While great success has been achieved using transformer architectures in this area, the intermediate representations of neural approaches still lack mechanistic interpretability. Recent developments in alternative compositional spaces, however, offer significant promise. By mapping a set of pre-generated text embeddings to a Wasserstein-Fourier space similar to that proposed by Cazelles et. al. (Cazelles et. al. 2020), Zadeh's fuzzy logic framework (Zadeh, 1965) can be used for computationally efficient, scalable, and interpretable embedding composition. The resulting distributions can then be evaluated using Earthmover's Distances (EMDs) between their power spectra, in a manner similar to the Word Mover's Distance (Kusner et. al. 2015).
By synthesizing recent developments in optimal transport-based similarity metrics with a fuzzy logic grounding framework, I propose a deterministic map to a unique Distributional-Compositional (DisCo) text embedding space. More specifically, PCA-reduced MiniLM lemma embeddings are mapped to Fourier expansions of 2\pi-periodic Gaussian kernels in L^2. Baselines consisting of fuzzified mean lemma embeddings, MiniLM sentence embeddings, and several toy composition models are evaluated on a subset of the WiC dataset (Pilehvar and Camacho-Collados, 2019). Relative to these baselines, we demonstrate the effectiveness of various metrics compared to those defined in the original MiniLM embedding space.