Synaptic and nonsynaptic plasticity approximating probabilistic inference

Fast Hebbian plasticity and working memory

Theories and models of working memory (WM) were at least since the mid-1990s dominated by the persistent activity hypothesis. The past decade has seen rising concerns about the shortcomings of sustained activity as the mechanism for short-term maintenance of WM information in the light of accumulating experimental evidence for so-called activity-silent WM and the fundamental difficulty in explaining robust multi-item WM. In consequence, alternative theories are now explored mostly in the direction of fast synaptic plasticity as the underlying mechanism. The question of non-Hebbian vs Hebbian synaptic plasticity emerges naturally in this context. In this review, we focus on fast Hebbian plasticity and trace the origins of WM theories and models building on this form of associative learning.

Traces of semantization - from episodic to semantic memory in a spiking cortical network model

Episodic memory is a recollection of past personal experiences associated with particular times and places. This kind of memory is commonly subject to loss of contextual information or" semantization", which gradually decouples the encoded memory items from their associated contexts while transforming them into semantic or gist-like representations. Novel extensions to the classical Remember/Know behavioral paradigm attribute the loss of episodicity to multiple exposures of an item in different contexts. Despite recent advancements explaining semantization at a behavioral level, the underlying neural mechanisms remain poorly understood. In this study, we suggest and evaluate a novel hypothesis proposing that Bayesian-Hebbian synaptic plasticity mechanisms might cause semantization of episodic memory. We implement a cortical spiking neural network model with a Bayesian-Hebbian learning rule called Bayesian Confidence Propagation Neural Network (BCPNN), which captures the semantization phenomenon and offers a mechanistic explanation for it. Encoding items across multiple contexts leads to item-context decoupling akin to semantization. We compare BCPNN plasticity with the more commonly used spike-timing dependent plasticity (STDP) learning rule in the same episodic memory task. Unlike BCPNN, STDP does not explain the decontextualization process. We further examine how selective plasticity modulation of isolated salient events may enhance preferential retention and resistance to semantization. Our model reproduces important features of episodicity on behavioral timescales under various biological constraints whilst also offering a novel neural and synaptic explanation for semantization, thereby casting new light on the interplay between episodic and semantic memory processes.Significance StatementRemembering single episodes is a fundamental attribute of cognition. Difficulties recollecting contextual information is a key sign of episodic memory loss or semantization. Behavioral studies demonstrate that semantization of episodic memory can occur rapidly, yet the neural mechanisms underlying this effect are insufficiently investigated. In line with recent behavioral findings, we show that multiple stimulus exposures in different contexts may advance item-context decoupling. We suggest a Bayesian-Hebbian synaptic plasticity hypothesis of memory semantization and further show that a transient modulation of plasticity during salient events may disrupt the decontextualization process by strengthening memory traces, and thus, enhancing preferential retention. The proposed cortical network-of-networks model thus bridges micro and mesoscale synaptic effects with network dynamics and behavior.

Mapping the BCPNN Learning Rule to a Memristor Model

The Bayesian Confidence Propagation Neural Network (BCPNN) has been implemented in a way that allows mapping to neural and synaptic processes in the human cortexandhas been used extensively in detailed spiking models of cortical associative memory function and recently also for machine learning applications. In conventional digital implementations of BCPNN, the von Neumann bottleneck is a major challenge with synaptic storage and access to it as the dominant cost. The memristor is a non-volatile device ideal for artificial synapses that fuses computation and storage and thus fundamentally overcomes the von Neumann bottleneck. While the implementation of other neural networks like Spiking Neural Network (SNN) and even Convolutional Neural Network (CNN) on memristor has been studied, the implementation of BCPNN has not. In this paper, the BCPNN learning rule is mapped to a memristor model and implemented with a memristor-based architecture. The implementation of the BCPNN learning rule is a mixed-signal design with the main computation and storage happening in the analog domain. In particular, the nonlinear dopant drift phenomenon of the memristor is exploited to simulate the exponential decay of the synaptic state variables in the BCPNN learning rule. The consistency between the memristor-based solution and the BCPNN learning rule is simulated and verified in Matlab, with a correlation coefficient as high as 0.99. The analog circuit is designed and implemented in the SPICE simulation environment, demonstrating a good emulation effect for the BCPNN learning rule with a correlation coefficient as high as 0.98. This work focuses on demonstrating the feasibility of mapping the BCPNN learning rule to in-circuit computation in memristor. The feasibility of the memristor-based implementation is evaluated and validated in the paper, to pave the way for a more efficient BCPNN implementation, toward a real-time brain emulation engine.

