Local Perturbation Theory Explains Cross-Domain Interference in Multi-Domain RL Fine-Tuning

Single-domain RL post-training produces sparse, small-magnitude parameter edits that share active computation routes across domains, causing interference even when full-model gradients are nearly orthogonal — contradicting catastrophic forgetting and global gradient conflict explanations. The paper proves this under a local perturbation model and derives conditions for synergistic versus conflicting updates.