Quantum-tunnelling deep neural network for optical illusion recognition

TL;DR

The paper addresses the challenge of enabling AI to emulate human optical illusion perception by introducing a quantum-tunnelling activation in a deep neural network (QT-DNN). It develops an architecture with $L=100$, $N=20$, $M=2$, and an activation $\phi_{QT}$ derived from the transmission coefficient $T$ through a rectangular barrier, trained via backpropagation; the approach is validated on Necker cube and Rubin's vase tasks using true-random numbers from a quantum source and a neuromorphic viewpoint. The results show time-series perceptual switching between $|0\rangle$ and $|1\rangle$, with intermediate superpositions consistent with quantum cognition, and DTW analyses suggesting QT-DNN captures dynamics closer to biological models than ReLU-based counterparts. The work discusses implications for quantum cognition, alignment with biology-inspired networks, and potential hardware realizations in quantum neuromorphic computing, highlighting practical uses in AI-assisted perception and cognitive diagnostics.

Abstract

The discovery of the quantum tunnelling (QT) effect -- the transmission of particles through a high potential barrier -- was one of the most impressive achievements of quantum mechanics made in the 1920s. Responding to the contemporary challenges, I introduce a deep neural network (DNN) architecture that processes information using the effect of QT. I demonstrate the ability of QT-DNN to recognise optical illusions like a human. Tasking QT-DNN to simulate human perception of the Necker cube and Rubin's vase, I provide arguments in favour of the superiority of QT-based activation functions over the activation functions optimised for modern applications in machine vision, also showing that, at the fundamental level, QT-DNN is closely related to biology-inspired DNNs and models based on the principles of quantum information processing.

Figures (7)

• Figure 1: (a) The Necker cube: The answer to the question 'Is the shaded face of the cube at the front or at the rear?' will randomly switch between two stable perceptual states corresponding to the front ($|0\rangle$) and rear ($|1\rangle$) face of the cube. (b) Rubin's vase: Do you see two people looking towards each other ($|0\rangle$) or a vase ($|1\rangle$)?' (c) As per the traditional theory, the change from one perceptual state to another is binary (the dotted line), i.e. it is from $|0\rangle$ to $|1\rangle$ and vice versa. However, the current research works demonstrate that humans might see a superposition of the states $|0\rangle$ and $|1\rangle$ (the solid curve).
• Figure 2: (a) Sketch of QT-DNN structure. $W^{(n)}$ with $n=1\dots4$ are the matrices of the weights of the network connections. (b) QT-DNN model employs the physical effect of QT as the activation function of its nodes. Panel (b.i): one-dimensional rectangular potential barrier of thickness $a$ and height $V_0$. Panel (b.ii): unlike in classical mechanics, in quantum mechanics there is a non-zero probability for an electron with energy $E<V_0$ to be transmitted through the barrier.
• Figure 3: Neuromorphic algorithm involving the training of the network on distinguishable images of objects and its further exploitation aimed to recognise optical illusions.
• Figure 4: (a) Perceptual switching data (with the lines serving as a guide to the eye) produced by QT-DNN trained on the Necker cube. The data points located in between 0 and 1 are in a superposition of the states $|0\rangle$ and $|1\rangle$. (b) Classical perception computed using the procedure explained in the main text.
• Figure 5: The same as in Fig. \ref{['Fig_Necker_result']} but for Rubin's vase.