Searching for Quantum Effects in the Brain: A Bell-Type Test for Nonclassical Latent Representations in Autoencoders

TL;DR

A model-agnostic, information-theoretic test of nonclassicality that bypasses microscopic assumptions and instead probes the structure of neural representations themselves is proposed, opening a new route for probing the fundamental physics of neural computation.

Abstract

Whether neural information processing is entirely classical or involves quantum-mechanical elements remains an open question. Here we propose a model-agnostic, information-theoretic test of nonclassicality that bypasses microscopic assumptions and instead probes the structure of neural representations themselves. Using autoencoders as a transparent model system, we introduce a Bell-type consistency test in latent space, and ask whether decoding statistics obtained under multiple readout contexts can be jointly explained by a single positive latent-variable distribution. By shifting the search for quantum-like signatures in neural systems from microscopic dynamics to experimentally testable constraints on information processing, this work opens a new route for probing the fundamental physics of neural computation.

Figures (2)

• Figure 1: (a) An autoencoder maps high-dimensional inputs $x$ to a low-dimensional latent representation and reconstructs outputs $y$ through multiple decoder settings $\theta$. The latent variables are treated as unobserved degrees of freedom probed indirectly via observable decoding marginals. Nonclassicality in the latent space reflects the impossibility to account for all marginal output statistics (different decoder settings $\theta$) with a unique positive latent distribution. (b) Analogy between Bell nonlocality tests and nonclassicality tests in the latent space of autoencoders.
• Figure 2: (a) Nonclassicality detection probability $P_{\rm det}$ as a function of the noise parameter $\alpha$. For the numerical implementation, a 2d latent phase space $(\zeta,\eta)$ is discretized on a uniform $100\times100$ grid over the square $[-L,L]\times[-L,L]$, with $L=4$, yielding $N=10^4$ latent basis points. The readout family consists of $J=25$ projection angles $\theta_j=j\pi/J$. For each $\theta_j$, the projected coordinate $y=\zeta\cos\theta_j+\eta\sin\theta_j$ is discretized into $K=100$ uniformly spaced outcome bins over the interval $[-y_{\max},y_{\max}]$, with $y_{\max}=1.05\sqrt{2}\,L$. This construction defines a forward matrix $A\in\mathbb{R}^{(JK)\times N}=\mathbb{R}^{2500\times10000}$. (b) The heat map again displays $P_{\rm det}$, but now as a function of the noise parameter $\alpha$and the quantum mixing parameter $\beta$. (c) Possible experimental realization of the proposed paradigm. Optogenetic stimulation and electrode recordings provide access to population-level activity and enable variation of decoding contexts.