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We consider the deterministic evolution of a time-discretized spiking network of neurons with connection weights having delays, modeled as a discretized neural network of the generalized integrate and fire (gIF) type. The purpose is to study a class of algorithmic methods allowing to calculate the proper parameters to reproduce exactly a given spike train generated by an hidden (unknown) neural network. This standard problem is known as NP-hard when delays are to be calculated. We propose here a reformulation, now expressed as a Linear-Programming (LP) problem, thus allowing to provide an efficient resolution. This allows us to back-engineer a neural network, i.e. to find out, given a set of initial conditions, which parameters (i.e., connection weights in this case), allow to simulate the network spike dynamics. More precisely we make explicit the fact that the back-engineering of a spike train, is a Linear (L) problem if the membrane potentials are observed and a LP problem if only spike times are observed, with a gIF model. Numerical robustness is discussed. We also explain how it is the use of a generalized IF neuron model instead of a leaky IF model that allows us to derive this algorithm. Furthermore, we point out how the L or LP adjustment mechanism is local to each unit and has the same structure as an Hebbian rule. A step further, this paradigm is easily generalizable to the design of input-output spike train transformations. This means that we have a practical method to program a spiking network, i.e. find a set of parameters allowing us to exactly reproduce the network output, given an input. Numerical verifications and illustrations are provided.
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Spiking neural networks (SNN) are usually more energy-efficient as compared to Artificial neural networks (ANN), and the way they work has a great similarity with our brain. Back-propagation (BP) has shown its strong power in training ANN in recent years. However, since spike behavior is non-differentiable, BP cannot be applied to SNN directly. Although prior works demonstrated several ways to approximate the BP-gradient in both spatial and temporal directions either through surrogate gradient or randomness, they omitted the temporal dependency introduced by the reset mechanism between each step. In this article, we target on theoretical completion and investigate the effect of the missing term thoroughly. By adding the temporal dependency of the reset mechanism, the new algorithm is more robust to learning-rate adjustments on a toy dataset but does not show much improvement on larger learning tasks like CIFAR-10. Empirically speaking, the benefits of the missing term are not worth the additional computational overhead. In many cases, the missing term can be ignored.
Degree assortativity refers to the increased or decreased probability of connecting two neurons based on their in- or out-degrees, relative to what would be expected by chance. We investigate the effects of such assortativity in a network of theta neurons. The Ott/Antonsen ansatz is used to derive equations for the expected state of each neuron, and these equations are then coarse-grained in degree space. We generate families of effective connectivity matrices parametrised by assortativity coefficient and use SVD decompositions of these to efficiently perform numerical bifurcation analysis of the coarse-grained equations. We find that of the four possible types of degree assortativity, two have no effect on the networks dynamics, while the other two can have a significant effect.
We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics of neurons with the same in-degree. A Gaussian copula is used to introduce correlations between a neurons in- and out-degree and numerical bifurcation analysis is used determine the effects of these correlations on the networks dynamics. For excitatory coupling we find that inducing positive correlations has a similar effect to increasing the coupling strength between neurons, while for inhibitory coupling it has the opposite effect. We also determine the propensity of various two- and three-neuron motifs to occur as correlations are varied and give a plausible explanation for the observed changes in dynamics.
Computation using brain-inspired spiking neural networks (SNNs) with neuromorphic hardware may offer orders of magnitude higher energy efficiency compared to the current analog neural networks (ANNs). Unfortunately, training SNNs with the same number of layers as state of the art ANNs remains a challenge. To our knowledge the only method which is successful in this regard is supervised training of ANN and then converting it to SNN. In this work we directly train deep SNNs using backpropagation with surrogate gradient and find that due to implicitly recurrent nature of feed forward SNNs the exploding or vanishing gradient problem severely hinders their training. We show that this problem can be solved by tuning the surrogate gradient function. We also propose using batch normalization from ANN literature on input currents of SNN neurons. Using these improvements we show that is is possible to train SNN with ResNet50 architecture on CIFAR100 and Imagenette object recognition datasets. The trained SNN falls behind in accuracy compared to analogous ANN but requires several orders of magnitude less inference time steps (as low as 10) to reach good accuracy compared to SNNs obtained by conversion from ANN which require on the order of 1000 time steps.
As neural networks get widespread adoption in resource-constrained embedded devices, there is a growing need for low-power neural systems. Spiking Neural Networks (SNNs)are emerging to be an energy-efficient alternative to the traditional Artificial Neural Networks (ANNs) which are known to be computationally intensive. From an application perspective, as federated learning involves multiple energy-constrained devices, there is a huge scope to leverage energy efficiency provided by SNNs. Despite its importance, there has been little attention on training SNNs on a large-scale distributed system like federated learning. In this paper, we bring SNNs to a more realistic federated learning scenario. Specifically, we propose a federated learning framework for decentralized and privacy-preserving training of SNNs. To validate the proposed federated learning framework, we experimentally evaluate the advantages of SNNs on various aspects of federated learning with CIFAR10 and CIFAR100 benchmarks. We observe that SNNs outperform ANNs in terms of overall accuracy by over 15% when the data is distributed across a large number of clients in the federation while providing up to5.3x energy efficiency. In addition to efficiency, we also analyze the sensitivity of the proposed federated SNN framework to data distribution among the clients, stragglers, and gradient noise and perform a comprehensive comparison with ANNs.
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