research
Topology Guided Long-Horizon Reasoning
SAGE combined algebraic sparsification and hyperbolic guidance across 12 benchmarks and seven model families.
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
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
- arXiv preprint 2609.30192arXiv · primary research
Corrections
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