Compositionality Unlocks Deep Interpretable Models

We propose $\chi$-net, an intrinsically interpretable architecture combining the compositional multilinear structure of tensor networks with the expressivity and efficiency of deep neural networks. $\chi$-nets retain equal accuracy compared to their baseline counterparts. Our novel, efficient diagonalisation algorithm, ODT, reveals linear low-rank structure in a multilayer SVHN model. We leverage this toward formal weight-based interpretability and model compression.

Quantum Methods for Managing Ambiguity in Natural Language Processing

The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks and quantum circuits. DisCoCat diagrams have been connected to density matrices in various contexts in Quantum Natural Language Processing (QNLP). Previous use of density matrices in QNLP entails modelling ambiguous words as probability distributions over more basic words (the word \texttt{queen}, e.g., might mean the reigning queen or the chess piece). In this article, we investigate using probability distributions over processes to account for syntactic ambiguity in sentences. The meanings of these sentences are represented by density matrices. We show how to create probability distributions on quantum circuits that represent the meanings of sentences and explain how this approach generalises tasks from the literature. We conduct an experiment to validate the proposed theory.