training a rank-one adapter on a full-rank 3×3 layer

W = W₀ + AB

Each 3×3 matrix is a map from inputs to outputs, and matching a target map is a small learning task. Navy is held fixed during training, periwinkle is the current map W, and teal is the target.

W₀
011
101
110
p₁p₂p₃
W_target
p₁p₂p₃
step 0
W₀
+
A
·
B
=
W