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Mounir Boukadoum
Microelectronics Prototyping Research Lab. University of Quebec at Montreal (UQAM) Montreal, Quebec, Canada Email: boukadoum.mounir@uqam.ca
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I NTRODUCTION
Spiking Spiking Neural Networks (SNNs) have application potential in a wide range of areas, including pattern recognition, clustering and computations. The emerging memristor devices can help implement efficient SNNS as their analog memory property makes them suitable to model biological synapses. These two-terminal devices have triggered research in many areas such as memory [1], logic [2][3][4], neural networks [5] and neuromorphic computing [6][7]. In [8], it was shown that the adaptive behavior of memristor devices allows them to reproduce Spike-Timing-Dependent-Plasticity (STDP), the main learning mechanism found in SNNs. Several works have been published on implementing SNNs with STDP learning. Most of these works rely on the Leaky Integrate and Fire (LIF) neuron model for simplicity [6][7]. However, using a more biologically plausible neuron model can give better insight of brain activity. The classic HodgkinHuxley neuron model [9] is a good candidate for this, since it has already been used with success to represent the ionic mechanisms underlying the initiation and propagation of action potentials in biological organisms. In this paper, an SNN is implemented with HodgkinHuxley neurons as neurons and the current-controlled memristor devices as synapses. Then, basic pattern recognition tasks are applied to the obtained SNN to test its functionality. The rest of this paper is organized as follows: In section II, the Hodgkin-Huxley neuron is defined, and in Section III, STDP learning with the memristor synapse is explained. The
where I , V and CM are the total membrane current, the membrane potential and the membrane capacitance, respectively, and I ionic is the total ionic current from Sodium, Potassium and leakage channels. It is defined as follows: Iionic = INa + IK + IL , where INa = gNa (V − ENa ), with gNa = g ¯Na m3 h, (3) (4) (2)
Brain-inspired Pattern Classification with Memristive Neural Network Using the Hodgkin-Huxley Neuron
Amirali Amirsoleimani, Majid Ahmadi and Arash Ahmadi
Research Center for Integrated Microsystems University of Windsor Windsor, Ontario, Canada Email: {amirsol, ahmadi, aahmadi}@uwindsor.ca
Abstract—Recent findings about using memristor devices to mimic biological synapses in neuromorphic systems open a new vision in neuroscience. Ultra-dense learning architectures can be implemented through the Spike-Timing-Dependent-Plasticity (STDP) mechanism by exploiting these nanoscale nonvolatile devices. In this paper, a Spiking Neural Network (SNN) that uses biologically plausible mechanisms is implemented. The proposed SNN relies on Hodgkin-Huxley neurons and memristor-based synapses to implement a bio-inspired neuromorphic platform. The behavior of the proposed SNN and its learning mechanism are discussed, and test results are provided to show the effectiveness of the proposed design for pattern classification applications. Keywords—Memristor, Hudgkin Huxley, Spike-TimingDependent-Plasticity (STDP), Spiking Neural Network (SNN).
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Fig. 3. Illustration of STDP learning for neurons coupled with a memristive synapse in the implemented SNN architecture. The crossbar memristive array of synapses connects Hodgkin-Huxley neurons.
Fig. 1. Equivalent memristive circuit schematic for the Hodgkin-Huxley neuron model (top). Memristor I -V curves to model the sodium and potassium channels (bottom right and left)
Value 6 1.8 0.015 Parameters ENA (V) EK (mV) EL (mV) Value 2.3 -240 212 Parameters CM (nF) Value 50
Fig. 2. (a) Hodgkin-Huxley membrane voltage for a 15 μA/cm2 stimulus current. (b) Sodium and potassium channel currents, with parameters taken from [9]. (c) Sodium and potassium channel currents versus membrane voltage. (d) Hodgkin-Huxley neuron state variables behavior.
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TABLE I.
Parameters g ¯Na (mScm−2 ) g ¯K (mScm−2 ) g ¯L (mScm−2 )
S CALED H ODGKIN -H UXLEY NEURON PARAMETERS
proposed SNN structure and its behavior are described in Section IV, and the pattern classification results are presented in section V. Finally, section VI provides a summary and conclusion. II. H UDGKIN H UXLEY N EURON
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The conductance-based Hodgkin-Huxley model [9] is one of the first accurate neuron models for explaining the biological mechanisms of neuron behavior. The current across the neural membrane is divided in two major parts. One is associated with the membrane capacitance and the other is the current generated by the flow of ions through resistive channels. The fundamental equation of the Hodgkin-Huxley model is [9]: I = CM dV + Iionic . dt (1)