  In a recent, strongly emergent literature on few-shot CLIP adaptation, Linear
Probe (LP) has been often reported as a weak baseline. This has motivated
intensive research building convoluted prompt learning or feature adaptation
strategies. In this work, we propose and examine from convex-optimization
perspectives a generalization of the standard LP baseline, in which the linear
classifier weights are learnable functions of the text embedding, with
class-wise multipliers blending image and text knowledge. As our objective
function depends on two types of variables, i.e., the class visual prototypes
and the learnable blending parameters, we propose a computationally efficient
block coordinate Majorize-Minimize (MM) descent algorithm. In our full-batch MM
optimizer, which we coin LP++, step sizes are implicit, unlike standard
gradient descent practices where learning rates are intensively searched over
validation sets. By examining the mathematical properties of our loss (e.g.,
Lipschitz gradient continuity), we build majorizing functions yielding
data-driven learning rates and derive approximations of the loss's minima,
which provide data-informed initialization of the variables. Our image-language
objective function, along with these non-trivial optimization insights and
ingredients, yields, surprisingly, highly competitive few-shot CLIP
performances. Furthermore, LP++ operates in black-box, relaxes intensive
validation searches for the optimization hyper-parameters, and runs
orders-of-magnitudes faster than state-of-the-art few-shot CLIP adaptation
methods. Our code is available at:
\url{https://github.com/FereshteShakeri/FewShot-CLIP-Strong-Baseline.git}.
