  Recognizing elementary underlying concepts from observations
(disentanglement) and generating novel combinations of these concepts
(compositional generalization) are fundamental abilities for humans to support
rapid knowledge learning and generalize to new tasks, with which the deep
learning models struggle. Towards human-like intelligence, various works on
disentangled representation learning have been proposed, and recently some
studies on compositional generalization have been presented. However, few works
study the relationship between disentanglement and compositional
generalization, and the observed results are inconsistent. In this paper, we
study several typical disentangled representation learning works in terms of
both disentanglement and compositional generalization abilities, and we provide
an important insight: vector-based representation (using a vector instead of a
scalar to represent a concept) is the key to empower both good disentanglement
and strong compositional generalization. This insight also resonates the
neuroscience research that the brain encodes information in neuron population
activity rather than individual neurons. Motivated by this observation, we
further propose a method to reform the scalar-based disentanglement works
($\beta$-TCVAE and FactorVAE) to be vector-based to increase both capabilities.
We investigate the impact of the dimensions of vector-based representation and
one important question: whether better disentanglement indicates higher
compositional generalization. In summary, our study demonstrates that it is
possible to achieve both good concept recognition and novel concept
composition, contributing an important step towards human-like intelligence.
