The question, anchored

You noticed two things in your Week 10 Conversion Engine fine-tunes that look paradoxical: tiny LoRA adapters often shifted model behavior dramatically, while raising LoRA rank sometimes barely helped and sometimes destabilized outputs. Both observations have a single mechanism behind them — the intrinsic-low-rank hypothesis of fine-tuning. This explainer narrows hard to that mechanism, derives why low rank suffices, and shows you with a runnable script what actually changes when you raise rank.

What LoRA mechanically adapts

A transformer layer has weight matrices in the attention block (Q, K, V, O projections) and the MLP block (gate, up, down). For a hidden dimension d , each is roughly d × d .…