Sharp Rates and a One-Line Correction for Spectral Representation Learning
The paper says spectral self-supervised features should be judged by task-alignment, not isotropy, and proposes a positive-pair reweighting when they miss.
Tang, Tan, and Han argue that transfer risk depends on the task covariance’s compression onto the leading singular directions of the cross-view operator. They prove sharp regret rates, including a worst-case bound of exactly `1 - 1/κ(Λ)`, and say no task-agnostic representation can improve on the limit. The proposed diagnostic uses a small labeled budget and can refuse when the task bank cannot support the requested width. In experiments, the correction cuts controlled-data regret from `0.86` to `0.003`, while a CIFAR-100 encoder is predicted to need no correction. ArXiv · AI/CL/LG's note
Tang, Tan, and Han argue that transfer risk depends on the task covariance’s compression onto the leading singular directions of the cross-view operator. They prove sharp regret rates, including a worst-case bound of exactly `1 - 1/κ(Λ)`, and say no task-agnostic representation can improve on the limit. The proposed diagnostic uses a small labeled budget and can refuse when the task bank cannot support the requested width. In experiments, the correction cuts controlled-data regret from `0.86` to `0.003`, while a CIFAR-100 encoder is predicted to need no correction. ArXiv · AI/CL/LG's note
score 4