Unsupervised post-training learning in spiking neural networks

Spiking Neural Networks (SNNs), widely known as the third generation of neural networks, encode input information temporally using sparse spiking events, which can be harnessed to achieve higher computational efficiency for cognitive tasks. However, considering the rapid strides in accuracy enabled by state-of-the-art Analog Neural Networks (ANNs), SNN training algorithms are much less mature, leading to accuracy gap between SNNs and ANNs. In this paper, we propose different SNN training methodologies, varying in degrees of biofidelity, and evaluate their efficacy on complex image recognition datasets. First, we present biologically plausible Spike Timing Dependent Plasticity (STDP) based deterministic and stochastic algorithms for unsupervised representation learning in SNNs. Our analysis on the CIFAR-10 dataset indicates that STDP-based learning rules enable the convolutional layers to self-learn low-level input features using fewer training examples. However, STDP-based learning is limited in applicability to shallow SNNs (≤4 layers) while yielding considerably lower than state-of-the-art accuracy. In order to scale the SNNs deeper and improve the accuracy further, we propose conversion methodology to map off-the-shelf trained ANN to SNN for energy-efficient inference. We demonstrate 69.96% accuracy for VGG16-SNN on ImageNet. However, ANN-to-SNN conversion leads to high inference latency for achieving the best accuracy. In order to minimize the inference latency, we propose spike-based error backpropagation algorithm using differentiable approximation for the spiking neuron. Our preliminary experiments on CIFAR-10 show that spike-based error backpropagation effectively captures temporal statistics to reduce the inference latency by up to 8× compared to converted SNNs while yielding comparable accuracy

A forecast-based STDP rule suitable for neuromorphic implementation

Spiking neural networks (SNNs), inspired by the neuronal network in the brain, provide biologically relevant and low-power consuming models for information processing. Existing studies either mimic the learning mechanism of brain neural networks as closely as possible, for example, the temporally local learning rule of spike-timing-dependent plasticity (STDP), or apply the gradient descent rule to optimize a multilayer SNN with fixed structure. However, the learning rule used in the former is local and how the real brain might do the global-scale credit assignment is still not clear, which means that those shallow SNNs are robust but deep SNNs are difficult to be trained globally and could not work so well. For the latter, the nondifferentiable problem caused by the discrete spike trains leads to inaccuracy in gradient computing and difficulties in effective deep SNNs. Hence, a hybrid solution is interesting to combine shallow SNNs with an appropriate machine learning (ML) technique not requiring the gradient computing, which is able to provide both energy-saving and high-performance advantages. In this article, we propose a HybridSNN, a deep and strong SNN composed of multiple simple SNNs, in which data-driven greedy optimization is used to build powerful classifiers, avoiding the derivative problem in gradient descent. During the training process, the output features (spikes) of selected weak classifiers are fed back to the pool for the subsequent weak SNN training and selection. This guarantees HybridSNN not only represents the linear combination of simple SNNs, as what regular AdaBoost algorithm generates, but also contains neuron connection information, thus closely resembling the neural networks of a brain. HybridSNN has the benefits of both low power consumption in weak units and overall data-driven optimizing strength. The network structure in HybridSNN is learned from training samples, which is more flexible and effective compared with existing fixed multilayer SNNs. Moreover, the topological tree of HybridSNN resembles the neural system in the brain, where pyramidal neurons receive thousands of synaptic input signals through their dendrites. Experimental results show that the proposed HybridSNN is highly competitive among the state-of-the-art SNNs.

Spike timing dependent plasticity (STDP) learning rule is one of hot topics in neurobiology since it's been widely believed that synaptic plasticity mainly contribute to learning and memory in brain. Up to now, STDP has been observed in a wide variety of areas of brain, hippocampus, cortex and so on. Competition among synapses is an important behavior for this learning rule. In present study, we propose a single layer spiking neural network model using STDP learning rule in inhibitory synapses to investigate the competitive behavior. The experiments show that the synapses among neurons are both strengthened on the whole training process. Thus neurons inhibit the activities of one another, eventually the neuron with the highest input spike rate win the competition. We have found that the behavior is efficient when the differences of firing rates of input neurons without STDP are great than 5Hz, otherwise the winner neuron is random. In order to use the principle to artificial intelligent system, we use a mechanism of dynamic learning rate to let the neuron with the highest input to be selected by the competitive behavior as the winner. Therefore, a robust competitive spiking neural network is obtained.

