Spiking Neurons on GPUs

Engineering neural networks to perform specific tasks often represents a monumental challenge in determining network architecture and parameter values. In this work, we extend our previously-developed method for tuning networks of non-spiking neurons, the “Functional subnetwork approach” (FSA), to the tuning of networks composed of spiking neurons. This extension enables the direct assembly and tuning of networks of spiking neurons and synapses based on the network's intended function, without the use of global optimization or machine learning. To extend the FSA, we show that the dynamics of a generalized linear integrate and fire (GLIF) neuron model have fundamental similarities to those of a non-spiking leaky integrator neuron model. We derive analytical expressions that show functional parallels between: (1) A spiking neuron's steady-state spiking frequency and a non-spiking neuron's steady-state voltage in response to an applied current; (2) a spiking neuron's transient spiking frequency and a non-spiking neuron's transient voltage in response to an applied current; and (3) a spiking synapse's average conductance during steady spiking and a non-spiking synapse's conductance. The models become more similar as additional spiking neurons are added to each population “node” in the network. We apply the FSA to model a neuromuscular reflex pathway two different ways: Via non-spiking components and then via spiking components. These results provide a concrete example of how a single non-spiking neuron may model the average spiking frequency of a population of spiking neurons. The resulting model also demonstrates that by using the FSA, models can be constructed that incorporate both spiking and non-spiking units. This work facilitates the construction of large networks of spiking neurons and synapses that perform specific functions, for example, those implemented with neuromorphic computing hardware, by providing an analytical method for directly tuning their parameters without time-consuming optimization or learning.

As the desire for biologically realistic spiking neural networks (SNNs) increases, tuning the enormous number of open parameters in these models becomes a difficult challenge. SNNs have been used to successfully model complex neural circuits that explore various neural phenomena such as neural plasticity, vision systems, auditory systems, neural oscillations, and many other important topics of neural function. Additionally, SNNs are particularly well-adapted to run on neuromorphic hardware that will support biological brain-scale architectures. Although the inclusion of realistic plasticity equations, neural dynamics, and recurrent topologies has increased the descriptive power of SNNs, it has also made the task of tuning these biologically realistic SNNs difficult. To meet this challenge, we present an automated parameter tuning framework capable of tuning SNNs quickly and efficiently using evolutionary algorithms (EA) and inexpensive, readily accessible graphics processing units (GPUs). A sample SNN with 4104 neurons was tuned to give V1 simple cell-like tuning curve responses and produce self-organizing receptive fields (SORFs) when presented with a random sequence of counterphase sinusoidal grating stimuli. A performance analysis comparing the GPU-accelerated implementation to a single-threaded central processing unit (CPU) implementation was carried out and showed a speedup of 65× of the GPU implementation over the CPU implementation, or 0.35 h per generation for GPU vs. 23.5 h per generation for CPU. Additionally, the parameter value solutions found in the tuned SNN were studied and found to be stable and repeatable. The automated parameter tuning framework presented here will be of use to both the computational neuroscience and neuromorphic engineering communities, making the process of constructing and tuning large-scale SNNs much quicker and easier.

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.

With recent advances in learning algorithms, recurrent networks of spiking neurons are achieving performance that is competitive with vanilla recurrent neural networks. However, these algorithms are limited to small networks of simple spiking neurons and modest-length temporal sequences, as they impose high memory requirements, have difficulty training complex neuron models and are incompatible with online learning. Here, we show how the recently developed Forward-Propagation Through Time (FPTT) learning combined with novel liquid time-constant spiking neurons resolves these limitations. Applying FPTT to networks of such complex spiking neurons, we demonstrate online learning of exceedingly long sequences while outperforming current online methods and approaching or outperforming offline methods on temporal classification tasks. The efficiency and robustness of FPTT enable us to directly train a deep and performant spiking neural network for joint object localization and recognition, demonstrating the ability to train large-scale dynamic and complex spiking neural network architectures. Memory efficient online training of recurrent spiking neural networks without compromising accuracy is an open challenge in neuromorphic computing. Yin and colleagues demonstrate that training a recurrent neural network consisting of so-called liquid time-constant spiking neurons using an algorithm called Forward-Propagation Through Time allows for online learning and state-of-the-art performance at a reduced computational cost compared with existing approaches.

