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Topology Guided Long-Horizon Reasoning

SAGE combined algebraic sparsification and hyperbolic guidance across 12 benchmarks and seven model families.

Published Updated Story ID: mp-2026-09-26-012
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Summary

SAGE combined algebraic sparsification and hyperbolic guidance across 12 benchmarks and seven model families.

The framework treats long reasoning as a branching-space problem: locally plausible paths can be structurally unstable, and small deviations compound before a sparse reward arrives. SAGE projects candidates into operator-indexed subspaces and embeds reasoning states in negatively curved space to provide depth-wise guidance. The authors report gains over competing baselines, including up to an eightfold improvement on their Andrews-Curtis task. The result is benchmark evidence for these structural priors, not a solution to the underlying open mathematical problem.

Why it matters

SAGE combined algebraic sparsification and hyperbolic guidance across 12 benchmarks and seven model families.

Limits and context

  • The result is benchmark evidence for these structural priors, not a solution to the underlying open mathematical problem.

Key claims

  1. SAGE combined algebraic sparsification and hyperbolic guidance across 12 benchmarks and seven model families.

    Qualification: The result is benchmark evidence for these structural priors, not a solution to the underlying open mathematical problem.

    Evidence: source-2026-09-26-012

Sources

  1. arXiv preprint 2609.30192arXiv · primary research

Corrections

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