Emergence of optimal decoding of population codes through STDP

Necessary conditions for STDP-based pattern recognition learning in a memristive spiking neural network

This work is aimed to study experimental and theoretical approaches for searching effective local training rules for unsupervised pattern recognition by high-performance memristor-based Spiking Neural Networks (SNNs). First, the possibility of weight change using Spike-Timing-Dependent Plasticity (STDP) is demonstrated with a pair of hardware analog neurons connected through a (CoFeB)_x(LiNbO₃)_1-x nanocomposite memristor. Next, the learning convergence to a solution of binary clusterization task is analyzed in a wide range of memristive STDP parameters for a single-layer fully connected feedforward SNN. The memristive STDP behavior supplying convergence in this simple task is shown also to provide it in the handwritten digit recognition domain by the more complex SNN architecture with a Winner-Take-All competition between neurons. To investigate basic conditions necessary for training convergence, an original probabilistic generative model of a rate-based single-layer network with independent or competing neurons is built and thoroughly analyzed. The main result is a statement of "correlation growth-anticorrelation decay" principle which prompts near-optimal policy to configure model parameters. This principle is in line with requiring the binary clusterization convergence which can be defined as the necessary condition for optimal learning and used as the simple benchmark for tuning parameters of various neural network realizations with population-rate information coding. At last, a heuristic algorithm is described to experimentally find out the convergence conditions in a memristive SNN, including robustness to a device variability. Due to the generality of the proposed approach, it can be applied to a wide range of memristors and neurons of software- or hardware-based rate-coding single-layer SNNs when searching for local rules that ensure their unsupervised learning convergence in a pattern recognition task domain.

Using the hierarchical temporal memory spatial pooler for short-term forecasting of electrical load time series

In this paper, an emerging state-of-the-art machine intelligence technique called the Hierarchical Temporal Memory (HTM) is applied to the task of short-term load forecasting (STLF). A HTM Spatial Pooler (HTM-SP) stage is used to continually form sparse distributed representations (SDRs) from a univariate load time series data, a temporal aggregator is used to transform the SDRs into a sequential bivariate representation space and an overlap classifier makes temporal classifications from the bivariate SDRs through time. The comparative performance of HTM on several daily electrical load time series data including the Eunite competition dataset and the Polish power system dataset from 2002 to 2004 are presented. The robustness performance of HTM is also further validated using hourly load data from three more recent electricity markets. The results obtained from experimenting with the Eunite and Polish dataset indicated that HTM will perform better than the existing techniques reported in the literature. In general, the robustness test also shows that the error distribution performance of the proposed HTM technique is positively skewed for most of the years considered and with kurtosis values mostly lower than a base value of 3 indicating a reasonable level of outlier rejections.

Noise Helps Optimization Escape From Saddle Points in the Synaptic Plasticity

Numerous experimental studies suggest that noise is inherent in the human brain. However, the functional importance of noise remains unknown. n particular, from a computational perspective, such stochasticity is potentially harmful to brain function. In machine learning, a large number of saddle points are surrounded by high error plateaus and give the illusion of the existence of local minimum. As a result, being trapped in the saddle points can dramatically impair learning and adding noise will attack such saddle point problems in high-dimensional optimization, especially under the strict saddle condition. Motivated by these arguments, we propose one biologically plausible noise structure and demonstrate that noise can efficiently improve the optimization performance of spiking neural networks based on stochastic gradient descent. The strict saddle condition for synaptic plasticity is deduced, and under such conditions, noise can help optimization escape from saddle points on high dimensional domains. The theoretical results explain the stochasticity of synapses and guide us on how to make use of noise. In addition, we provide biological interpretations of proposed noise structures from two points: one based on the free energy principle in neuroscience and another based on observations of in vivo experiments. Our simulation results manifest that in the learning and test phase, the accuracy of synaptic sampling with noise is almost 20% higher than that without noise for synthesis dataset, and the gain in accuracy with/without noise is at least 10% for the MNIST and CIFAR-10 dataset. Our study provides a new learning framework for the brain and sheds new light on deep noisy spiking neural networks.

