Non-linear neuron models overcomes the limitations of linear binary models of neurons that have the inability to compute linearly non-separable functions such as XOR. While several biologically plausible models based on dendrite thresholds are reported in the previous studies, the hardware implementation of such non-linear neuron models remain as an open problem. In this paper, we propose a circuit design for implementing logical dendrite non-linearity response of dendrite spike and saturation types. The proposed dendrite cells are used to build XOR circuit and intensity detection circuit that consists of different combinations of dendrite cells with saturating and spiking responses. The dendrite cells are designed using a set of memristors, Zener diodes, and CMOS NOT gates. The circuits are designed, analyzed and verified on circuit boards.
Biological neural networks can perform intelligent computing task following a hierarchical, modular and sparse processing of signals [1], [2]. As opposed to the non-linear neuron models that can be used in a wide range of applications [3]- [5], the earlier neuron models were considered to have linear characteristics that allows to perform only several basic functions [6], [7]. There are several theoretical linear and non-linear neuron models proposed in recent years [2], [8]. However, the hardware implementations of nonlinear dendrite neuron model remains as an open challenge. Expanding the computational capacity of a single neu-ron, [9] proposes a biologically relevant non-linear model of neuron that allows to implement linearly non-separable Boolean functions. In this paper, we propose a hardware implementation of XOR function based on non-linear neuron model illustrated in [9] as well as the application of nonlinear neuron model for pixel intensity detection for possible use in color (or intensity) segmentation and edge detection in images. The proposed XOR function and pixel intensity detector circuit implementation based on non-linear neuron model consists of a combination of saturating and spiking dendrites response circuits.
Previously, it is believed that dendrites in neuron only function as a provider of signals where action potential doesn’t take place [10]. Discovery of various voltage-gated ion channels: sodium, potassium and calcium channels in dendrites; revealed more complex structure and functionality of the dendrites than it is previously thought [11]. Neuron has several mechanisms to intensify weak input signals in dendrites. One through spatial summation of synaptic inputs, second through placement of high density of voltage-gated sodium and calcium ion channels [12].
There are two distinctive regions in dendrite that receive synaptic inputs performant path (PP) placed 500-750µm from soma and Schaffer-collateral (SC) path 250-500µm from soma, PP stimulates spike formation and SC decides whether signal will be passed to the soma region [13].
Here SC region acts as threshold unit, although it can be with or without potassium channels, which in its turn also acts as threshold unit which regulates over excitement of the synaptic events in synaptic regions and inhibits action potential in dendrites by moving cations outwards [14]. Next aspect of neuron other than signal stimulation, propagation control is ability to learn and memorize. One of the suggested mechanisms of memorization and learning is though actin based plasticity of dendrites [15]. In other words, memorization and learning processes maintained through grow of actins in apical region of dendrites, forcing dendrites to hold certain position [10].
Those advances in understanding of neuron physiology gives some suggestions about what architecture might be viable for artificial neuron design [1]. There are several points that we need to consider to be able to create artificial neuron. Point one, we need to maintain multiple inputs as there are multiple dendrites in neuron, second, we need to have threshold units in dendrite regions as well as in soma region, third, algorithm functioning in multiple input and single output environment has to be established.
Recently, it was found that linearly non-separable functions, as XOR, can be constructed by a binary neuron model with a single non-linear dendrite [9]. In [9], it is suggested that dendrites are capable of computing linearly nonseparable functions as Boolean mathematics, and the best way to maintain functionality as in biological counterpart is using Exclusive OR function. Here, we present functional design of dendritic threshold logic neuron model closely resembling biological counterpart [1].
In comparison to linear binary models of neurons that cannot compute linearly non-separable functions [6], [7], non-linear neuron models allow to implement Boolean functions due to the ability of non-linearly changing the stage from active to inactive and vice versa [3]. Fig. 1 illustrates the dendrite spike and dendrite saturation functions. The a for the XOR functionality which has been proposed in the work [9] and (b) is its circuit implementation. . The saturating transfer function Fsat, as mentioned in [16], is given in Eq. 2, where θ2 is the dendrite threshold and a is the input. The threshold unit based on this function is implemented using a Zener diode.
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In this section dendrite spike type and saturation type neuron models are used in combination to build XOR gate. Apart from being a logical gate, XOR as a function is While using Zener diode, Eq. 2 will changes to Eq. 3, where θ2 is the peak inverse voltage of Zener diode and a is the input.
. Detection of binary edges from an image requires atleast two intensity threshold operations around the spatially continuous edge regions in an object. The aim of this section to create a pixel intensity detection circuit that respo
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