arXiv: cs.AI preprintsInternational6 November 2026
FILO: A Unified Fisher-Geometric Framework for Low-Rank Adaptation
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arXiv:2605.08734v2 Announce Type: replace-cross Abstract: Low-Rank Adaptation (LoRA) reparameterizes a weight matrix $W$ as a product of two low-rank factors, but the Jacobian $J_G$ of the generator mapping the factors to the weight matrix is rank-deficient, so the factor-space preconditioner $J_G^* F_t J_G$ induced by any $W$-space preconditioner $F_t$ is singular, and consequently the standard chain rule cannot be uniquely inverted to map a preconditioned $W$-space direction back to a factor-space update. Therefore, we introduce FILO, a unified Fisher-geometric framework for low-rank adaptat
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