Symbolic Disentangled Representations for Images

The idea of disentangled representations is to reduce the data to a set of generative factors that produce it. Typically, such representations are vectors in latent space, where each coordinate corresponds to one of the generative factors. The object can then be modified by changing the value of a particular coordinate, but it is necessary to determine which coordinate corresponds to the desired generative factor -- a difficult task if the vector representation has a high dimension. In this article, we propose ArSyD (Architecture for Symbolic Disentanglement), which represents each generative factor as a vector of the same dimension as the resulting representation. In ArSyD, the object representation is obtained as a superposition of the generative factor vector representations. We call such a representation a \textit{symbolic disentangled representation}. We use the principles of Hyperdimensional Computing (also known as Vector Symbolic Architectures), where symbols are represented as hypervectors, allowing vector operations on them. Disentanglement is achieved by construction, no additional assumptions about the underlying distributions are made during training, and the model is only trained to reconstruct images in a weakly supervised manner. We study ArSyD on the dSprites and CLEVR datasets and provide a comprehensive analysis of the learned symbolic disentangled representations. We also propose new disentanglement metrics that allow comparison of methods using latent representations of different dimensions. ArSyD allows to edit the object properties in a controlled and interpretable way, and the dimensionality of the object property representation coincides with the dimensionality of the object representation itself.