Spectral Rewiring Improves LLM Reasoning, Merging, and Exploration.

Reinforcement learning is a common post-training technique for large language models (LLMs), but it often leads to two significant bottlenecks: suppressed reasoning performance and interference when combining multiple capabilities through multi-domain training or model merging. This study reveals that the reasoning-effective elements of these updates are largely concentrated within the base model's spectral space. Motivated by this insight, the researchers developed Subspace-Aligned Rewiring (SAR), a post-hoc editing method. SAR works by retaining this crucial spectral core while discarding orthogonal components of the updates. This approach effectively preserves reasoning gains and filters out residual update directions that might otherwise degrade performance or amplify cross-domain interference. Across various model families and scales, SAR successfully extracts compact reasoning cores using a minimal fraction (around 0.58%) of total parameters. It maintains over 99% of post-training performance, improves high-k exploration in mathematical reasoning, and enhances agentic coding across multiple benchmarks. Furthermore, SAR purifies mixed-domain training updates, releasing suppressed coding capabilities while preserving math reasoning and instruction following. It also facilitates superior model merging, yielding cross-domain generalization that surpasses previous merging baselines and even the best single-domain experts. Overall, SAR demonstrates that extracting reasoning-effective updates from parameter geometry offers a training-free mechanism to boost reasoning and multi-domain performance.