SAGE Uses Topological Guidance to Fix Long-Horizon LLM Reasoning Biases

Xinyue Zeng · hf · 2026-09-28

A new HF paper, "SAGE: Mitigating Long-Horizon Reasoning Biases via Topological Guidance," attributes brittle long-horizon reasoning under sparse rewards to two biases: exploration bias (models drawn to locally plausible but structurally unstable branches) and compounding bias (small local deviations accumulate across depth).

It introduces Symbolic Closure Analysis (SCA) as both a theoretical lens and design principle, and builds SAGE combining algebraic sparsification (projecting candidates onto operator-indexed algebraic subspaces) with hyperbolic structural guidance (embedding reasoning states in negatively curved space for dense depth-wise signals).

Across 12 benchmarks and 7 model families SAGE beats competitive baselines, with up to an 8-fold improvement on the open Andrews-Curtis problem. Code is open-sourced.

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