Invariant-equivariant representation learning for multi-class data
This provides a more interpretable representation learning method for data with discrete classes, such as images or language, though it is incremental as it builds on existing probabilistic modeling approaches.
The paper tackles the problem of opaque deep representations by introducing a probabilistic model that learns separate invariant and equivariant representations for multi-class data, demonstrating competitive performance in supervised and semi-supervised settings with little fine-tuning.
Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two separate deep representations: an invariant representation that encodes the information of the class from which the data belongs, and an equivariant representation that encodes the symmetry transformation defining the particular data point within the class manifold (equivariant in the sense that the representation varies naturally with symmetry transformations). This approach is based primarily on the strategic routing of data through the two latent variables, and thus is conceptually transparent, easy to implement, and in-principle generally applicable to any data comprised of discrete classes of continuous distributions (e.g. objects in images, topics in language, individuals in behavioural data). We demonstrate qualitatively compelling representation learning and competitive quantitative performance, in both supervised and semi-supervised settings, versus comparable modelling approaches in the literature with little fine tuning.