Geraint A. Wiggins

Keshav Bhandari, Geraint A. Wiggins, Simon Colton

Transformer models have made great strides in generating symbolically represented music with local coherence. However, controlling the development of motifs in a structured way with global form remains an open research area. One of the reasons for this challenge is due to the note-by-note autoregressive generation of such models, which lack the ability to correct themselves after deviations from the motif. In addition, their structural performance on datasets with shorter durations has not been studied in the literature. In this study, we propose Yin-Yang, a framework consisting of a phrase generator, phrase refiner, and phrase selector models for the development of motifs into melodies with long-term structure and controllability. The phrase refiner is trained on a novel corruption-refinement strategy which allows it to produce melodic and rhythmic variations of an original motif at generation time, thereby rectifying deviations of the phrase generator. We also introduce a new objective evaluation metric for quantifying how smoothly the motif manifests itself within the piece. Evaluation results show that our model achieves better performance compared to state-of-the-art transformer models while having the advantage of being controllable and making the generated musical structure semi-interpretable, paving the way for musical analysis. Our code and demo page can be found at https://github.com/keshavbhandari/yinyang.

Ward Gauderis, Thomas Dooms, Steven T. Holmer et al.

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be objectively verified, compared, or composed. We introduce compositional interpretability, a category-theoretic framework grounded in the principles of compositionality and minimum description length. Compositional interpretations are pairs of syntactic and semantic mappings that must commute to enforce consistency between a model's decomposition and its observed behaviour. We deconstruct explanation quality into measures of faithfulness and complexity to cast interpretability as a constrained optimisation problem, and introduce compressive refinement to systematically restructure models into simpler parts without altering their function. Finally, we prove a parsimony criterion under which syntactic compression theoretically guarantees more concise, human-aligned explanations. Our framework situates prominent mechanistic methods as subclasses of refinement, and clarifies why their compressibility heuristics tend to align with human interpretability. Our work provides a measurable, optimisable foundation for automating the discovery and evaluation of mechanistic explanations.

Thomas Dooms, Ward Gauderis, Geraint A. Wiggins et al.

We propose $χ$-net, an intrinsically interpretable architecture combining the compositional multilinear structure of tensor networks with the expressivity and efficiency of deep neural networks. $χ$-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.

Jurek Eisinger, Ward Gauderis, Lin de Huybrecht et al.

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.