Elsevier

Neurocomputing

Volume 74, Issue 17, October 2011, Pages 3502-3508
Neurocomputing

The neural dynamics for hysteresis in visual perception

https://doi.org/10.1016/j.neucom.2011.06.004Get rights and content

Abstract

The hysteresis in the perception has been observed in many perceptual experiments, but little is known about the underlying dynamical mechanism. We simulate a visual discrimination task, as an example of hysteresis in the perception, using a spiking neuron network and the corresponding slow dynamic system. The hysteresis in visual perception has been reproduced in our simulation. We find that hysteresis is influenced by the change speed of the external stimuli and the excitatory recurrent interaction inside the selective neuron pool. The slow dynamic system reveals the dynamical mechanism underlying the hysteresis: emerging from the lag between the response of neural system and the fast change external stimuli when the slow dynamic system has a single steady state; emerging from the multiple steady states regardless of the change speed of the external stimuli. In particularly, the multiplicity of the steady state of the slow dynamic system comes from the codimension three swallowtail catastrophe which exhibits two interacting cusp catastrophes.

Introduction

The hysteresis in the perception means that what is perceived depends on previous experiences. Hysteresis is a typical phenomenon in visual, auditory, and somatosensory perceptions and has been extensively observed for many perceptual tasks [1], [2], [3], [4], [5], [6]. An example of this phenomenon is a motion perception task in which some dots were moving in random directions, while other dots were moving coherently in a vertical direction on the screen. The coherence level gradually increased at first and then gradually decreased. The subjects could perceive the vertical motion at a threshold of the coherence level and note the disappearance of the vertical motion at another threshold. The experiment showed that the former threshold was larger than the latter threshold, which implied that the perception of the vertical motion depends on the history of the stimuli presentation [1]. In another experiment [2], the subjects were required to detect a hidden letter on the screen whose contrast gradually increased at first and then gradually decreased. The subjects were aware of the letter at one threshold when the contrast was increased. However, the subjects noted the disappearance of the letter at another threshold when the contrast was decreased. This experiment showed that the threshold of the increasing contrast was larger than that of the decreasing contrast. At the same time, the magnetic resonance signal also demonstrated the hysteresis phenomenon [2]. For an auditory system, the threshold to detect a tone whose amplitude increased was higher than the threshold for a tone that became inaudible. A recent study about the mosquito's auditory system showed the hysteresis of the antennal response to a sound with a single frequency [6].

Hysteresis in the perception has been observed for a long time, but little is known about the underlying neural mechanism, especially how hysteresis can emerge from single neuron activities. Hirai and Fukushima proposed a multiple layer model to investigate the binocular parallax, and their model exhibited hysteresis in binocular depth perception as observed by Fender and Jules but without explanation of the key factors that induced hysteresis [21], [22]. Recently, Wilson and his coworkers proposed that positive feedback and recurrent inhibition between neural units could cause hysteresis [23]. A more quantitative explanation is that cusp catastrophe or bistability underlies the hysteresis in the perception [3], [4], [7]. Actually, a cusp catastrophe system has two stable steady states and the back-and-forth transition pathway between two stable steady states depending on the increase or decrease of the control parameter. However, the cusp catastrophe is only an analogous explanation of hysteresis in the perception, and the relationship between the microscopic neural activities and the hysteresis in the perception for macroscopic behavior has not yet been established. Therefore, we apply a network with spiking neurons to simulate a simple visual discrimination task and the neural activities are demonstrated as an example of hysteresis in the perception. At the same time, we derive a two-variable slow dynamic system from the spiking neuron network. By analyzing the steady states of the slow dynamic system, we find that the slow dynamic system can operate under different regimes and the multiple stable states lead to hysteresis in the perception. We also find that stronger recurrent excitation and faster change of the external stimuli both favor hysteresis.

Section snippets

The spiking neuron model and the slow dynamic system

To investigate the neural dynamics underlying hysteresis in the perception, we start from a comparable simple task described in [3], [4], [5], [7]. In this visual perception experiment, the subjects have to observe a series of figures one after another and to discriminate those in which the visual stimuli gradually change from a man's face to a kneeling girl (Fig. 1). Subjects notice the jump from the man's face to the kneeling girl at one point when subjects watch the figures from left to

Hysteresis of the neural activity

Assuming that subjects take 20 s (T=20 s) to finish one trial of observation from left to right, the frequency of the Poisson spike train to the neuron pool I decreases from 60 to 0 Hz and that to the neuron pool II increases from 0 to 60 Hz in the simulation (the bottom panel of Fig. 2(a)). The raster plot, shown in the upper panel of Fig. 2(a), indicates that the activity of the nonselective neuron pool is almost invariant to the changing inputs. However, the activity of the man's face selective

The effects of asymptotic and transient behavior of neural networks on hysteresis

The hysteresis of neural activity in this visual perception task have been demonstrated in Section 3. In this section, we will investigate the factors that influence hysteresis. Generally speaking, the dynamics of the neuron network, including asymptotic and transient behavior, have important impacts on neural activity. As for the asymptotic behavior, the relative connection strength inside the selective neuron pools w+ plays a significant role. The bigger w+ results in a stronger recurrent

Multiple stable steady states lead to hysteresis in the perception

Fig. 3 demonstrates that the increase of the relative excitation in the selective neuron pool or speedup of the external stimuli leads to more obvious hysteresis in the perception. The similarity between the results about the spiking neuron model and the slow dynamic system suggests that we can reveal the neural dynamics of the hysteresis in the perception using nonlinear analysis of the slow dynamic system. By setting the right hand side of Eqs. (6), (7) as zero, we obtain two algebra

Conclusion and discussion

In conclusion, we demonstrate the hysteresis in the perception using an example of simple visual discrimination task. By simulation of a spiking neuron network and analysis of the corresponding slow dynamic system, we find two factors affecting the hysteresis of perception: one is the strength of the synapse, the other is the change speed of the external stimuli. The simulation shows that a stronger connection inside the selective neuron pool leads to a larger hysteresis loop of the neuron

Acknowledgments

This work was supported by the NSFC under Grant No. 60974075 and the Open Funding of the National Key Laboratory of Cognitive Neuroscience and Learning of China. The computation was supported by the HSCC of BNU. The authors are grateful for the helpful comments and suggestions by the anonymous reviewers.

Hongzhi You is a Ph.D. candidate in Department of Systems Science in Beijing Normal University. His research interests include neural mechanism of perceptual decision making, working memory.

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    Hongzhi You is a Ph.D. candidate in Department of Systems Science in Beijing Normal University. His research interests include neural mechanism of perceptual decision making, working memory.

    Yan Meng is a Master student in Department of Systems Science in Beijing Normal University, China. Her current research interest is the neuron network of decision making with reference criteria and the dynamics of neural computation.

    Di Huan is now in pursuit for M.Sc. degree in Department of Systems Science, Beijing Normal University. His research is related to neuron network modeling and neuronal oscillation.

    Da-Hui Wang received Ph.D in Systems Theory from Beijing Normal University in 2002. He is an associate professor at Department of Systems Science. He works on computational neuroscience, especially, the nonlinear dynamics of neural system, dynamics underlying oscillation, working memory, and decision making.

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