# Lightning Weave: Improving the Accuracy-Efficiency Frontier of Reasoning Models through Capability Composition

arXiv: https://arxiv.org/abs/2609.14708 · HTML: https://mlsanity.com/paper/2609.14708/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 33 of its 75 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 33)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Branch-Train-Merge: Embarrassingly Parallel Training of Expert Language Models](https://mlsanity.com/paper/2208.03306/) (2022)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [MiMo: Unlocking the Reasoning Potential of Language Model -- From Pretraining to Posttraining](https://mlsanity.com/paper/2505.07608/) (2025)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [Scaling Reasoning Efficiently via Relaxed On-Policy Distillation](https://mlsanity.com/paper/2603.11137/) (2026)
- [MOPD: Multi-Teacher On-Policy Distillation for Capability Integration in LLM Post-Training](https://mlsanity.com/paper/2606.30406/) (2026)
- [Unlocking Efficient Long-to-Short LLM Reasoning with Model Merging](https://mlsanity.com/paper/2503.20641/) (2025)
- [Nemotron-Cascade 2: Post-Training LLMs with Cascade RL and Multi-Domain On-Policy Distillation](https://mlsanity.com/paper/2603.19220/) (2026)
- [Not All Disagreement Is Learnable: Token Teachability in On-Policy Distillation](https://mlsanity.com/paper/2605.26844/) (2026)
- [Klear-Reasoner: Advancing Reasoning Capability via Gradient-Preserving Clipping Policy Optimization](https://mlsanity.com/paper/2508.07629/) (2025)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [DLER: Doing Length pEnalty Right - Incentivizing More Intelligence per Token via Reinforcement Learning](https://mlsanity.com/paper/2510.15110/) (2025)
- [Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation](https://mlsanity.com/paper/2604.13010/) (2026)
- [Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why](https://mlsanity.com/paper/2605.10889/) (2026)
- [Counteraction-Aware Multi-Teacher On-Policy Distillation for General Capability Recovery with Domain Preservation](https://mlsanity.com/paper/2605.27115/) (2026)
- [Weak-to-Strong Generalization via Direct On-Policy Distillation](https://mlsanity.com/paper/2607.05394/) (2026)
- [Open-MOPD: Diagnosing and Fixing Capability Imbalance in Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2608.19098/) (2026)
- [Revisiting Model Interpolation for Efficient Reasoning](https://mlsanity.com/paper/2510.10977/) (2025)
- [PromptCoT 2.0: Scaling Prompt Synthesis for Large Language Model Reasoning](https://mlsanity.com/paper/2509.19894/) (2025)
- [Weak-to-Strong On-Policy Distillation](https://mlsanity.com/paper/2607.26246/) (2026)
- [ORBIT: On-policy Exploration-Exploitation for Controllable Multi-Budget Reasoning](https://mlsanity.com/paper/2601.08310/) (2026)
- [Cross-Tokenizer On-Policy Distillation via Byte-Prefix Marginalization](https://mlsanity.com/paper/2607.22334/) (2026)
- [The Thinking Spectrum: An Empirical Study of Tunable Reasoning in LLMs through Model Merging](https://mlsanity.com/paper/2509.22034/) (2025)
- [SimpleOPD: Simple Tokenizer-Agnostic On-Policy Distillation for Long-Context Reasoning](https://mlsanity.com/paper/2608.14277/) (2026)

## Abstract (arXiv)

A core goal of efficient reasoning is to improve the accuracy-efficiency frontier. However, jointly improving reasoning accuracy and inference efficiency can be challenging, as the two objectives can favor different reasoning behaviors. Independently post-trained models already offer distinct strengths in accuracy and efficiency. We introduce Lightning Weave, a post-training framework that extracts and composes these independently learned capabilities in a single student through on-policy distillation. Each acquired capability is represented by the policy shift from the model before post-training to the resulting specialist. Lightning Weave combines aligned log-ratio shifts at shared student token states and uses Tilted-Target DOPD to convert the cached signals into a stable learning target. Each anchor pair scores the cached trajectories once, enabling subsequent student training without serving multiple live anchor models concurrently. Across diverse student models and benchmarks in mathematics and code, Lightning Weave substantially improves upon the base students and achieves a state-of-the-art accuracy-efficiency frontier. On Qwen3.5-4B, it raises HMMT 2025 accuracy from 59.2% to 64.0% with 10.7% fewer response tokens, and LiveCodeBench v5 accuracy from 41.7% to 54.2% with 9.6% fewer response tokens. Adjusting the relative strengths of the anchor signals yields a strong empirical accuracy-efficiency Pareto frontier. These results establish Lightning Weave as a new practical route to efficient reasoning through capability composition. Code is released at https://github.com/jet-ai-projects/Lightning-Weave.