Does the Deep-Layer Alignment Collapse Predict Anything? Representation vs. Behavior in Low-Rank and Full Fine-Tuning

When a contrastive vision-language encoder is fine-tuned, low-rank adaptation (LoRA) and full fine-tuning produce similar early-layer features but different late-layer features. This late-layer gap, measured by centered kernel alignment (CKA), has been read as proof that a small LoRA budget cannot adapt the target task well enough. We test whether this gap actually predicts the target accuracy it is supposed to explain. Across six datasets and three seeds, it does not. The deep-layer CKA gap swings over a range of $0.30$, while the accuracy gap between the two methods stays within three points; the two barely correlate, Spearman $\rho=-0.20$ ($p=0.42$). On two datasets the CKA gap even flips sign, yet the accuracy gap stays just as small. The real difference between the two methods shows up in how much each one forgets: full fine-tuning loses $19.7$ points of held-out transfer accuracy after adaptation, while LoRA loses only $15.3$ points, at matched target accuracy, the opposite of what has been reported for language models. The takeaway is that a representation-similarity score should not stand in for the behavior a fine-tuning method actually needs to deliver.