Probabilistic Inference in General Graphical Models through Sampling in Stochastic Networks of Spiking Neurons

An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows (“explaining away”) and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons

Training Dynamic Exponential Family Models with Causal and Lateral Dependencies for Generalized Neuromorphic Computing

Neuromorphic hardware platforms, such as Intel's Loihi chip, support the implementation of Spiking Neural Networks (SNNs) as an energy-efficient alternative to Artificial Neural Networks (ANNs). SNNs are networks of neurons with internal analogue dynamics that communicate by means of binary time series. In this work, a probabilistic model is introduced for a generalized set-up in which the synaptic time series can take values in an arbitrary alphabet and are characterized by both causal and instantaneous statistical dependencies. The model, which can be considered as an extension of exponential family harmoniums to time series, is introduced by means of a hybrid directed-undirected graphical representation. Furthermore, distributed learning rules are derived for Maximum Likelihood and Bayesian criteria under the assumption of fully observed time series in the training set.Comment: Published in IEEE ICASSP 2019. Author's Accepted Manuscrip

Distributed Bayesian Computation and Self-Organized Learning in Sheets of Spiking Neurons with Local Lateral Inhibition

During the last decade, Bayesian probability theory has emerged as a framework in cognitive science and neuroscience for describing perception, reasoning and learning of mammals. However, our understanding of how probabilistic computations could be organized in the brain, and how the observed connectivity structure of cortical microcircuits supports these calculations, is rudimentary at best. In this study, we investigate statistical inference and self-organized learning in a spatially extended spiking network model, that accommodates both local competitive and large-scale associative aspects of neural information processing, under a unified Bayesian account. Specifically, we show how the spiking dynamics of a recurrent network with lateral excitation and local inhibition in response to distributed spiking input, can be understood as sampling from a variational posterior distribution of a well-defined implicit probabilistic model. This interpretation further permits a rigorous analytical treatment of experience-dependent plasticity on the network level. Using machine learning theory, we derive update rules for neuron and synapse parameters which equate with Hebbian synaptic and homeostatic intrinsic plasticity rules in a neural implementation. In computer simulations, we demonstrate that the interplay of these plasticity rules leads to the emergence of probabilistic local experts that form distributed assemblies of similarly tuned cells communicating through lateral excitatory connections. The resulting sparse distributed spike code of a well-adapted network carries compressed information on salient input features combined with prior experience on correlations among them. Our theory predicts that the emergence of such efficient representations benefits from network architectures in which the range of local inhibition matches the spatial extent of pyramidal cells that share common afferent input

Probabilistic spiking neural networks : Supervised, unsupervised and adversarial trainings

Spiking Neural Networks (SNNs), or third-generation neural networks, are networks of computation units, called neurons, in which each neuron with internal analogue dynamics receives as input and produces as output spiking, that is, binary sparse, signals. In contrast, second-generation neural networks, termed as Artificial Neural Networks (ANNs), rely on simple static non-linear neurons that are known to be energy-intensive, hindering their implementations on energy-limited processors such as mobile devices. The sparse event-based characteristics of SNNs for information transmission and encoding have made them more feasible for highly energy-efficient neuromorphic computing architectures. The most existing training algorithms for SNNs are based on deterministic spiking neurons that limit their flexibility and expressive power. Moreover, the SNNs are typically trained based on the back-propagation method, which unlike ANNs, it becomes challenging due to the non-differentiability nature of the spike dynamics. Considering these two key issues, this dissertation is devoted to develop probabilistic frameworks for SNNs that are tailored to the solution of supervised and unsupervised cognitive tasks. The SNNs utilize rich model, flexible and computationally tractable properties of Generalized Linear Model (GLM) neuron. The GLM is a probabilistic neural model that was previously considered within the computational neuroscience literature. A novel training method is proposed for the purpose of classification with a first-to-spike decoding rule, whereby the SNN can perform an early classification decision once spike firing is detected at an output neuron. This method is in contrast with conventional classification rules for SNNs that operate offline based on the number of output spikes at each output neuron. As a result, the proposed method improves the accuracy-inference complexity trade-off with respect to conventional decoding. For the first time in the field, the sensitivity of SNNs trained via Maximum Likelihood (ML) is studied under white-box adversarial attacks. Rate and time encoding, as well as rate and first-to-spike decoding, are considered. Furthermore, a robust training mechanism is proposed that is demonstrated to enhance the resilience of SNNs under adversarial examples. Finally, unsupervised training task for probabilistic SNNs is studied. Under generative model framework, multi-layers SNNs are designed for both encoding and generative parts. In order to train the Variational Autoencoders (VAEs), the standard ML approach is considered. To tackle the intractable inference part, variational learning approaches including doubly stochastic gradient learning, Maximum A Posterior (MAP)-based, and Rao-Blackwellization (RB)-based are considered. The latter is referred as the Hybrid Stochastic-MAP Variational Learning (HSM-VL) scheme. The numerical results show performance improvements using the HSM-VL method compared to the other two training schemes

Stochasticity from function -- why the Bayesian brain may need no noise

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may, in fact, have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functionally Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial