Spiking neural network

Pulsed neuron model

Artificial synapses based on FTJs

Multi-layer artificial neural networks are usually fully connected, receiving input from every neuron in the previous layer and signalling every neuron in the subsequent layer. Although these networks have achieved breakthroughs in many fields, they are biologically inaccurate and do not mimic the operation mechanism of neurons in the brain of a living thing.[3]

The biologically-inspired Hodgkin–Huxley model of a spiking neuron was proposed in 1952. This model describes how action potentials are initiated and propagated. Communication between neurons, which requires the exchange of chemical neurotransmitters in the synaptic gap, is described in various models, such as the integrate-and-fire model, FitzHugh–Nagumo model (1961–1962), and Hindmarsh–Rose model (1984). The leaky integrate-and-fire model (or a derivative) is commonly used as it is easier to compute than the Hodgkin–Huxley model.[4]

In July 2019 at the DARPA Electronics Resurgence Initiative summit, Intel unveiled an 8-million-neuron neuromorphic system comprising 64 Loihi research chips.[5]

From the information theory perspective, the problem is to explain how information is encoded and decoded by a series of trains of pulses, i.e. action potentials. Thus, a fundamental question of neuroscience is to determine whether neurons communicate by a rate or temporal code.[6] Temporal coding suggests that a single spiking neuron can replace hundreds of hidden units on a sigmoidal neural net.[1]

A spiking neural network considers temporal information. The idea is that not all neurons are activated in every iteration of propagation (as is the case in a typical multilayer perceptron network), but only when its membrane potential reaches a certain value. When a neuron is activated, it produces a signal that is passed to connected neurons, raising or lowering their membrane potential.

In a spiking neural network, the neuron's current state is defined as its level of activation (modeled as a differential equation). An input pulse causes the current state value to rise for a period of time and then gradually decline. Encoding schemes have been constructed to interpret these output pulse sequences as a number, taking into account both pulse frequency and pulse interval. A neural network model based on pulse generation time can be established accurately. Spike coding is adopted in this new neural network. Using the exact time of pulse occurrence, a neural network can employ more information and offer stronger computing power.

Pulse-coupled neural networks (PCNN) are often confused with SNNs. A PCNN can be seen as a kind of SNN.

The SNN approach uses a binary output (signal/no signal) instead of the continuous output of traditional ANNs. Further, pulse trainings are not easily interpretable. But pulse training increases the ability to process spatiotemporal data (or real-world sensory data). Space refers to the fact that neurons connect only to nearby neurons so that they can process input blocks separately (similar to CNN using filters). Time refers to the fact that pulse training occurs over time so that the information lost in binary coding can be retrieved from the time information. This avoids the additional complexity of a recurrent neural network (RNN). It turns out that impulse neurons are more powerful computational units than traditional artificial neurons.[3]

SNN is theoretically more powerful than second-generation networks, however SNN training issues and hardware requirements limit their use. Although unsupervised biological learning methods are available, such as Hebbian learning and STDP, no effective supervised training method is suitable for SNN that can provide better performance than second-generation networks. Spike based activation of SNNs is not differentiable thus making it hard to develop gradient descent based training methods to perform error backpropagation, though a few recent algorithms such as NormAD[7] and multilayer NormAD[8] have demonstrated good training performance through suitable approximation of the gradient of spike based activation.

SNNs have much larger computational costs for simulating realistic neural models than traditional ANNs.

SNNs can in principle apply to the same applications as traditional ANNs.[9] In addition, SNNs can model the central nervous system of biological organisms, such as an insect seeking food without prior knowledge of the environment.[10] Due to their relative realism, they can be used to study the operation of biological neural circuits. Starting with a hypothesis about the topology of a biological neuronal circuit and its function, recordings of this circuit can be compared to the output of the corresponding SNN, evaluating the plausibility of the hypothesis. However, there is a lack of effective training mechanisms for SNNs, which can be inhibitory for some applications, including computer vision tasks.

As of 2019 SNNs lag ANNs in terms of accuracy, but the gap is decreasing, and has vanished on some tasks.[11]

A diverse range of application software can simulate SNNs. This software can be classified according to its uses:

SNN simulation

Unsupervised learning with ferroelectric synapses

These simulate complex neural models with a high level of detail and accuracy. Large networks usually require lengthy processing. Candidates include:[12]

• GENESIS (the GEneral NEural SImulation System[13]) – developed in James Bower's laboratory at Caltech;
• NEURON – mainly developed by Michael Hines, John W. Moore and Ted Carnevale in Yale University and Duke University;
• Brian – developed by Romain Brette and Dan Goodman at the École Normale Supérieure;
• NEST – developed by the NEST Initiative;
• BindsNET – developed by the Biologically Inspired Neural and Dynamical Systems (BINDS) lab at the University of Massachusetts Amherst.[14]
• SpykeTorch - a framework based on PyTorch optimized specifically for convolutional SNNs with at most one spike per neuron. Runs on GPUs.[15]

