SpectraGain: Rank-Decoupled Weight Adaptation via Low-Rank Spectral Gains

Directly factorizing a weight correction ties its rank to the trainable-parameter budget. We introduce Carrier-Conditioned Spectral Gain Adaptation (SpectraGain), which instead factorizes a real-valued spectral gain and applies it to the frozen weight spectrum. This produces a carrier-conditioned circular update whose realized rank can exceed the generator rank, while preserving the pretrained model at initialization. We characterize the resulting update structure and evaluate SpectraGain across language, reasoning, and vision tasks. Controlled comparisons with closely related operators, same-generator coupling replacements, and fixed-checkpoint rank interventions examine how coupling geometry and correction structure shape downstream performance. A rematerialized implementation further enables long-context training, with its memory and runtime costs characterized against standard and fused low-rank adaptation.