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This paper introduces Subspace-Aligned Rewiring (SAR), a novel post-hoc editing method that optimally retains the spectral core of large language models while eliminating orthogonal components that hinder performance. By focusing on the spectral space of model parameters, SAR preserves over 99% of post-training performance and enhances exploration in mathematical reasoning, achieving significant improvements across multiple benchmarks. The approach also facilitates effective model merging, enabling cross-domain generalization that outperforms both previous merging techniques and single-domain experts.
Extracting reasoning-effective updates from model geometry can dramatically enhance multi-domain performance while maintaining high reasoning capabilities.
Reinforcement learning has become a standard post-training recipe for large language models, but dense full-parameter updates create two deployment-relevant bottlenecks: suppressed reasoning performance, often reflected by premature saturation of test-time scaling, and interference when consolidating multiple capabilities through multi-domain training or model merging. We show that the reasoning-effective component of these updates is largely concentrated in the base model's spectral space, motivating Subspace-Aligned Rewiring (SAR), a post-hoc editing method that retains this spectral core while removing orthogonal components. SAR therefore preserves reasoning gains and filters residual update directions that suppress performance or amplify cross-domain interference. Across several model families and scales, SAR extracts compact reasoning cores using as little as approximately 0.58% of total parameters: it preserves over 99% of post-training performance and improves high-k exploration in mathematical reasoning, and generalizes to agentic coding by improving six of seven open benchmarks on an in-house model. SAR also purifies mixed-domain training updates by releasing suppressed coding capability while maintaining math reasoning and instruction following. It further enables model merging across experts, yielding cross-domain generalization that surpasses previous merging baselines and even the best single-domain experts. Overall, SAR shows that extracting reasoning-effective updates from parameter geometry can serve as a training-free mechanism to improve reasoning and multi-domain performance.
