  A good visual representation is an inference map from observations (images)
to features (vectors) that faithfully reflects the hidden modularized
generative factors (semantics). In this paper, we formulate the notion of
"good" representation from a group-theoretic view using Higgins' definition of
disentangled representation, and show that existing Self-Supervised Learning
(SSL) only disentangles simple augmentation features such as rotation and
colorization, thus unable to modularize the remaining semantics. To break the
limitation, we propose an iterative SSL algorithm: Iterative Partition-based
Invariant Risk Minimization (IP-IRM), which successfully grounds the abstract
semantics and the group acting on them into concrete contrastive learning. At
each iteration, IP-IRM first partitions the training samples into two subsets
that correspond to an entangled group element. Then, it minimizes a
subset-invariant contrastive loss, where the invariance guarantees to
disentangle the group element. We prove that IP-IRM converges to a fully
disentangled representation and show its effectiveness on various benchmarks.
Codes are available at https://github.com/Wangt-CN/IP-IRM.
