  Supervised learning can be viewed as distilling relevant information from
input data into feature representations. This process becomes difficult when
supervision is noisy as the distilled information might not be relevant. In
fact, recent research shows that networks can easily overfit all labels
including those that are corrupted, and hence can hardly generalize to clean
datasets. In this paper, we focus on the problem of learning with noisy labels
and introduce compression inductive bias to network architectures to alleviate
this over-fitting problem. More precisely, we revisit one classical
regularization named Dropout and its variant Nested Dropout. Dropout can serve
as a compression constraint for its feature dropping mechanism, while Nested
Dropout further learns ordered feature representations w.r.t. feature
importance. Moreover, the trained models with compression regularization are
further combined with Co-teaching for performance boost.
  Theoretically, we conduct bias-variance decomposition of the objective
function under compression regularization. We analyze it for both single model
and Co-teaching. This decomposition provides three insights: (i) it shows that
over-fitting is indeed an issue for learning with noisy labels; (ii) through an
information bottleneck formulation, it explains why the proposed feature
compression helps in combating label noise; (iii) it gives explanations on the
performance boost brought by incorporating compression regularization into
Co-teaching. Experiments show that our simple approach can have comparable or
even better performance than the state-of-the-art methods on benchmarks with
real-world label noise including Clothing1M and ANIMAL-10N. Our implementation
is available at https://yingyichen-cyy.github.io/CompressFeatNoisyLabels/.