Predicting STDP learning with ferroelectric synapses

Neuron-to-neuron mesh routing model

Future neuromorphic architectures[16] will comprise billions of such nanosynapses, which require a clear understanding of the physical mechanisms responsible for plasticity. Experimental systems based on ferroelectric tunnel junctions have been used to show that STDP can be harnessed from heterogeneous polarization switching. Through combined scanning probe imaging, electrical transport and atomic-scale molecular dynamics, conductance variations can be modelled by nucleation-dominated reversal of domains. Simulations show that arrays of ferroelectric nanosynapses can autonomously learn to recognize patterns in a predictable way, opening the path towards unsupervised learning.[17]

Unsupervised learning with ferroelectric synapses

• Brainchip's Akida NSoC has effectively 1.2 million neurons and 10 billion synapses, representing orders of magnitude better efficiency than other neural processing devices on the market.[18]
• Neurogrid is a board that can simulate spiking neural networks directly in hardware. (Stanford University)
• SpiNNaker (Spiking Neural Network Architecture) uses ARM processors as the building blocks of a massively parallel computing platform based on a six-layer thalamocortical model. (University of Manchester)[19] The SpiNNaker system is based on numerical models running in real time on custom digital multicore chips using the ARM architecture. It provides custom digital chips, each with eighteen cores and a shared local 128 Mbyte RAM, with a total of over 1,000,000 cores.[20] A single chip can simulate 16,000 neurons with eight million plastic synapses running in real time.[21]
• TrueNorth is a processor that contains 5.4 billion transistors that consumes only 70 milliwatts; most processors in personal computers contain about 1.4 billion transistors and require 35 watts or more. IBM refers to the design principle behind TrueNorth as neuromorphic computing. Its primary purpose is pattern recognition. While critics say the chip isn't powerful enough, its supporters point out that this is only the first generation, and the capabilities of improved iterations will become clear. (IBM)[22]
• Dynamic Neuromorphic Asynchronous Processor (DYNAP)[23] combines slow, low-power, inhomogeneous sub-threshold analog circuits, and fast programmable digital circuits. It supports reconfigurable, general-purpose, real-time neural networks of spiking neurons. This allows the implementation of real-time spike-based neural processing architectures[24][25] in which memory and computation are co-localized. It solves the von Neumann bottleneck problem and enables real-time multiplexed communication of spiking events for realising massive networks. Recurrent networks, feed-forward networks, convolutional networks, attractor networks, echo-state networks, deep networks, and sensor fusion networks are a few of the possibilities.[26]

Core Top-Level Microarchitecture

• Loihi is a 14-nm Intel chip that offers 128 cores and 130,000 neurons on a 60-mm package.[27] It integrates a wide range of features, such as hierarchical connectivity, dendritic compartments, synaptic delays and programmable synaptic learning rules.[28] Running a spiking convolutional form of the Locally Competitive Algorithm, Loihi can solve LASSO optimization problems with over three orders of magnitude superior energy-delay product compared to conventional solvers running on a CPU isoprocess/voltage/area.[29] A 64 Loihi research system offers 8-million-neuron neuromorphic system. Loihi is about 1,000 times as fast as a CPU and 10,000 times as energy efficient.[5]
• BrainScaleS is based on physical emulations of neuron, synapse and plasticity models with digital connectivity, running up to ten thousand times faster than real time. It was developed by the European Human Brain Project.[20] The BrainScaleS system contains 20 8-inch silicon wafers in 180 nm process technology. Each wafer incorporates 50 x 106 plastic synapses and 200,000 biologically realistic neurons. The system does not execute pre-programmed code but evolves according to the physical properties of the electronic devices, running at up to 10 thousand times faster than real time.[21]

Classification capabilities of spiking networks trained according to unsupervised learning methods[30] have been tested on the common benchmark datasets, such as, Iris, Wisconsin Breast Cancer or Statlog Landsat dataset.[31][32][33] Various approaches to information encoding and network design have been used. For example, a 2-layer feedforward network for data clustering and classification. Based on the idea proposed in Hopfield (1995) the authors implemented models of local receptive fields combining the properties of radial basis functions (RBF) and spiking neurons to convert input signals (classified data) having a floating-point representation into a spiking representation.[34][35]

• CoDi
• Cognitive architecture
• Cognitive map
• Cognitive computer
• Computational neuroscience
• Neural coding
• Neural correlate
• Neural decoding
• Neuroethology
• Neuroinformatics
• Models of neural computation
• Motion perception
• Systems neuroscience

• Full text of the book Spiking Neuron Models. Single Neurons, Populations, Plasticity by Wulfram Gerstner and Werner M. Kistler (ISBN 0-521-89079-9)