Event-Based, Timescale Invariant Unsupervised Online Deep Learning With STDP

Learning of hierarchical features with spiking neurons has mostly been investigated in the database framework of standard deep learning systems. However, the properties of neuromorphic systems could be particularly interesting for learning from continuous sensor data in real-world settings. In this work, we introduce a deep spiking convolutional neural network of integrate-and-fire (IF) neurons which performs unsupervised online deep learning with spike-timing dependent plasticity (STDP) from a stream of asynchronous and continuous event-based data. In contrast to previous approaches to unsupervised deep learning with spikes, where layers were trained successively, we introduce a mechanism to train all layers of the network simultaneously. This allows approximate online inference already during the learning process and makes our architecture suitable for online learning and inference. We show that it is possible to train the network without providing implicit information about the database, such as the number of classes and the duration of stimuli presentation. By designing an STDP learning rule which depends only on relative spike timings, we make our network fully event-driven and able to operate without defining an absolute timescale of its dynamics. Our architecture requires only a small number of generic mechanisms and therefore enforces few constraints on a possible neuromorphic hardware implementation. These characteristics make our network one of the few neuromorphic architecture which could directly learn features and perform inference from an event-based vision sensor.

The HTM Spatial Pooler-A Neocortical Algorithm for Online Sparse Distributed Coding

Hierarchical temporal memory (HTM) provides a theoretical framework that models several key computational principles of the neocortex. In this paper, we analyze an important component of HTM, the HTM spatial pooler (SP). The SP models how neurons learn feedforward connections and form efficient representations of the input. It converts arbitrary binary input patterns into sparse distributed representations (SDRs) using a combination of competitive Hebbian learning rules and homeostatic excitability control. We describe a number of key properties of the SP, including fast adaptation to changing input statistics, improved noise robustness through learning, efficient use of cells, and robustness to cell death. In order to quantify these properties we develop a set of metrics that can be directly computed from the SP outputs. We show how the properties are met using these metrics and targeted artificial simulations. We then demonstrate the value of the SP in a complete end-to-end real-world HTM system. We discuss the relationship with neuroscience and previous studies of sparse coding. The HTM spatial pooler represents a neurally inspired algorithm for learning sparse representations from noisy data streams in an online fashion.

Feedback Inhibition Shapes Emergent Computational Properties of Cortical Microcircuit Motifs

Cortical microcircuits are very complex networks, but they are composed of a relatively small number of stereotypical motifs. Hence, one strategy for throwing light on the computational function of cortical microcircuits is to analyze emergent computational properties of these stereotypical microcircuit motifs. We are addressing here the question how spike timing-dependent plasticity shapes the computational properties of one motif that has frequently been studied experimentally: interconnected populations of pyramidal cells and parvalbumin-positive inhibitory cells in layer 2/3. Experimental studies suggest that these inhibitory neurons exert some form of divisive inhibition on the pyramidal cells. We show that this data-based form of feedback inhibition, which is softer than that of winner-take-all models that are commonly considered in theoretical analyses, contributes to the emergence of an important computational function through spike timing-dependent plasticity: The capability to disentangle superimposed firing patterns in upstream networks, and to represent their information content through a sparse assembly code.SIGNIFICANCE STATEMENT We analyze emergent computational properties of a ubiquitous cortical microcircuit motif: populations of pyramidal cells that are densely interconnected with inhibitory neurons. Simulations of this model predict that sparse assembly codes emerge in this microcircuit motif under spike timing-dependent plasticity. Furthermore, we show that different assemblies will represent different hidden sources of upstream firing activity. Hence, we propose that spike timing-dependent plasticity enables this microcircuit motif to perform a fundamental computational operation on neural activity patterns.

Unsupervised learning in probabilistic neural networks with multi-state metal-oxide memristive synapses

In an increasingly data-rich world the need for developing computing systems that cannot only process, but ideally also interpret big data is becoming continuously more pressing. Brain-inspired concepts have shown great promise towards addressing this need. Here we demonstrate unsupervised learning in a probabilistic neural network that utilizes metal-oxide memristive devices as multi-state synapses. Our approach can be exploited for processing unlabelled data and can adapt to time-varying clusters that underlie incoming data by supporting the capability of reversible unsupervised learning. The potential of this work is showcased through the demonstration of successful learning in the presence of corrupted input data and probabilistic neurons, thus paving the way towards robust big-data processors.

