S³: Spectral Null-Space Swap Makes Reasoning Models Efficient
Published in arXiv preprint, 2026
Recommended citation: Hongbo Ma, Sansheng Cao, Jiajun Fan, Bangji Yang, Ge Liu. "S³: Spectral Null-Space Swap Makes Reasoning Models Efficient." arXiv preprint arXiv:2609.37976, 2026. https://arxiv.org/abs/2609.37976
S³ makes reasoning models cheaper without any training. Reasoning capacity is found to live in the Thinking model’s weights outside the dominant singular subspace of its paired Non-thinking model; swapping in that null-space component composes the two checkpoints into a model that reasons with fewer tokens at the same accuracy, across dense and mixture-of-experts models from 2B to 30B.