Bilinear Optimization Divergence: Diagnosing Factor-Constrained LoRA Continual Learning
Orthogonality in a LoRA factor does not by itself specify what the composed update protects: the answer depends on the task-start state, the parameterization, and the realized optimizer displacement. We formalize this question through Bilinear Optimization Divergence (BOD), an anchor-relative diagnostic of effective-update response on selected historical features. The finite-step analysis distinguishes two cases. In a shared adapter, protecting the routing displacement leaves a learned-anchor residual through the changing companion factor. In a fresh zero-output block, a feasible routing state can protect the composed update while both current factors remain trainable. These conditions yi...
| Authors | YongShun Wang, JianLin Su, Yong Ma |
|---|---|
| Primary category | cs.LG |
| Published | 20 September 2026 |
| Last updated at source | 20 September 2026 |
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