Spiking Neural Networks (SNN) is one special implementation of Artificial Neural Networks (ANN), where the input signals are encoded in the temporal relationship between consecutive spikes (spike trains) instead of real-numbered values. Nevertheless, SNN is believed to be a closer representation of the biological neural system, because it imitates the current spikes that are transmitted between neurons in real biological systems. Practical and simplified SNN models include the Leaky Integrate-and-Fire (LIF) function of the neurons and the Spiking Timing Dependent Plasticity (STDP) function of the synapses. While most ANN architectures can be implemented with digital logic gates, SNN is more suitable to be implemented in analog circuits. In this paper, we propose revised analog circuit implementations of SNN neurons with LIF and STDP functions. Compared with previous works by other researchers, our proposed analog designs use fewer components and can be cascaded to form a complete neural system. The circuits are designed and simulated with SMIC 55nm CMOS LP process. The simulated results demonstrate that the analog neural system can work under a very small current (less than 10 µA) and voltage supply (1.0 Volts), and consumes less power consumption than digital implementations.

Recently, spiking neural networks (SNNs) have been shown capable of approximating the dynamics of biological neuronal networks, and of being trainable by biologically-plausible learning mechanisms, such as spike-timing-dependent synaptic plasticity. Numerical simulations also support the possibility that they may possess universal function approximation abilities. However the effectiveness of training algorithms to date is far inferior to those of other artificial neural networks. Moreover, they rely on directly manipulating the SNN weights, which may not be feasible in a number of their potential applications. This paper presents a novel indirect training approach to modulate spike-timing-dependent plasticity (STDP) in an action SNN that serves as a flight controller without directly manipulating its weights. A critic SNN is directly trained with a reward-based Hebbian approach to send spike trains to the action SNN, which in turn controls the aircraft and learns via STDP. The approach is demonstrated by training the action SNN to act as a flight controller for stability augmentation. Its performance and dynamics are analyzed before and after training through numerical simulations and Poincaré maps.

We present a compact mixed-signal implementation of synaptic plasticity for both Spike Timing Dependent Plasticity (STDP) and Spike Timing Dependent Delay Plasticity (STDDP). The proposed mixed-signal implementation consists of an a VLSI time window generator and a digital adaptor. The weight and delay values are stored in a digital memory, and the adaptor will send these values to the time window generator using a digital spike of which the duration is modulated according to these values. The analogue time window generator will then generate a time window, which is required for the implementation of STDP and STDDP. The digital adaptor will carry out the weight/delay adaption using this time window. The aVLSI time window generator is compact (50 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in IBM 130nm process) and we use a time multiplexing approach to achieve up to 65536 (64k) virtual digital adaptors with one physical adaptor, consuming only a fraction of the hardware resource on a Virtex 6 FPGA. Since the digital adaptor has been implemented on an FPGA, it can be easily reconfigured for different adaptation algorithms, which leaves it open for future development. Our mixed-signal implementation is therefore practical for implementing the synaptic plasticity in large-scale spiking neural networks running in real time. We show circuit simulation results illustrating both weight and delay adaptation.

