Network Plasticity as Bayesian Inference

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.Comment: 33 pages, 5 figures, the supplement is available on the author's web page http://www.igi.tugraz.at/kappe

Particle-filtering approaches for nonlinear Bayesian decoding of neuronal spike trains

The number of neurons that can be simultaneously recorded doubles every seven years. This ever increasing number of recorded neurons opens up the possibility to address new questions and extract higher dimensional stimuli from the recordings. Modeling neural spike trains as point processes, this task of extracting dynamical signals from spike trains is commonly set in the context of nonlinear filtering theory. Particle filter methods relying on importance weights are generic algorithms that solve the filtering task numerically, but exhibit a serious drawback when the problem dimensionality is high: they are known to suffer from the 'curse of dimensionality' (COD), i.e. the number of particles required for a certain performance scales exponentially with the observable dimensions. Here, we first briefly review the theory on filtering with point process observations in continuous time. Based on this theory, we investigate both analytically and numerically the reason for the COD of weighted particle filtering approaches: Similarly to particle filtering with continuous-time observations, the COD with point-process observations is due to the decay of effective number of particles, an effect that is stronger when the number of observable dimensions increases. Given the success of unweighted particle filtering approaches in overcoming the COD for continuous- time observations, we introduce an unweighted particle filter for point-process observations, the spike-based Neural Particle Filter (sNPF), and show that it exhibits a similar favorable scaling as the number of dimensions grows. Further, we derive rules for the parameters of the sNPF from a maximum likelihood approach learning. We finally employ a simple decoding task to illustrate the capabilities of the sNPF and to highlight one possible future application of our inference and learning algorithm

Comparing Offline Decoding Performance in Physiologically Defined Neuronal Classes

Objective: Recently, several studies have documented the presence of a bimodal distribution of spike waveform widths in primary motor cortex. Although narrow and wide spiking neurons, corresponding to the two modes of the distribution, exhibit different response properties, it remains unknown if these differences give rise to differential decoding performance between these two classes of cells. Approach: We used a Gaussian mixture model to classify neurons into narrow and wide physiological classes. Using similar-size, random samples of neurons from these two physiological classes, we trained offline decoding models to predict a variety of movement features. We compared offline decoding performance between these two physiologically defined populations of cells. Main results: We found that narrow spiking neural ensembles decode motor parameters better than wide spiking neural ensembles including kinematics, kinetics, and muscle activity. Significance: These findings suggest that the utility of neural ensembles in brain machine interfaces may be predicted from their spike waveform widths

Local learning algorithms for stochastic spiking neural networks

This dissertation focuses on the development of machine learning algorithms for spiking neural networks, with an emphasis on local three-factor learning rules that are in keeping with the constraints imposed by current neuromorphic hardware. Spiking neural networks (SNNs) are an alternative to artificial neural networks (ANNs) that follow a similar graphical structure but use a processing paradigm more closely modeled after the biological brain in an effort to harness its low power processing capability. SNNs use an event based processing scheme which leads to significant power savings when implemented in dedicated neuromorphic hardware such as Intel’s Loihi chip. This work is distinguished by the consideration of stochastic SNNs based on spiking neurons that employ a stochastic spiking process, implementing generalized linear models (GLM) rather than deterministic thresholded spiking. In this framework, the spiking signals are random variables which may be sampled from a distribution defined by the neurons. The spiking signals may be observed or latent variables, with neurons whose outputs are observed termed visible neurons and otherwise termed hidden neurons. This choice provides a strong mathematical basis for maximum likelihood optimization of the network parameters via stochastic gradient descent, avoiding the issue of gradient backpropagation through the discontinuity created by the spiking process. Three machine learning algorithms are developed for stochastic SNNs with a focus on power efficiency, learning efficiency and model adaptability; characteristics that are valuable in resource constrained settings. They are studied in the context of applications where low power learning on the edge is key. All of the learning rules that are derived include only local variables along with a global learning signal, making these algorithms tractable to implementation in current neuromorphic hardware. First, a stochastic SNN that includes only visible neurons, the simplest case for probabilistic optimization, is considered. A policy gradient reinforcement learning (RL) algorithm is developed in which the stochastic SNN defines the policy, or state-action distribution, of an RL agent. Action choices are sampled directly from the policy by interpreting the outputs of the read-out neurons using a first to spike decision rule. This study highlights the power efficiency of the SNN in terms of spike frequency. Next, an online meta-learning framework is proposed with the goal of progressively improving the learning efficiency of an SNN over a stream of tasks. In this setting, SNNs including both hidden and visible neurons are considered, posing a more complex maximum likelihood learning problem that is solved using a variational learning method. The meta-learning rule yields a hyperparameter initialization for SNN models that supports fast adaptation of the model to individualized data on edge devices. Finally, moving away from the supervised learning paradigm, a hybrid adver-sarial training framework for SNNs, termed SpikeGAN, is developed. Rather than optimize for the likelihood of target spike patterns at the SNN outputs, the training is mediated by an auxiliary discriminator that provides a measure of how similar the spiking data is to a target distribution. Because no direct spiking patterns are given, the SNNs considered in adversarial learning include only hidden neurons. A Bayesian adaptation of the SpikeGAN learning rule is developed to broaden the range of temporal data that a single SpikeGAN can estimate. Additionally, the online meta-learning rule is extended to include meta-learning for SpikeGAN, to enable efficient generation of data from sequential data distributions