An Indexing Theory for Working Memory Based on Fast Hebbian Plasticity

Working memory (WM) is a key component of human memory and cognition. Computational models have been used to study the underlying neural mechanisms, but neglected the important role of short-term memory (STM) and long-term memory (LTM) interactions for WM. Here, we investigate these using a novel multiarea spiking neural network model of prefrontal cortex (PFC) and two parietotemporal cortical areas based on macaque data. We propose a WM indexing theory that explains how PFC could associate, maintain, and update multimodal LTM representations. Our simulations demonstrate how simultaneous, brief multimodal memory cues could build a temporary joint memory representation as an “index” in PFC by means of fast Hebbian synaptic plasticity. This index can then reactivate spontaneously and thereby also the associated LTM representations. Cueing one LTM item rapidly pattern completes the associated uncued item via PFC. The PFC–STM network updates flexibly as new stimuli arrive, thereby gradually overwriting older representations.

Introducing double bouquet cells into a modular cortical associative memory model

We present an electrophysiological model of double bouquet cells and integrate them into an established cortical columnar microcircuit model that has previously been used as a spiking attractor model for memory. Learning in that model relies on a Hebbian-Bayesian learning rule to condition recurrent connectivity between pyramidal cells. We here demonstrate that the inclusion of a biophysically plausible double bouquet cell model can solve earlier concerns about learning rules that simultaneously learn excitation and inhibition and might thus violate Dale’s principle. We show that learning ability and resulting effective connectivity between functional columns of previous network models is preserved when pyramidal synapses onto double bouquet cells are plastic under the same Hebbian-Bayesian learning rule. The proposed architecture draws on experimental evidence on double bouquet cells and effectively solves the problem of duplexed learning of inhibition and excitation by replacing recurrent inhibition between pyramidal cells in functional columns of different stimulus selectivity with a plastic disynaptic pathway. We thus show that the resulting change to the microcircuit architecture improves the model’s biological plausibility without otherwise impacting the model’s spiking activity, basic operation, and learning abilities.

Probabilistic associative learning suffices for learning the temporal structure of multiple sequences

From memorizing a musical tune to navigating a well known route, many of our underlying behaviors have a strong temporal component. While the mechanisms behind the sequential nature of the underlying brain activity are likely multifarious and multi-scale, in this work we attempt to characterize to what degree some of this properties can be explained as a consequence of simple associative learning. To this end, we employ a parsimonious firing-rate attractor network equipped with the Hebbian-like Bayesian Confidence Propagating Neural Network (BCPNN) learning rule relying on synaptic traces with asymmetric temporal characteristics. The proposed network model is able to encode and reproduce temporal aspects of the input, and offers internal control of the recall dynamics by gain modulation. We provide an analytical characterisation of the relationship between the structure of the weight matrix, the dynamical network parameters and the temporal aspects of sequence recall. We also present a computational study of the performance of the system under the effects of noise for an extensive region of the parameter space. Finally, we show how the inclusion of modularity in our network structure facilitates the learning and recall of multiple overlapping sequences even in a noisy regime.

Neuromodulated Synaptic Plasticity on the SpiNNaker Neuromorphic System

SpiNNaker is a digital neuromorphic architecture, designed specifically for the low power simulation of large-scale spiking neural networks at speeds close to biological real-time. Unlike other neuromorphic systems, SpiNNaker allows users to develop their own neuron and synapse models as well as specify arbitrary connectivity. As a result SpiNNaker has proved to be a powerful tool for studying different neuron models as well as synaptic plasticity—believed to be one of the main mechanisms behind learning and memory in the brain. A number of Spike-Timing-Dependent-Plasticity(STDP) rules have already been implemented on SpiNNaker and have been shown to be capable of solving various learning tasks in real-time. However, while STDP is an important biological theory of learning, it is a form of Hebbian or unsupervised learning and therefore does not explain behaviors that depend on feedback from the environment. Instead, learning rules based on neuromodulated STDP (three-factor learning rules) have been shown to be capable of solving reinforcement learning tasks in a biologically plausible manner. In this paper we demonstrate for the first time how a model of three-factor STDP, with the third-factor representing spikes from dopaminergic neurons, can be implemented on the SpiNNaker neuromorphic system. Using this learning rule we first show how reward and punishment signals can be delivered to a single synapse before going on to demonstrate it in a larger network which solves the credit assignment problem in a Pavlovian conditioning experiment. Because of its extra complexity, we find that our three-factor learning rule requires approximately 2× as much processing time as the existing SpiNNaker STDP learning rules. However, we show that it is still possible to run our Pavlovian conditioning model with up to 1 × 10⁴ neurons in real-time, opening up new research opportunities for modeling behavioral learning on SpiNNaker.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we document lognormal distributions for spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears as a functional property that is present everywhere.  Secondly, we created a generic neural model to show that Hebbian learning will create and maintain lognormal distributions. We could prove with the model that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This settles a long-standing question about the type of plasticity exhibited by intrinsic excitability.

