Soft Tensor Product Representations for Fully Continuous, Compositional Visual Representations

Since the inception of the classicalist vs. connectionist debate, it has been argued that the ability to systematically combine symbol-like entities into compositional representations is crucial for human intelligence. In connectionist systems, the field of disentanglement has emerged to address this need by producing representations with explicitly separated factors of variation (FoV). By treating the overall representation as a *string-like concatenation* of the inferred FoVs, however, disentanglement provides a fundamentally *symbolic* treatment of compositional structure, one inherently at odds with the underlying *continuity* of deep learning vector spaces. We hypothesise that this symbolic-continuous mismatch produces broadly suboptimal performance in deep learning models that learn or use such representations. To fully align compositional representations with continuous vector spaces, we extend Smolensky's Tensor Product Representation (TPR) and propose a new type of inherently *continuous* compositional representation, *Soft TPR*, along with a theoretically-principled architecture, *Soft TPR Autoencoder*, designed specifically for learning Soft TPRs. In the visual representation learning domain, our Soft TPR confers broad benefits over symbolic compositional representations: state-of-the-art disentanglement and improved representation learner convergence, along with enhanced sample efficiency and superior low-sample regime performance for downstream models, empirically affirming the value of our inherently continuous compositional representation learning framework.