Improving the accuracy‑efficiency frontier is a central goal of efficient reasoning. Accuracy and inference speed often favor different reasoning behaviors, so optimizing one can hurt the other. Existing post‑training models each excel at either accuracy or efficiency, offering complementary capabilities.
We introduce Lightning Weave, a post‑training framework that extracts those independently learned capabilities and composes them in a single student via on‑policy distillation. Each capability is captured as a policy shift—the change from the pre‑training model to a specialist. The framework aligns log‑ratio shifts at shared student token states and employs Tilted‑Target DOPD to turn cached signals into a stable learning target.
Practically, each anchor pair scores its cached trajectories once, allowing subsequent student training without running multiple live anchor models concurrently. This preserves signal fidelity while dramatically reducing compute overhead.
Across diverse student models and benchmarks in mathematics and code, Lightning Weave substantially outperforms the baselines and reaches a state‑of‑the‑art accuracy‑efficiency frontier. On Qwen3.5‑4B, HMMT 2025 accuracy rises from 59.2% to 64.0% with 10.7% fewer response tokens, and LiveCodeBench v5 accuracy climbs from 41.7% to 54.2% with 9.6% fewer tokens. Adjusting the relative strengths of anchor signals yields a strong empirical Pareto frontier.
These findings establish Lightning Weave as a practical route to efficient reasoning through capability composition. Code will be released soon.
Review