  Learning compact discrete representations of data is a key task on its own or
for facilitating subsequent processing of data. In this paper we present a
model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic
encoder that yields k-way d-dimensional codes associated with input data. Our
model's learning objective is to maximize the mutual information between codes
and labels with a regularization, which enforces entries of a codeword to be as
independent as possible. We show that the infomax principle also justifies
previous loss functions (e.g., cross-entropy) as its special cases. Our
analysis also shows that using shorter codes, as DIMCO does, reduces
overfitting in the context of few-shot classification. Through experiments in
various domains, we observe this implicit meta-regularization effect of DIMCO.
Furthermore, we show that the codes learned by DIMCO are efficient in terms of
both memory and retrieval time compared to previous methods.
