A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons

Intrinsically-generated fluctuating activity in excitatory-inhibitory networks

Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in networks of deterministic, but randomly connected rate units. How this type of intrinsi- cally generated fluctuations appears in more realistic networks of spiking neurons has been a long standing question. To ease the comparison between rate and spiking networks, recent works investigated the dynami- cal regimes of randomly-connected rate networks with segregated excitatory and inhibitory populations, and firing rates constrained to be positive. These works derived general dynamical mean field (DMF) equations describing the fluctuating dynamics, but solved these equations only in the case of purely inhibitory networks. Using a simplified excitatory-inhibitory architecture in which DMF equations are more easily tractable, here we show that the presence of excitation qualitatively modifies the fluctuating activity compared to purely inhibitory networks. In presence of excitation, intrinsically generated fluctuations induce a strong increase in mean firing rates, a phenomenon that is much weaker in purely inhibitory networks. Excitation moreover induces two different fluctuating regimes: for moderate overall coupling, recurrent inhibition is sufficient to stabilize fluctuations, for strong coupling, firing rates are stabilized solely by the upper bound imposed on activity, even if inhibition is stronger than excitation. These results extend to more general network architectures, and to rate networks receiving noisy inputs mimicking spiking activity. Finally, we show that signatures of the second dynamical regime appear in networks of integrate-and-fire neurons

Spiking-YOLO: Spiking Neural Network for Energy-Efficient Object Detection

Over the past decade, deep neural networks (DNNs) have demonstrated remarkable performance in a variety of applications. As we try to solve more advanced problems, increasing demands for computing and power resources has become inevitable. Spiking neural networks (SNNs) have attracted widespread interest as the third-generation of neural networks due to their event-driven and low-powered nature. SNNs, however, are difficult to train, mainly owing to their complex dynamics of neurons and non-differentiable spike operations. Furthermore, their applications have been limited to relatively simple tasks such as image classification. In this study, we investigate the performance degradation of SNNs in a more challenging regression problem (i.e., object detection). Through our in-depth analysis, we introduce two novel methods: channel-wise normalization and signed neuron with imbalanced threshold, both of which provide fast and accurate information transmission for deep SNNs. Consequently, we present a first spiked-based object detection model, called Spiking-YOLO. Our experiments show that Spiking-YOLO achieves remarkable results that are comparable (up to 98%) to those of Tiny YOLO on non-trivial datasets, PASCAL VOC and MS COCO. Furthermore, Spiking-YOLO on a neuromorphic chip consumes approximately 280 times less energy than Tiny YOLO and converges 2.3 to 4 times faster than previous SNN conversion methods.Comment: Accepted to AAAI 202

Rhythmic inhibition allows neural networks to search for maximally consistent states

Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to search for network configurations that best reconcile external inputs with an internal consistency model encoded in the network connectivity. We show that Hebbian plasticity allows the networks to learn the consistency model by example. The search dynamics driven by rhythmic inhibition enable the described networks to solve difficult constraint satisfaction problems without making assumptions about the form of stochastic fluctuations in the network. We show that the search dynamics are well approximated by a stochastic sampling process. We use the described networks to reproduce perceptual multi-stability phenomena with switching times that are a good match to experimental data and show that they provide a general neural framework which can be used to model other 'perceptual inference' phenomena

Fast and Efficient Asynchronous Neural Computation with Adapting Spiking Neural Networks

Biological neurons communicate with a sparing exchange of pulses - spikes. It is an open question how real spiking neurons produce the kind of powerful neural computation that is possible with deep artificial neural networks, using only so very few spikes to communicate. Building on recent insights in neuroscience, we present an Adapting Spiking Neural Network (ASNN) based on adaptive spiking neurons. These spiking neurons efficiently encode information in spike-trains using a form of Asynchronous Pulsed Sigma-Delta coding while homeostatically optimizing their firing rate. In the proposed paradigm of spiking neuron computation, neural adaptation is tightly coupled to synaptic plasticity, to ensure that downstream neurons can correctly decode upstream spiking neurons. We show that this type of network is inherently able to carry out asynchronous and event-driven neural computation, while performing identical to corresponding artificial neural networks (ANNs). In particular, we show that these adaptive spiking neurons can be drop in replacements for ReLU neurons in standard feedforward ANNs comprised of such units. We demonstrate that this can also be successfully applied to a ReLU based deep convolutional neural network for classifying the MNIST dataset. The ASNN thus outperforms current Spiking Neural Networks (SNNs) implementations, while responding (up to) an order of magnitude faster and using an order of magnitude fewer spikes. Additionally, in a streaming setting where frames are continuously classified, we show that the ASNN requires substantially fewer network updates as compared to the corresponding ANN

Fast and Efficient Asynchronous Neural Computation with Adapting Spiking Neural Networks

Biological neurons communicate with a sparing exchange of pulses - spikes. It is an open question how real spiking neurons produce the kind of powerful neural computation that is possible with deep artificial neural networks, using only so very few spikes to communicate. Building on recent insights in neuroscience, we present an Adapting Spiking Neural Network (ASNN) based on adaptive spiking neurons. These spiking neurons efficiently encode information in spike-trains using a form of Asynchronous Pulsed Sigma-Delta coding while homeostatically optimizing their firing rate. In the proposed paradigm of spiking neuron computation, neural adaptation is tightly coupled to synaptic plasticity, to ensure that downstream neurons can correctly decode upstream spiking neurons. We show that this type of network is inherently able to carry out asynchronous and event-driven neural computation, while performing identical to corresponding artificial neural networks (ANNs). In particular, we show that these adaptive spiking neurons can be drop in replacements for ReLU neurons in standard feedforward ANNs comprised of such units. We demonstrate that this can also be successfully applied to a ReLU based deep convolutional neural network for classifying the MNIST dataset. The ASNN thus outperforms current Spiking Neural Networks (SNNs) implementations, while responding (up to) an order of magnitude faster and using an order of magnitude fewer spikes. Additionally, in a streaming setting where frames are continuously classified, we show that the ASNN requires substantially fewer network updates as compared to the corresponding ANN

Optimizing the energy consumption of spiking neural networks for neuromorphic applications

In the last few years, spiking neural networks have been demonstrated to perform on par with regular convolutional neural networks. Several works have proposed methods to convert a pre-trained CNN to a Spiking CNN without a significant sacrifice of performance. We demonstrate first that quantization-aware training of CNNs leads to better accuracy in SNNs. One of the benefits of converting CNNs to spiking CNNs is to leverage the sparse computation of SNNs and consequently perform equivalent computation at a lower energy consumption. Here we propose an efficient optimization strategy to train spiking networks at lower energy consumption, while maintaining similar accuracy levels. We demonstrate results on the MNIST-DVS and CIFAR-10 datasets