  Class Incremental Learning (CIL) aims at learning a multi-class classifier in
a phase-by-phase manner, in which only data of a subset of the classes are
provided at each phase. Previous works mainly focus on mitigating forgetting in
phases after the initial one. However, we find that improving CIL at its
initial phase is also a promising direction. Specifically, we experimentally
show that directly encouraging CIL Learner at the initial phase to output
similar representations as the model jointly trained on all classes can greatly
boost the CIL performance. Motivated by this, we study the difference between a
na\"ively-trained initial-phase model and the oracle model. Specifically, since
one major difference between these two models is the number of training
classes, we investigate how such difference affects the model representations.
We find that, with fewer training classes, the data representations of each
class lie in a long and narrow region; with more training classes, the
representations of each class scatter more uniformly. Inspired by this
observation, we propose Class-wise Decorrelation (CwD) that effectively
regularizes representations of each class to scatter more uniformly, thus
mimicking the model jointly trained with all classes (i.e., the oracle model).
Our CwD is simple to implement and easy to plug into existing methods.
Extensive experiments on various benchmark datasets show that CwD consistently
and significantly improves the performance of existing state-of-the-art methods
by around 1\% to 3\%. Code will be released.
