Quantum-Inspired Non-Manifold Embeddings for Language Models

Wang’s proof that human language is fundamentally non-manifold challenges the smooth manifold assumptions in NLP embeddings. Simultaneously, Asselmeyer-Maluga’s work on exotic (\mathbb{R}^4) shows how non-standard smoothness structures enable quantum states in 4-manifolds. This research proposes quantum-inspired embeddings that replace Euclidean latent spaces with exotic smooth structures. By encoding language data into "wildly embedded" submanifolds (as quantum states in Asselmeyer-Maluga), we can model semantic singularities (e.g., idioms, metaphors) as topological defects. This diverges from current Word2Vec/BERT approaches by embracing non-manifoldness through tools like skein algebras and Connes’ quantized calculus. Potential impact: Improved handling of linguistic edge cases and new geometric invariants for NLP.

References:

1. Smooth quantum gravity: Exotic smoothness and Quantum gravity. T. Asselmeyer-Maluga (2016).
2. Human Language is Non-manifold. Hao Wang (2024). ICON.