Machine Heart

Oct 7, 2026 · Artificial Intelligence

SAGE: Topological Guidance Mitigates Long-Horizon Reasoning Biases, 8x Lean Pass Rate

Researchers from Virginia Tech, UW-Madison, and Dartmouth introduce SAGE, a post-training method that uses symbolic closure analysis to diagnose exploration and accumulation biases in long-horizon reasoning, applying algebraic sparsification and hyperbolic structure guidance to improve sampling and provide early feedback, achieving near 8x Lean verification pass rate on Andrews-Curtis tasks and outperforming baselines across 12 benchmarks.