The idea that synaptic plasticity holds the key to the neural basis of learning and memory is now widely accepted in neuroscience. The precise mechanism of changes in synaptic strength has, however, remained elusive. Neurobiological research has led to the postulation of many models of plasticity, and among the most contemporary are spike-timing dependent plasticity (STDP) and long-term potentiation (LTP). The STDP model is based on the observation of single, distinct pairs of pre- and post- synaptic spikes, but it is less clear how it evolves dynamically under the input of long trains of spikes, which characterise normal brain activity. This research explores the emergent properties of a spiking artificial neural network which incorporates both STDP and LTP. Previous findings are replicated in most instances, and some interesting additional observations are made. These highlight the profound influence which initial conditions and synaptic input have on the evolution of synaptic weights.KeywordsFiring RateSpike TrainPlasticity ModelSynaptic WeightSynaptic StrengthThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Artificial neural systems for computation were first proposed three quarters of a century ago and the concepts developed by the pioneers still shape the field today. The first generation of neural systems was developed in the nineteen forties in the context of analogue electronics and the theoretical research in logic and mathematics that led to the first digital computers in nineteen forties and fifties. The second generation of neural systems implemented on digital computers was born in the nineteen fifties and great progress was made in the subsequent half century with neural networks being applied to many problems in pattern recognition and machine learning. Through this history there has been an interplay between biologically inspired neural systems and their implementation by engineers on digital machines. This thesis concerns the third generation of neural networks, Spiking Neural Networks, which is making possible the creation of new kinds of brain inspired computing architectures that offer the potential to increase the level of realism and sophistication in terms of autonomous machine behaviour and cognitive computing. This thesis presents the development and demonstration of a new theoretical architecture for third generation neural systems, the Integrate-and-Fire based Spiking Neural Model with extended Neuro-modulated Spike Timing Dependent Plasticity capabilities. This proposed architecture overcomes the limitation of the homosynaptic architecture underlying existing implementations of spiking neural networks that it lacks a natural spike timing dependent plasticity regulation mechanism, and this results in ‘run away’ dynamics. To overcome this ad hoc procedures have been implemented to overcome the ‘run away’ dynamics that emerge from the use of spike timing dependent plasticity among other hebbian-based plasticity rules. The new heterosynaptic architecture presented, explicitly abstracts the modulation of complex biochemical mechanisms into a simplified mechanism that is suitable for the engineering of artificial systems with low computational complexity. Neurons work by receiving input signals from other neurons through synapses. The difference between homosynaptic and heterosynaptic plasticity is that, in the former the change in the properties of a synapse (e.g. synaptic efficacy) depends on the point to point activity in either of the sending and receiving neurons, in contrast for heterosynaptic plasticity the change in the properties of a synapse can be elicited by neurons that are not necessary presynaptic or postsynaptic to the synapse in question. The new architecture is tested by a number of implementations in simulated and real environments. This includes experiments with a simulation environment implemented in Netlogo, and an implementation using Lego Mindstorms as the physical robot platform. These experiments demonstrate the problems with the traditional Spike timing dependent plasticity homosynaptic architecture and how the new heterosynaptic approach can overcome them. It is concluded that the new theoretical architecture provides a natural, theoretically sound, and practical new direction for research into the role of modulatory neural systems applied to spiking neural networks.

Inspired by the human brain's function and efficiency, neuromorphic computing offers a promising solution for a wide set of tasks, ranging from brain machine interfaces to real-time classification. The spiking neural network (SNN), which encodes and processes information with bionic spikes, is an emerging neuromorphic model with great potential to drastically promote the performance and efficiency of computing systems. However, an energy efficient hardware implementation and the difficulty of training the model significantly limit the application of the spiking neural network. In this work, we address these issues by building an SNNbased energy efficient system for real time classification with metal-oxide resistive switching random-access memory (RRAM) devices. We implement different training algorithms of SNN, including Spiking Time Dependent Plasticity (STDP) and Neural Sampling method. Our RRAM SNN systems for these two training algorithms show good power efficiency and recognition performance on realtime classification tasks, such as the MNIST digit recognition. Finally, we propose a possible direction to further improve the classification accuracy by boosting multiple SNNs. Copyright © 2015 ACM.

