[Paper Review] Quantum-Inspired Neural Network Model of Optical Illusions

Ivan S. Maksymov|arXiv (Cornell University)|Dec 6, 2023

Neural Networks and Reservoir Computing4 citations

TL;DR

This paper proposes a quantum-inspired deep neural network that uses a quantum random number generator to model human perception of the Necker cube as a qubit-like superposition of perceptual states. The model demonstrates that perceptual switching is not classical binary alternation but a quantum-like superposition, aligning with emerging theories in quantum cognition and offering applications in VR, AI training, and neuroscience.

ABSTRACT

Ambiguous optical illusions have been a paradigmatic object of fascination, research and inspiration in arts, psychology and video games. However, accurate computational models of perception of ambiguous figures have been elusive. In this paper, we design and train a deep neural network model to simulate the human's perception of the Necker cube, an ambiguous drawing with several alternating possible interpretations. Defining the weights of the neural network connection using a quantum generator of truly random numbers, in agreement with the emerging concepts of quantum artificial intelligence and quantum cognition we reveal that the actual perceptual state of the Necker cube is a qubit-like superposition of the two fundamental perceptual states predicted by classical theories. Our results will find applications in video games and virtual reality systems employed for training of astronauts and operators of unmanned aerial vehicles. They will also be useful for researchers working in the fields of machine learning and vision, psychology of perception and quantum-mechanical models of human mind and decision-making.

Motivation & Objective

• To develop a computational model that accurately simulates human perception of ambiguous optical illusions, particularly the Necker cube.
• To investigate whether perceptual switching in ambiguous figures can be better explained by quantum-like superposition than classical binary alternation.
• To explore the applicability of quantum-inspired mechanisms—such as quantum random number generation and qubit-like states—in modeling human perception and decision-making.
• To provide a testable framework for validating quantum cognition theories using deep learning and experimental data from EEG and eye-tracking studies.
• To enable practical applications in training systems for astronauts and UAV operators in visually complex, ambiguous environments.

Proposed method

• A deep neural network is trained to simulate perception of the Necker cube based on visual input patterns.
• Quantum random number generation is used to define the network's connection weights, introducing true randomness aligned with quantum mechanics principles.
• The model's internal state is interpreted as a qubit-like superposition: |ψ⟩ = α|0⟩ + β|1⟩, where |0⟩ and |1⟩ represent the two perceptual interpretations of the cube.
• Projective measurement operators M₀ = |0⟩⟨0| and M₁ = |1⟩⟨1| are applied to simulate perceptual state collapse, with probabilities P(|0⟩) = |α|² and P(|1⟩) = |β|².
• The network's dynamics are validated against empirical data from EEG and eye-tracking studies showing continuous oscillation between perceptual states.
• The model is compared with a quantum oscillator model of optical illusions, showing consistent prediction of superposition states.

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 change suddenly depending on the observer’s perception, giving rise to a series of rectangular pulses corresponding to the front, $|0\rangle$ , and rear, $|1\rangle$ , percept

Experimental results

Research questions

• RQ1 Can a deep neural network powered by quantum random number generation accurately simulate the human perception of ambiguous optical illusions like the Necker cube?
• RQ2 Is the perceptual state of the Necker cube better described as a classical binary switch or a quantum superposition of states?
• RQ3 To what extent do the temporal dynamics of perceptual switching align with the predictions of quantum-inspired models?
• RQ4 How can quantum-inspired neural networks improve training systems for astronauts and UAV operators in ambiguous visual environments?
• RQ5 Can this model serve as a computational testbed for quantum cognition theories in human decision-making and perception?

Key findings

• The neural network model successfully simulates perceptual switching of the Necker cube as a qubit-like superposition of the two perceptual states, rather than a classical binary alternation.
• The model's output matches empirical data showing continuous oscillation between perceptual states, as observed in EEG and eye-tracking experiments.
• The use of a quantum random number generator in defining network weights leads to perceptual dynamics that are consistent with quantum measurement theory.
• The model's predictions align with a recently proposed quantum oscillator model of optical illusions, reinforcing the validity of quantum-inspired approaches.
• The model demonstrates that perceptual states are not isolated but exist in a coherent superposition, supporting the quantum cognition hypothesis.
• The model is publicly available via GitHub, enabling replication and extension by researchers in AI, neuroscience, and psychology.

Figure 2: (a) Projective measurement of a qubit. (b) Projective qubit-like measurement applied to the Necker cube. The two-dimensional shadows of the cubes are identical and perceived by an observer as an ambiguous Necker cube. Considering the shadows as a qubit-like superposition of $|0\rangle$ and