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Abstract
We demonstrate a variety of biologically relevant dynamical behaviors building on a recently introduced ultra-compact neuron (UCN) model. We provide the detailed circuits which all share a common basic block that realizes the leaky-integrate-and-fire (LIF) spiking behavior. All circuits have a small number of active components and the basic block has only three, two transistors and a silicon controlled rectifier (SCR). We also demonstrate that numerical simulations can faithfully represent the variety of spiking behavior and can be used for further exploration of dynamical behaviors. Taking Izhikevich’s set of biologically relevant behaviors as a reference, our work demonstrates that a circuit of a LIF neuron model can be used as a basis to implement a large variety of relevant spiking patterns. These behaviors may be useful to construct neural networks that can capture complex brain dynamics or may also be useful for artificial intelligence applications. Our UCN model can therefore be considered the electronic circuit counterpart of Izhikevich’s (2003) mathematical neuron model, sharing its two seemingly contradicting features, extreme simplicity and rich dynamical behavior.
Highlights
In his 2003 landmark paper Izhikevich (2003) emphasized that to develop a large-scale model of the brain one faces seemingly mutually exclusive requirements: on one hand the model had to be simple enough to allow for efficient computation and, on the other, it had to be able to produce a rich variety of biologically relevant firing patterns
We firstly describe the biologically relevant behaviors obtained through the numerical simulations study of circuits that are variations from the ultra-compact neuron (UCN) basic block
Secondly, we describe the results of the measurements made on actual electronic circuits, whose implementation was informed by the numerical simulations study
Summary
In his 2003 landmark paper Izhikevich (2003) emphasized that to develop a large-scale model of the brain one faces seemingly mutually exclusive requirements: on one hand the model had to be simple enough to allow for efficient computation and, on the other, it had to be able to produce a rich variety of biologically relevant firing patterns. We shall demonstrate that the UCN is a circuit block that, with minimal variations, may realize at least 12 out of the 20 biological relevant behaviors highlighted by Izhikevich (2004) To reproduce those behaviors has become a de facto standard to demonstrate the relevance of a spiking neuron model implemented on different physical supports. The literature is very diverse and growing fast, so we shall only cite a few examples here and refer the Behaviors in Ultra-Compact Neuron Model readers to further references in those works and in the review of Indiveri et al (2011): the digital processor chips TrueNorth developed by IBM (Cassidy et al, 2013; Merolla et al, 2014) and the more recent ODIN by ICTEAM (Frenkel et al, 2019); the compact neuron circuit, with only 14 MOSFET transistors proposed by Wijekoon and Dudek (2008); or the radically different spiking neuron based on vanadium dioxide (Yi et al, 2018), a Mott insulator memristive material (del Valle et al, 2018, del Valle et al, 2019). Other interesting proposals, which aimed at a faithful physical implementation of the Izhikevich mathematical model equations are: a compact circuit of MOS transistors in the subthreshold regime, simulated with MOSIS libraries (Rangan et al, 2010); a CMOS digital neuron for eventdriven computation, simulated in Spice (Imam et al, 2010)
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