We investigated spontaneous activity and excitability in large networks of artificial spiking neurons. We compared three different spiking neuron models: integrate-and-fire (IF), regular-spiking (RS), and resonator (RES). First, we show that different models have different frequency-dependent response properties, yielding large differences in excitability. Then, we investigate the responsiveness of these models to a single afferent inhibitory/excitatory spike and calibrate the total synaptic drive such that they would exhibit similar peaks of the postsynaptic potentials (PSP). Based on the synaptic calibration, we build large microcircuits of IF, RS, and RES neurons and show that the resonance property favors homeostasis and self-sustainability of the network activity. On the other hand, integration produces instability while it endows the network with other useful properties, such as responsiveness to external inputs. We also investigate other potential sources of stable self-sustained activity and their relation to the membrane properties of neurons. We conclude that resonance and integration at the neuron level might interact in the brain to promote stability as well as flexibility and responsiveness to external input and that membrane properties, in general, are essential for determining the behavior of large networks of neurons.

A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks.

Conventional hardware platforms are far from reaching real-time simulation requirements of complex spiking neural networks (SNN). Therefore we designed an accelerator board with a neuro-processor-chip, called NeuroPipe-Chip. In this paper, we introduce two new concepts on chip-level to speed up the simulation of SNN. The concepts are implemented in the architecture of the NeuroPipe-Chip. We present the hardware structure of the NeuroPipe-Chip, which is modelled on register-transfer-level (RTL) using the hardware description language VHDL. We evaluate the performance of the NeuroPipe-Chip in a system simulation, where the rest of the accelerator board is modelled in behavioral VHDL. For a simple SNN for image segmentation, the NeuroPipe-Chip operating at 100 MHz shows an improvement of more than two orders of magnitude compared to an Alpha 500 MHz workstation and approaches real-time requirements for SNN in the order of 10/sup 6/ neurons. Hence, such an accelerator would allow real-time simulations of complex SNN for image processing. Currently, the implementation of the NeuroPipe-Chip in a 0.35 m digital CMOS technology is investigated.

Building accurate and efficient deep neural network (DNN) models for intelligent sensing systems to process data locally is essential. Spiking neural networks (SNNs) have gained significant popularity in recent years because they are more biological-plausible and energy-efficient than DNNs. However, SNNs usually have lower accuracy than DNNs. In this paper, we propose to use SNNs for image sensing applications. Moreover, we introduce the DNN-SNN knowledge distillation algorithm to reduce the accuracy gap between DNNs and SNNs. Our DNNSNN knowledge distillation improves the accuracy of an SNN by transferring knowledge between a DNN and an SNN. To better transfer the knowledge, our algorithm creates two learning paths from a DNN to an SNN. One path is between the output layer and another path is between the intermediate layer. DNNs use real numbers to propagate information between neurons while SNNs use 1-bit spikes. To empower the communication between DNNs and SNNs, we utilize a decoder to decode spikes into real numbers. Also, our algorithm creates a learning path from an SNN to a DNN. This learning path better adapts the DNN to the SNN by allowing the DNN to learn the knowledge from the SNN. Our SNN models are deployed on Loihi, which is a specialized chip for SNN models. On the MNIST dataset, our SNN models trained by the DNN-SNN knowledge distillation achieve better accuracy than the SNN models on GPU trained by other training algorithms with much lower energy consumption per image.

Developmental plasticity plays a prominent role in shaping the brain's structure during ongoing learning in response to dynamically changing environments. However, the existing network compression methods for deep artificial neural networks (ANNs) and spiking neural networks (SNNs) draw little inspiration from brain's developmental plasticity mechanisms, thus limiting their ability to learn efficiently, rapidly, and accurately. This paper proposed a developmental plasticity-inspired adaptive pruning (DPAP) method, with inspiration from the adaptive developmental pruning of dendritic spines, synapses, and neurons according to the "use it or lose it, gradually decay" principle. The proposed DPAP model considers multiple biologically realistic mechanisms (such as dendritic spine dynamic plasticity, activity-dependent neural spiking trace, and local synaptic plasticity), with additional adaptive pruning strategy, so that the network structure can be dynamically optimized during learning without any pre-training and retraining. Extensive comparative experiments show consistent and remarkable performance and speed boost with the extremely compressed networks on a diverse set of benchmark tasks for deep ANNs and SNNs, especially the spatio-temporal joint pruning of SNNs in neuromorphic datasets. This work explores how developmental plasticity enables complex deep networks to gradually evolve into brain-like efficient and compact structures, eventually achieving state-of-the-art (SOTA) performance for biologically realistic SNNs.

The paper presents a modification of the structure of a biological neural network (BNN) based on spiking neuron models. The proposed modification allows to influence the level of the stimulus response of particular neurons in the BNN. We consider an extended, three-dimensional Hodgkin-Huxley model of the neural cell. A typical BNN composed of such neural cells have been expanded by addition of resistors in each branch point. The resistors can be treated as the weights in such BNN. We demonstrate that adding these elements to the BNN significantly affects the waveform of the potential on the membrane of the neuron, causing an uncontrolled excitation. This provides a better description of processes that take place in nervous cell. Such BNN enables an easy adaptation of the learning rules used in artificial or spiking neural networks. The modified BNN has been implemented on Graphics Processing Unit (GPU) in the CUDA C language. This platform enables a parallel data processing, which is an important feature in such applications.

