# Quantum-Inspired Neural Network Model of Optical Illusions
## 4 Discussion  
### Neural Network Model versus Quantum Oscillator Model  
In Figure 7a.ii, we can see that the quantum oscillator model with a single potential well predicts a periodic switching between the two fundamental perceptual states, with a quick but not instantaneous change from one fundamental perceptual state to another. This result is in good agreement with the prediction of the previous quantum mechanical models proposed, for example, in Refs. [9; 21], and it implies the existence of a superposition of the fundamental perceptual states. Qualitatively similar results are also predicted by the neural network, which can be seen in Figure 5 in the time intervals from approximately \(T=5\) to \(T=20\).  
Furthermore, a periodic switching between the two fundamental perceptual states predicted by the neural network model alternates with the periods of irregular switching between these states (e.g., from \(T=80\) to approximately \(T=90\) in Figure 5). This behaviour is qualitatively reproduced by the quantum oscillator model that uses the double periodic well with the barrier (Figure 7b.ii). We note that the time units used in the quantum oscillator model are different from those used in the neural network model, which means that the timescale of alternations between the perceptual states is different in these two models. This difference is inconsequential for the current discussion and, if needed, it can be eliminated using a different profile of the parabolic potential wells.  
Thus, we conclude that the quantum oscillator model can reproduce the predictions of the neural network model provided that the outputs of the single and double parabolic potential well oscillators are combined together, which can be achieved, for example, by coupling them into a chain oscillator. While the discussion of an implementation of this approach is beyond the scope of this paper, the similarity of the outputs of the neural  
Figure 7: **(a)** A single parabolic potential well model and the Necker cube perception switching predicted by it. **(b)** The respective double parabolic model with a barrier and its predictions. In both panels, labels \(|0\rangle\) and \(|1\rangle\) denote the fundamental perceptual states of the Necker cube. The time units used in this figure are different from those in Figure 5.  
network model and the quantum oscillator model has a clear physical meaning: both models are dynamical systems that operate according to the fundamental laws of quantum mechanics [99; 100; 101].  
Moreover, the results obtained using the neural network model speak in favour of the hypothesis that originates from the quantum oscillator model and that suggests that the phase change in the response of the dynamical system has the effect of eye blinking, an action known to induce a reversal of the perceptual state of the Necker cube [11; 14; 48]. Although this hypothesis has not been verified yet, it is known that the dynamics of eye blinks can be studied using the methods developed to investigate highly nonlinear and chaotic processes [102; 103; 104]. Hence, since the neural network model employs data produced by a generator of truly random numbers, its predictions should be consistent with the dynamics of the eye blink [84; 105].  
It is plausible that one can obtain, at least in principle, a quantitative agreement between two or more different models. However, such a comparison must be preceded by research aimed to compare the outcomes of a particular theoretical model with experimental psychological or neurobiological data. Although several attempts to conduct such studies have been undertaken (see, e.g., refs. [106; 107; 108]), a comprehensive validation of different models against the same experimental dataset is yet to be carried out.