We introduce Extended-SVD Low-Rank Adaptation, a parameter-efficient framework that extends the pretrained singular subspace while retaining a frozen spectral coordinate system and fixed singular-value-derived scaling. Its stabilized variant, PLORA (Procrustes Low-Rank Adaptation), applies localized Procrustes-inspired reorientation to the extended basis and confines task-specific learning to compact routing matrices P, R, and Q.

Across GLUE and vision benchmarks, PLORA achieves competitive performance with substantially fewer trainable parameters. In the full-network comparison, PLORA-r8 uses substantially fewer trainable parameters, although the performance gap varies by task. Beyond accuracy, PLORA produces task- and architecture-dependent changes in conditioning, effective rank, and subspace evolution.

Ablations show that Random Bases produce poorer routing-core conditioning and markedly lower top-r right-subspace overlap in the evaluated NLP tasks. In the evaluated settings, pretrained spectral bases are associated with more favorable optimization geometry, while Procrustes reorientation acts as an optimization-geometric regularizer. Overall, Extended-SVD provides a structured low-rank adaptation framework for studying the role of pretrained geometry in PEFT.