A stochastic approach to STDP

Abstract

Abstract-We present a digital implementation of the Spike Timing Dependent Plasticity (STDP) learning rule. The proposed digital implementation consists of an exponential decay generator array and a STDP adaptor array. On the arrival of a pre-and post-synaptic spike, the STDP adaptor will send a digital spike to the decay generator. The decay generator will then generate an exponential decay, which will be used by the STDP adaptor to perform the weight adaption. The exponential decay, which is computational expensive, is efficiently implemented by using a novel stochastic approach, which we analyse and characterise here. We use a time multiplexing approach to achieve 8192 (8k) virtual STDP adaptors and decay generators with only one physical implementation of each. We have validated our stochastic STDP approach with measurement results of a balanced excitation/inhibition experiment. Our stochastic approach is ideal for implementing the STDP learning rule in large-scale spiking neural networks running in real time. I.BACKGROUNDThe Spike Timing Dependent Plasticity (STDP) algorithm [1], which has been observed in the mammalian brain, modulates the weight of a synapse based on the relative timing of pre-synaptic and post-synaptic spikes. In STDP, the synaptic weight will be increased (or decreased) if a presynaptic spike arrives several milliseconds before (or after) the post-synaptic spike fires. This learning rule is computationally intensive as it exponential functions and divisions.In neuromorphic systems, various implementations of the STDP algorithm have been proposed, such as a circuit based on analogue blocks and flip-flops [2], a bistable synapse with a very compact analogue implementation of the STDP [3], and analogue blocks and switches to implement exponential STDP [4]. We have previously presented a compact implementation of the STDP using linear decays [5], [6]. Here, we present a novel stochastic approach that works with our previous system and can efficiently implement the STDP operations. II. EXPONENTIAL DECAY A. Infinite Impulse Response (IIR) filter approachA discrete time first order exponential decay implemented with an IIR filter can be expressed by the following equation:where, t represents the index of the time step, and [ ] represent the previous value of V and the IIR filter constant is defined as:where, τ is the time constant (in clock cycles) and the decay d is given by:When τ is large, is only a little less than 1, and a large number of bits are needed to encode its value accurately in a digital system. If the number of bits used to encode V is less than, the number of bits used to encode , the above recursive multiplication just results in a linear decay.This situation occurs, for example, when simulating a neural network with many millions of neurons using time multiplexing [7]-[10]. With a standard IIR filter approach, a large number of bits would be needed for each state variable to achieve enough resolution to calculate long time constants. Large memory storage per state variable w...

Compacted Self‐Assembly Graphene with Hydrogen Plasma Surface Modification for Robust Artificial Electronic Synapses of Gadolinium Oxide Memristors

“…Figure 6c,d presents the STDP behaviors of the Gd x O y memristors with a pristine and a 10 min H 2 plasma surface modified CSA graphene BEs, respectively. The STDP rule which fits the change in synaptic weight for both potentiation and depression by a hyperbolic exponential relationship is shown in Equation () [ 66 ] where A + / A − and τ + /τ − are synaptic weight change factors and time constants for potentiation and depression increment, respectively. The parameter of w indicates the connection strength between pre‐ and postsynaptic spikes.…”

Neuromorphic Engineering: From Biological to Spike‐Based Hardware Nervous Systems

“…[159,160] One feasible approach to mimic neuronal dynamics is with analog CMOS circuits that replicate the spiking behavior of neurons by mapping nonlinear differential equations. [161][162][163][164][165][166] Inspired by the Izhikevich neuron model, a silicon neuron circuit containing 14 metal-oxide-semiconductor field-effect Figure 6. Comparison of spiking dynamics of different neuron models.…”

An FPGA-Based Massively Parallel Neuromorphic Cortex Simulator

“…Rather than using a mathematical computational model with floating-point numbers, the physical neuron has been efficiently implemented using fixed-point numbers to minimise the number of bits that need to be stored for each state variable. The minimisation of memory use was effectively achieved using a stochastic method to implement exponential decays for the conductance-based neuron model (Wang et al, 2016), (Wang et al, 2014c). We store only the most significant bits (MSBs) and generate the least significant bits (LSBs) on the fly with a random number generator.…”