A Spiking Working Memory Model Based on Hebbian Short-Term Potentiation

A dominant theory of working memory (WM), referred to as the persistent activity hypothesis, holds that recurrently connected neural networks, presumably located in the prefrontal cortex, encode and maintain WM memory items through sustained elevated activity. Reexamination of experimental data has shown that prefrontal cortex activity in single units during delay periods is much more variable than predicted by such a theory and associated computational models. Alternative models of WM maintenance based on synaptic plasticity, such as short-term nonassociative (non-Hebbian) synaptic facilitation, have been suggested but cannot account for encoding of novel associations. Here we test the hypothesis that a recently identified fast-expressing form of Hebbian synaptic plasticity (associative short-term potentiation) is a possible mechanism for WM encoding and maintenance. Our simulations using a spiking neural network model of cortex reproduce a range of cognitive memory effects in the classical multi-item WM task of encoding and immediate free recall of word lists. Memory reactivation in the model occurs in discrete oscillatory bursts rather than as sustained activity. We relate dynamic network activity as well as key synaptic characteristics to electrophysiological measurements. Our findings support the hypothesis that fast Hebbian short-term potentiation is a key WM mechanism.

SIGNIFICANCE STATEMENT Working memory (WM) is a key component of cognition. Hypotheses about the neural mechanism behind WM are currently under revision. Reflecting recent findings of fast Hebbian synaptic plasticity in cortex, we test whether a cortical spiking neural network model with such a mechanism can learn a multi-item WM task (word list learning). We show that our model can reproduce human cognitive phenomena and achieve comparable memory performance in both free and cued recall while being simultaneously compatible with experimental data on structure, connectivity, and neurophysiology of the underlying cortical tissue. These findings are directly relevant to the ongoing paradigm shift in the WM field.

DNA methylation mediates neural processing after odor learning in the honeybee

DNA methyltransferases (Dnmts) - epigenetic writers catalyzing the transfer of methyl-groups to cytosine (DNA methylation) - regulate different aspects of memory formation in many animal species. In honeybees, Dnmt activity is required to adjust the specificity of olfactory reward memories and bees' relearning capability. The physiological relevance of Dnmt-mediated DNA methylation in neural networks, however, remains unknown. Here, we investigated how Dnmt activity impacts neuroplasticity in the bees' primary olfactory center, the antennal lobe (AL) an equivalent of the vertebrate olfactory bulb. The AL is crucial for odor discrimination, an indispensable process in forming specific odor memories. Using pharmacological inhibition, we demonstrate that Dnmt activity influences neural network properties during memory formation in vivo. We show that Dnmt activity promotes fast odor pattern separation in trained bees. Furthermore, Dnmt activity during memory formation increases both the number of responding glomeruli and the response magnitude to a novel odor. These data suggest that Dnmt activity is necessary for a form of homoeostatic network control which might involve inhibitory interneurons in the AL network.

Synapse-Centric Mapping of Cortical Models to the SpiNNaker Neuromorphic Architecture

While the adult human brain has approximately 8.8 × 10(10) neurons, this number is dwarfed by its 1 × 10(15) synapses. From the point of view of neuromorphic engineering and neural simulation in general this makes the simulation of these synapses a particularly complex problem. SpiNNaker is a digital, neuromorphic architecture designed for simulating large-scale spiking neural networks at speeds close to biological real-time. Current solutions for simulating spiking neural networks on SpiNNaker are heavily inspired by work on distributed high-performance computing. However, while SpiNNaker shares many characteristics with such distributed systems, its component nodes have much more limited resources and, as the system lacks global synchronization, the computation performed on each node must complete within a fixed time step. We first analyze the performance of the current SpiNNaker neural simulation software and identify several problems that occur when it is used to simulate networks of the type often used to model the cortex which contain large numbers of sparsely connected synapses. We then present a new, more flexible approach for mapping the simulation of such networks to SpiNNaker which solves many of these problems. Finally we analyze the performance of our new approach using both benchmarks, designed to represent cortical connectivity, and larger, functional cortical models. In a benchmark network where neurons receive input from 8000 STDP synapses, our new approach allows 4× more neurons to be simulated on each SpiNNaker core than has been previously possible. We also demonstrate that the largest plastic neural network previously simulated on neuromorphic hardware can be run in real time using our new approach: double the speed that was previously achieved. Additionally this network contains two types of plastic synapse which previously had to be trained separately but, using our new approach, can be trained simultaneously.

