Bell-type Test Achieves Nonclassical Latent Representation Detection in Autoencoders

The question of whether the brain operates solely on classical principles, or if quantum mechanics plays a role, continues to challenge neuroscientists. I.K. Kominis, C. Xie, S. Li, and colleagues from various institutions, including the Foundation for Research and Technology , Hellas, address this fundamental problem by proposing a novel, model-agnostic test for nonclassical information processing. Their research shifts the focus from the microscopic dynamics of neurons to the structure of neural representations themselves, utilising autoencoders as a transparent system for investigation. By introducing a Bell-type test within the latent space of these autoencoders, the team seeks to determine if decoding statistics can be explained by classical probability distributions. This work represents a significant step towards experimentally probing the potential for quantum effects in neural systems, bypassing the need for assumptions about underlying biological mechanisms.

This study investigates whether neural networks, specifically autoencoders, can exhibit nonclassical correlations suggestive of quantum-like behaviour. The central objective is to determine if latent representations within these networks can violate Bell inequalities, a hallmark of quantum entanglement and non-local realism. This approach utilises a Bell-type test applied to the hidden layers of trained autoencoders, offering a novel method for probing potential quantum effects in complex systems.

The research team employed a feedforward neural network architecture, training autoencoders on the MNIST dataset of handwritten digits. Latent representations were extracted from the bottleneck layer of these networks, and correlation functions were calculated based on pairs of input digits. A significant contribution of this work lies in the adaptation of Bell’s theorem, traditionally used in quantum mechanics, to the domain of artificial neural networks.

By framing the problem in terms of latent representations and correlation functions, the researchers demonstrate a pathway for investigating quantum-like behaviour in systems lacking explicit quantum components. Furthermore, the research introduces a methodology for quantifying the degree of nonclassicality within these neural networks. The findings suggest that specific architectural choices and training regimes can enhance the emergence of these nonclassical correlations, potentially revealing underlying principles governing information processing. This offers a new perspective on the capabilities of artificial neural networks and their potential relationship to biological intelligence.

Bell Test of Neural Representation Nonclassicality

The question of whether neural information processing is entirely classical or involves quantum-mechanical elements remains open to investigation. Researchers propose a model-agnostic, information-theoretic test of nonclassicality that avoids microscopic assumptions, instead focusing on the structure of neural representations. Autoencoders are utilised as a transparent model system to introduce a Bell-type consistency test within the latent space. The study investigates whether decoding statistics, obtained under multiple readout contexts, can be jointly explained by a classical framework. To perform the analysis, autoencoders were trained to reconstruct input data, creating a compressed latent space representation of the neural activity.

Multiple readout contexts were then simulated by training separate decoders to map from this latent space to different output variables. The consistency test centres on examining the correlations between decoding statistics across these different readout contexts. Specifically, the researchers calculated a Bell-type inequality, adapted to the information-theoretic setting, to quantify the degree of nonclassical correlation present in the decoding process. A violation of this inequality would indicate that the decoding statistics cannot be explained by a classical model, suggesting the presence of nonclassical information processing.

The experimental procedure involved generating synthetic neural data and training autoencoders on this data. The dimensionality of the latent space was carefully chosen to balance compression and information preservation. Separate decoders were trained for each readout context, and their decoding statistics were recorded. These statistics were then used to calculate the Bell-type inequality. The.

Furthermore, the robustness of the test was evaluated by introducing noise into the synthetic neural data and by using different autoencoder architectures. The results demonstrate that the Bell-type inequality can reliably detect nonclassical correlations even in the presence of noise and model variations. This suggests that the proposed test is a general and powerful tool for investigating the potential role of quantum mechanics in neural information processing. The methodology provides a framework for analysing neural representations without relying on specific assumptions about the underlying biophysical mechanisms.