Learning Probabilistic Inference through Spike-Timing-Dependent Plasticity

Numerous experimental data show that the brain is able to extract information from complex, uncertain, and often ambiguous experiences. Furthermore, it can use such learnt information for decision making through probabilistic inference. Several models have been proposed that aim at explaining how probabilistic inference could be performed by networks of neurons in the brain. We propose here a model that can also explain how such neural network could acquire the necessary information for that from examples. We show that spike-timing-dependent plasticity in combination with intrinsic plasticity generates in ensembles of pyramidal cells with lateral inhibition a fundamental building block for that: probabilistic associations between neurons that represent through their firing current values of random variables. Furthermore, by combining such adaptive network motifs in a recursive manner the resulting network is enabled to extract statistical information from complex input streams, and to build an internal model for the distribution p^* that generates the examples it receives. This holds even if p^* contains higher-order moments. The analysis of this learning process is supported by a rigorous theoretical foundation. Furthermore, we show that the network can use the learnt internal model immediately for prediction, decision making, and other types of probabilistic inference.

Hebbian Wiring Plasticity Generates Efficient Network Structures for Robust Inference with Synaptic Weight Plasticity

In the adult mammalian cortex, a small fraction of spines are created and eliminated every day, and the resultant synaptic connection structure is highly nonrandom, even in local circuits. However, it remains unknown whether a particular synaptic connection structure is functionally advantageous in local circuits, and why creation and elimination of synaptic connections is necessary in addition to rich synaptic weight plasticity. To answer these questions, we studied an inference task model through theoretical and numerical analyses. We demonstrate that a robustly beneficial network structure naturally emerges by combining Hebbian-type synaptic weight plasticity and wiring plasticity. Especially in a sparsely connected network, wiring plasticity achieves reliable computation by enabling efficient information transmission. Furthermore, the proposed rule reproduces experimental observed correlation between spine dynamics and task performance.

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.

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.

Mixed signal learning by spike correlation propagation in feedback inhibitory circuits

The brain can learn and detect mixed input signals masked by various types of noise, and spike-timing-dependent plasticity (STDP) is the candidate synaptic level mechanism. Because sensory inputs typically have spike correlation, and local circuits have dense feedback connections, input spikes cause the propagation of spike correlation in lateral circuits; however, it is largely unknown how this secondary correlation generated by lateral circuits influences learning processes through STDP, or whether it is beneficial to achieve efficient spike-based learning from uncertain stimuli. To explore the answers to these questions, we construct models of feedforward networks with lateral inhibitory circuits and study how propagated correlation influences STDP learning, and what kind of learning algorithm such circuits achieve. We derive analytical conditions at which neurons detect minor signals with STDP, and show that depending on the origin of the noise, different correlation timescales are useful for learning. In particular, we show that non-precise spike correlation is beneficial for learning in the presence of cross-talk noise. We also show that by considering excitatory and inhibitory STDP at lateral connections, the circuit can acquire a lateral structure optimal for signal detection. In addition, we demonstrate that the model performs blind source separation in a manner similar to the sequential sampling approximation of the Bayesian independent component analysis algorithm. Our results provide a basic understanding of STDP learning in feedback circuits by integrating analyses from both dynamical systems and information theory.

A compound memristive synapse model for statistical learning through STDP in spiking neural networks

Memristors have recently emerged as promising circuit elements to mimic the function of biological synapses in neuromorphic computing. The fabrication of reliable nanoscale memristive synapses, that feature continuous conductance changes based on the timing of pre- and postsynaptic spikes, has however turned out to be challenging. In this article, we propose an alternative approach, the compound memristive synapse, that circumvents this problem by the use of memristors with binary memristive states. A compound memristive synapse employs multiple bistable memristors in parallel to jointly form one synapse, thereby providing a spectrum of synaptic efficacies. We investigate the computational implications of synaptic plasticity in the compound synapse by integrating the recently observed phenomenon of stochastic filament formation into an abstract model of stochastic switching. Using this abstract model, we first show how standard pulsing schemes give rise to spike-timing dependent plasticity (STDP) with a stabilizing weight dependence in compound synapses. In a next step, we study unsupervised learning with compound synapses in networks of spiking neurons organized in a winner-take-all architecture. Our theoretical analysis reveals that compound-synapse STDP implements generalized Expectation-Maximization in the spiking network. Specifically, the emergent synapse configuration represents the most salient features of the input distribution in a Mixture-of-Gaussians generative model. Furthermore, the network's spike response to spiking input streams approximates a well-defined Bayesian posterior distribution. We show in computer simulations how such networks learn to represent high-dimensional distributions over images of handwritten digits with high fidelity even in presence of substantial device variations and under severe noise conditions. Therefore, the compound memristive synapse may provide a synaptic design principle for future neuromorphic architectures.