A spiking neural network (SNN) is a bottom-up tool used to describe information processing in brain microcircuits. It is becoming a crucial neuromorphic computational model. Spike-timing-dependent plasticity (STDP) is an unsupervised brain-like learning rule implemented in many SNNs and neuromorphic chips. However, a significant performance gap exists between ideal model simulation and neuromorphic implementation. The performance of STDP learning in neuromorphic chips deteriorates because the resolution of synaptic efficacy in such chips is generally restricted to 6 bits or less, whereas simulations employ the entire 64-bit floating-point precision available on digital computers. Previously, we introduced a bio-inspired learning rule named adaptive STDP and demonstrated via numerical simulation that adaptive STDP (using only 4-bit fixed-point synaptic efficacy) performs similarly to STDP learning (using 64-bit floating-point precision) in a noisy spike pattern detection model. Herein, we present the experimental results demonstrating the performance of adaptive STDP learning. To the best of our knowledge, this is the first study that demonstrates unsupervised noisy spatiotemporal spike pattern detection to perform well and maintain the simulation performance on a mixed-signal CMOS neuromorphic chip with low-resolution synaptic efficacy. The chip was designed in Taiwan Semiconductor Manufacturing Company (TSMC) 250 nm CMOS technology node and comprises a soma circuit and 256 synapse circuits along with their learning circuitry.

The problem with training spiking neural networks (SNNs) is relevant due to the ultra-low power consumption these networks could exhibit when implemented in neuromorphic hardware. The ongoing progress in the fabrication of memristors, a prospective basis for analogue synapses, gives relevance to studying the possibility of SNN learning on the base of synaptic plasticity models, obtained by fitting the experimental measurements of the memristor conductance change. The dynamics of memristor conductances is (necessarily) nonlinear, because conductance changes depend on the spike timings, which neurons emit in an all-or-none fashion. The ability to solve classification tasks was previously shown for spiking network models based on the bio-inspired local learning mechanism of spike-timing-dependent plasticity (STDP), as well as with the plasticity that models the conductance change of nanocomposite (NC) memristors. Input data were presented to the network encoded into the intensities of Poisson input spike sequences. This work considers another approach for encoding input data into input spike sequences presented to the network: temporal encoding, in which an input vector is transformed into relative timing of individual input spikes. Since temporal encoding uses fewer input spikes, the processing of each input vector by the network can be faster and more energy-efficient. The aim of the current work is to show the applicability of temporal encoding to training spiking networks with three synaptic plasticity models: STDP, NC memristor approximation, and PPX memristor approximation. We assess the accuracy of the proposed approach on several benchmark classification tasks: Fisher’s Iris, Wisconsin breast cancer, and the pole balancing task (CartPole). The accuracies achieved by SNN with memristor plasticity and conventional STDP are comparable and are on par with classic machine learning approaches.

Many efforts have been taken to train spiking neural networks (SNNs), but most of them still need improvements due to the discontinuous and non-differential characteristics of SNNs. While the mammalian brains solve these kinds of problems by integrating a series of biological plasticity learning rules. In this paper, we will focus on two biological plausible methodologies and try to solve these catastrophic training problems in SNNs. Firstly, the biological neural network will try to keep a balance between inputs and outputs on both the neuron and the network levels. Secondly, the biological synaptic weights will be passively updated by the changes of the membrane potentials of the neighbour-hood neurons, and the plasticity of synapses will not propagate back to other previous layers. With these biological inspirations, we propose Voltage-driven Plasticity-centric SNN (VPSNN), which includes four steps, namely: feed forward inference, unsupervised equilibrium state learning, supervised last layer learning and passively updating synaptic weights based on spike-timing dependent plasticity (STDP). Finally we get the accuracy of 98.52% on the hand-written digits classification task on MNIST. In addition, with the help of a visualization tool, we try to analyze the black box of SNN and get better understanding of what benefits have been acquired by the proposed method.

Enhanced Spiking Neural Network with forgetting phenomenon based on electronic synaptic devices

Predictive coding can be regarded as a function which reduces the error between an input signal and a top-down prediction. If reducing the error is equivalent to reducing the influence of stimuli from the environment, predictive coding can be regarded as stimulation avoidance by prediction. Our previous studies showed that action and selection for stimulation avoidance emerge in spiking neural networks through spike-timing dependent plasticity (STDP). In this study, we demonstrate that spiking neural networks with random structure spontaneously learn to predict temporal sequences of stimuli based solely on STDP.