Bell-based classification of machine learning architectures

Develop a Bell-style classification of machine learning architectures that characterizes which faces of the marginal-compatibility polytope their representable distributions can access, and identify classical architectures that saturate or approach the quantum gap.

Background

The authors propose using the polytope framework to analyze the expressiveness of ML models by mapping architectural constraints to attainable regions of correlation space.

They suggest a taxonomy based on which polytope faces (classical vs. quantum-like correlations) different architectures can represent, highlighting this as an open direction.

References

The unified framework raises several open questions that span the boundaries of quantum information, causal inference, and statistical computation. K-GAM networks implement the KST and provide the classical architecture closest to quantum function evaluation. Can other classical architectures—transformers, diffusion models, normalizing flows—be characterized in terms of which polytope faces they can access? A "Bell classification" of machine learning architectures, based on the correlations they can represent, would connect expressiveness theory to quantum information in a concrete way.

— Bell's Inequality, Causal Bounds, and Quantum Bayesian Computation: A Unified Framework  (2603.28973 - Polson et al., 30 Mar 2026) in Section 7, Open Problems