  Incremental learning aims to enable machine learning models to continuously
acquire new knowledge given new classes, while maintaining the knowledge
already learned for old classes. Saving a subset of training samples of
previously seen classes in the memory and replaying them during new training
phases is proven to be an efficient and effective way to fulfil this aim. It is
evident that the larger number of exemplars the model inherits the better
performance it can achieve. However, finding a trade-off between the model
performance and the number of samples to save for each class is still an open
problem for replay-based incremental learning and is increasingly desirable for
real-life applications. In this paper, we approach this open problem by tapping
into a two-step compression approach. The first step is a lossy compression, we
propose to encode input images and save their discrete latent representations
in the form of codes that are learned using a hierarchical Vector Quantised
Variational Autoencoder (VQ-VAE). In the second step, we further compress codes
losslessly by learning a hierarchical latent variable model with bits-back
asymmetric numeral systems (BB-ANS). To compensate for the information lost in
the first step compression, we introduce an Information Back (IB) mechanism
that utilizes real exemplars for a contrastive learning loss to regularize the
training of a classifier. By maintaining all seen exemplars' representations in
the format of `codes', Discrete Representation Replay (DRR) outperforms the
state-of-art method on CIFAR-100 by a margin of 4% accuracy with a much less
memory cost required for saving samples. Incorporated with IB and saving a
small set of old raw exemplars as well, the accuracy of DRR can be further
improved by 2% accuracy.