Rethinking the performance comparison between SNNS and ANNS

Artificial neural network (ANN) research is inspired by how information is dynamically and massively processed in parallel by biological neural networks. Spiking neural networks (SNNs) are versions of artificial neural networks that are more biologically realistic than commonly used static models. As in actual brains, neurons signal each other through current spikes (rather than constant inputs, as in conventional ANNs), and spike timing plays a key role in SNN functioning. In this work, we give an overview of SNNs, and we describe and implement three different mathematical models (integrate and fire, leaky integrate and fire, conductance-based) using the Brian2 software simulator. We also describe the training of SNNs using the spike-timing-dependent plasticity (STDP) algorithm, and discuss an experiment by Diehl and Cook that shows the ability of SNNs to learn to distinguish handwritten digits. Lastly, we describe a few available software SNN simulators and hardware SNN implementations with possible practical applications of SNNs.

Brain-inspired spiking neural networks (SNNs) are becoming a promising energy-efficient alternative to traditional artificial neural networks (ANNs). However, the performance gap between SNNs and ANNs has been a significant hindrance to deploying SNNs ubiquitously. To leverage the full potential of SNNs, in this paper we study the attention mechanisms, which can help human focus on important information. We present our idea of attention in SNNs with a multi-dimensional attention module, which infers attention weights along the temporal, channel, as well as spatial dimension separately or simultaneously. Based on the existing neuroscience theories, we exploit the attention weights to optimize membrane potentials, which in turn regulate the spiking response. Extensive experimental results on event-based action recognition and image classification datasets demonstrate that attention facilitates vanilla SNNs to achieve sparser spiking firing, better performance, and energy efficiency concurrently. In particular, we achieve top-1 accuracy of 75.92% and 77.08% on ImageNet-1 K with single/4-step Res-SNN-104, which are state-of-the-art results in SNNs. Compared with counterpart Res-ANN-104, the performance gap becomes -0.95/+0.21 percent and the energy efficiency is 31.8×/7.4×. To analyze the effectiveness of attention SNNs, we theoretically prove that the spiking degradation or the gradient vanishing, which usually holds in general SNNs, can be resolved by introducing the block dynamical isometry theory. We also analyze the efficiency of attention SNNs based on our proposed spiking response visualization method. Our work lights up SNN's potential as a general backbone to support various applications in the field of SNN research, with a great balance between effectiveness and energy efficiency.

Disrupting the pathological synchronous firing patterns of neurons with high frequency stimulation is a common treatment for Parkinsonian symptoms and epileptic seizures when pharmaceutical drugs fail. In this paper, our goal is to design a desynchronization strategy for large networks of spiking neurons such that the neuronal activity of the network remains in the desynchronized regime for a long period of time after the removal of the stimulation. We develop a novel “Forced Temporal-Spike Time Stimulation (FTSTS)” strategy that harnesses the spike-timing dependent plasticity to control the synchronization of neural activity in the network by forcing the neurons in the network to artificially fire in a specific temporal pattern. Our strategy modulates the synaptic strengths of selective synapses to achieve a desired synchrony of neural activity in the network. Our simulation results show that the FTSTS strategy can effectively synchronize or desynchronize neural activity in large spiking neuron networks and keep them in the desired state for a long period of time after the removal of the external stimulation. Using simulations, we demonstrate the robustness of our strategy in desynchronizing neural activity of networks against uncertainties in the designed stimulation pulses and network parameters. Additionally, we show in simulation, how our strategy could be incorporated within the existing desynchronization strategies to improve their overall efficacy in desynchronizing large networks. Our proposed strategy provides complete control over the synchronization of neurons in large networks and can be used to either synchronize or desynchronize neural activity based on specific applications. Moreover, it can be incorporated within other desynchronization strategies to improve the efficacy of existing therapies for numerous neurological and psychiatric disorders associated with pathological synchronization.

Complex ideas are best conveyed through well-designed illustrations. Up to now, computational neuroscientists have mostly relied on box-and-arrow diagrams of even complex neuronal networks, often using ad hoc notations with conflicting use of symbols from paper to paper. This significantly impedes the communication of ideas in neuronal network modeling. We present here Connectivity Pattern Tables (CPTs) as a clutter-free visualization of connectivity in large neuronal networks containing two-dimensional populations of neurons. CPTs can be generated automatically from the same script code used to create the actual network in the NEST simulator. Through aggregation, CPTs can be viewed at different levels, providing either full detail or summary information. We also provide the open source ConnPlotter tool as a means to create connectivity pattern tables.