Neural networks leverage nominally quantum and post-quantum representations

TL;DR

Deep neural networks naturally develop representations akin to quantum and post-quantum models of their training data, performing iterative Bayesian inference during inference, which classical circuits cannot replicate.

Contribution

This work reveals that neural networks inherently discover and encode beliefs over complex quantum-inspired models, a capability absent in classical finite circuits.

Findings

Neural networks represent beliefs over quantum and post-quantum models.

Neural representations are largely architecture-independent.

Geometry of neural activations encodes history-dependent future probabilities.

Abstract

We show that deep neural networks, including transformers and RNNs, pretrained as usual on next-token prediction, intrinsically discover and represent beliefs over 'quantum' and 'post-quantum' low-dimensional generative models of their training data -- as if performing iterative Bayesian updates over the latent state of this world model during inference as they observe more context. Notably, neural nets easily find these representation whereas there is no finite classical circuit that would do the job. The corresponding geometric relationships among neural activations induced by different input sequences are found to be largely independent of neural-network architecture. Each point in this geometry corresponds to a history-induced probability density over all possible futures, and the relative displacement of these points reflects the difference in mechanism and magnitude for how these distinct pasts affect the future.