinned by two key components:

• Symbolic Closure Analysis (SCA): This theoretical lens is utilized to characterize the biases inherent in long-horizon reasoning, providing a foundational understanding of the issues at hand.
• Algebraic Sparsification: This technique projects locally admissible candidates onto operator-indexed algebraic subspaces, effectively reducing the complexity of the search space and enhancing the model's ability to explore relevant solutions.
• Hyperbolic Structural Guidance: This component embeds reasoning states into a negatively curved space, which aids in navigating the search space more effectively and reduces the likelihood of falling into local optima.

Results

SAGE was evaluated across 12 benchmarks involving 7 different model families, demonstrating superior performance compared to competitive baselines. Notably, in the Andrews-Curtis Problem, SAGE achieved up to an 8-fold improvement over a baseline, although the specific baseline model was not disclosed in the text. The results indicate a significant enhancement in the model's reasoning capabilities when utilizing the proposed framework.

Limitations

The authors do not report any limitations in their work. However, the absence of a specified baseline for the Andrews-Curtis Problem may limit the interpretability of the results. Additionally, as a preprint, the findings have yet to be validated through peer review, which could reveal further insights or critiques.

Why it matters

The implications of this work are substantial for downstream applications in AI that require robust long-horizon reasoning capabilities, such as complex decision-making systems and advanced planning algorithms. By addressing the biases that hinder performance in sparse-reward scenarios, SAGE could enhance the reliability and effectiveness of LLMs in real-world applications, paving the way for more sophisticated AI systems.