Frozen Factor or Spectral Band? Disentangling Two Choices in Low-Rank LoRA

Abstract

Spectral variants of low-rank adaptation (LoRA) choose both a subspace and which factor to freeze. We separate these choices by freezing the input factor A or output factor B on the top or bottom singular directions of pretrained weights, with learning rates selected separately. At rank 2, the same-band advantage of freezing A is larger than either within-factor band difference on all four task-model pairs with complete comparisons. Freezing B also trails comparable-budget free LoRA by 8-18 percentage points on five pairs spanning a formatting task and OpenBookQA. The A-frozen advantage persists in a single-GPU-model replication and within individual MLP module groups, including controls with equal or greater trainable counts for B frozen, and when A is frozen on a random orthonormal basis. The factor contrast weakens with rank. On OpenBookQA / Qwen2.5-1.5B at rank 16, PEFT's MiCA implementation trails comparable-budget LoRA by 3.08 points under a shared training recipe transferred from the MiCA paper. A trained oracle output subspace largely removes the low-rank deficit; partial warm-up gains recur across three direction seeds. The factor-versus-band ordering is descriptive; an approximate multiplicity audit weakens several earlier significance claims. These results extend known factor asymmetry by showing how its magnitude depends on spectral placement, rank and training conditions.

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