K-GAM optimality relative to Quantum Bayesian Computation

Determine whether Kolmogorov Superposition–based K-GAM networks achieve the same information-theoretic bounds as Quantum Bayesian Computation and/or whether K-GAM constitutes an optimal classical "shadow" of quantum computation in a rigorous sense.

Background

K-GAM implements Kolmogorov’s Superposition Theorem as a classical architecture, while QBC leverages non-commutativity and quantum states for inference speedups.

The authors compare the two and note that the parallels are suggestive but unproven; they highlight the open question of whether K-GAM can match QBC’s information-theoretic performance or be characterized as an optimal classical approximation.

References

Whether K-GAM can be shown to achieve the same information-theoretic bounds as QBC, or whether it serves as an optimal classical 'shadow' of quantum computation in a rigorous sense, remains open.

— Bell's Inequality, Causal Bounds, and Quantum Bayesian Computation: A Unified Framework  (2603.28973 - Polson et al., 30 Mar 2026) in Section 5, K-GAM as Classical Approximation to Quantum QBC (Status of this correspondence paragraph)