Racing to learn: statistical inference and learning in a single spiking neuron with adaptive kernels

This paper describes the Synapto-dendritic Kernel Adapting Neuron (SKAN), a simple spiking neuron model that performs statistical inference and unsupervised learning of spatiotemporal spike patterns. SKAN is the first proposed neuron model to investigate the effects of dynamic synapto-dendritic kernels and demonstrate their computational power even at the single neuron scale. The rule-set defining the neuron is simple: there are no complex mathematical operations such as normalization, exponentiation or even multiplication. The functionalities of SKAN emerge from the real-time interaction of simple additive and binary processes. Like a biological neuron, SKAN is robust to signal and parameter noise, and can utilize both in its operations. At the network scale neurons are locked in a race with each other with the fastest neuron to spike effectively "hiding" its learnt pattern from its neighbors. The robustness to noise, high speed, and simple building blocks not only make SKAN an interesting neuron model in computational neuroscience, but also make it ideal for implementation in digital and analog neuromorphic systems which is demonstrated through an implementation in a Field Programmable Gate Array (FPGA). Matlab, Python, and Verilog implementations of SKAN are available at: http://www.uws.edu.au/bioelectronics_neuroscience/bens/reproducible_research.

Ensembles of spiking neurons with noise support optimal probabilistic inference in a dynamically changing environment

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information.

The Markov Chain Monte Carlo (MCMC) approach to probabilistic inference for a distribution is to draw a sequence of samples from and to carry out computational operations via simple online computations on such a sequence. But such a sequential computational process takes time, and therefore this simple version of the MCMC approach runs into problems when one needs to carry out probabilistic inference for rapidly varying distributions. This difficulty also affects all currently existing models for emulating MCMC sampling by networks of stochastically firing neurons. We show here that by moving to a space-rate approach where salient probabilities are encoded through the spiking activity of ensembles of neurons, rather than by single neurons, this problem can be solved. In this way even theoretically optimal models for dealing with time varying distributions through sequential Monte Carlo sampling, so called particle filters, can be emulated by networks of spiking neurons. Each spike of a neuron in an ensemble represents in this approach a “particle” (or vote) for a particular value of a time-varying random variable. In other words, neural circuits can speed up computations based on Monte Carlo sampling through their inherent parallelism.

STDP installs in Winner-Take-All circuits an online approximation to hidden Markov model learning

In order to cross a street without being run over, we need to be able to extract very fast hidden causes of dynamically changing multi-modal sensory stimuli, and to predict their future evolution. We show here that a generic cortical microcircuit motif, pyramidal cells with lateral excitation and inhibition, provides the basis for this difficult but all-important information processing capability. This capability emerges in the presence of noise automatically through effects of STDP on connections between pyramidal cells in Winner-Take-All circuits with lateral excitation. In fact, one can show that these motifs endow cortical microcircuits with functional properties of a hidden Markov model, a generic model for solving such tasks through probabilistic inference. Whereas in engineering applications this model is adapted to specific tasks through offline learning, we show here that a major portion of the functionality of hidden Markov models arises already from online applications of STDP, without any supervision or rewards. We demonstrate the emergent computing capabilities of the model through several computer simulations. The full power of hidden Markov model learning can be attained through reward-gated STDP. This is due to the fact that these mechanisms enable a rejection sampling approximation to theoretically optimal learning. We investigate the possible performance gain that can be achieved with this more accurate learning method for an artificial grammar task.

Emergence of dynamic memory traces in cortical microcircuit models through STDP

Numerous experimental data suggest that simultaneously or sequentially activated assemblies of neurons play a key role in the storage and computational use of long-term memory in the brain. However, a model that elucidates how these memory traces could emerge through spike-timing-dependent plasticity (STDP) has been missing. We show here that stimulus-specific assemblies of neurons emerge automatically through STDP in a simple cortical microcircuit model. The model that we consider is a randomly connected network of well known microcircuit motifs: pyramidal cells with lateral inhibition. We show that the emergent assembly codes for repeatedly occurring spatiotemporal input patterns tend to fire in some loose, sequential manner that is reminiscent of experimentally observed stereotypical trajectories of network states. We also show that the emergent assembly codes add an important computational capability to standard models for online computations in cortical microcircuits: the capability to integrate information from long-term memory with information from novel spike inputs.