  Based on the notion of information bottleneck (IB), we formulate a
quantization problem called "IB quantization". We show that IB quantization is
equivalent to learning based on the IB principle. Under this equivalence, the
standard neural network models can be viewed as scalar (single sample) IB
quantizers. It is known, from conventional rate-distortion theory, that scalar
quantizers are inferior to vector (multi-sample) quantizers. Such a deficiency
then inspires us to develop a novel learning framework, AgrLearn, that
corresponds to vector IB quantizers for learning with neural networks. Unlike
standard networks, AgrLearn simultaneously optimizes against multiple data
samples. We experimentally verify that AgrLearn can result in significant
improvements when applied to several current deep learning architectures for
image recognition and text classification. We also empirically show that
AgrLearn can reduce up to 80% of the training samples needed for ResNet
training.
