Complexity Matters: Dynamics of Feature Learning in the Presence of
  Spurious Correlations
GuanWen Qiu Da Kuang Surbhi Goel
Existing research often posits spurious features as "easier" to learn than
core features in neural network optimization, but the impact of their relative
simplicity remains under-explored. Moreover they mainly focus on the end
performance intead of the learning dynamics of feature learning. In this paper,
we propose a theoretical framework and associated synthetic dataset grounded in
boolean function analysis which allows for fine-grained control on the relative
complexity (compared to core features) and correlation strength (with respect
to the label) of spurious features to study the dynamics of feature learning
under spurious correlation. Our setup uncovers several interesting phenomenon:
(1) stronger spurious correlations or simpler spurious features slow down the
rate of learning for the core features, (2) learning phases of spurious
features and core features are not always separable, (3) spurious features are
not forgotten even after core features are fully learned. We show that our
findings justify the success of retraining the last layer to remove spurious
correlation and also identifies limitations of popular debiasing algorithms
that exploit early learning of spurious features. We support our empirical
findings with theoretical analyses for the case of learning XOR features with a
one-hidden-layer ReLU network.