Functional Relevance of Different Basal Ganglia Pathways Investigated in a Spiking Model with Reward Dependent Plasticity

The brain enables animals to behaviorally adapt in order to survive in a complex and dynamic environment, but how reward-oriented behaviors are achieved and computed by its underlying neural circuitry is an open question. To address this concern, we have developed a spiking model of the basal ganglia (BG) that learns to dis-inhibit the action leading to a reward despite ongoing changes in the reward schedule. The architecture of the network features the two pathways commonly described in BG, the direct (denoted D1) and the indirect (denoted D2) pathway, as well as a loop involving striatum and the dopaminergic system. The activity of these dopaminergic neurons conveys the reward prediction error (RPE), which determines the magnitude of synaptic plasticity within the different pathways. All plastic connections implement a versatile four-factor learning rule derived from Bayesian inference that depends upon pre- and post-synaptic activity, receptor type, and dopamine level. Synaptic weight updates occur in the D1 or D2 pathways depending on the sign of the RPE, and an efference copy informs upstream nuclei about the action selected. We demonstrate successful performance of the system in a multiple-choice learning task with a transiently changing reward schedule. We simulate lesioning of the various pathways and show that a condition without the D2 pathway fares worse than one without D1. Additionally, we simulate the degeneration observed in Parkinson's disease (PD) by decreasing the number of dopaminergic neurons during learning. The results suggest that the D1 pathway impairment in PD might have been overlooked. Furthermore, an analysis of the alterations in the synaptic weights shows that using the absolute reward value instead of the RPE leads to a larger change in D1.

Spike-Based Bayesian-Hebbian Learning of Temporal Sequences

Many cognitive and motor functions are enabled by the temporal representation and processing of stimuli, but it remains an open issue how neocortical microcircuits can reliably encode and replay such sequences of information. To better understand this, a modular attractor memory network is proposed in which meta-stable sequential attractor transitions are learned through changes to synaptic weights and intrinsic excitabilities via the spike-based Bayesian Confidence Propagation Neural Network (BCPNN) learning rule. We find that the formation of distributed memories, embodied by increased periods of firing in pools of excitatory neurons, together with asymmetrical associations between these distinct network states, can be acquired through plasticity. The model’s feasibility is demonstrated using simulations of adaptive exponential integrate-and-fire model neurons (AdEx). We show that the learning and speed of sequence replay depends on a confluence of biophysically relevant parameters including stimulus duration, level of background noise, ratio of synaptic currents, and strengths of short-term depression and adaptation. Moreover, sequence elements are shown to flexibly participate multiple times in the sequence, suggesting that spiking attractor networks of this type can support an efficient combinatorial code. The model provides a principled approach towards understanding how multiple interacting plasticity mechanisms can coordinate hetero-associative learning in unison.

From one moment to the next, in an ever-changing world, and awash in a deluge of sensory data, the brain fluidly guides our actions throughout an astonishing variety of tasks. Processing this ongoing bombardment of information is a fundamental problem faced by its underlying neural circuits. Given that the structure of our actions along with the organization of the environment in which they are performed can be intuitively decomposed into sequences of simpler patterns, an encoding strategy reflecting the temporal nature of these patterns should offer an efficient approach for assembling more complex memories and behaviors. We present a model that demonstrates how activity could propagate through recurrent cortical microcircuits as a result of a learning rule based on neurobiologically plausible time courses and dynamics. The model predicts that the interaction between several learning and dynamical processes constitute a compound mnemonic engram that can flexibly generate sequential step-wise increases of activity within neural populations.

Large-Scale Simulations of Plastic Neural Networks on Neuromorphic Hardware

SpiNNaker is a digital, neuromorphic architecture designed for simulating large-scale spiking neural networks at speeds close to biological real-time. Rather than using bespoke analog or digital hardware, the basic computational unit of a SpiNNaker system is a general-purpose ARM processor, allowing it to be programmed to simulate a wide variety of neuron and synapse models. This flexibility is particularly valuable in the study of biological plasticity phenomena. A recently proposed learning rule based on the Bayesian Confidence Propagation Neural Network (BCPNN) paradigm offers a generic framework for modeling the interaction of different plasticity mechanisms using spiking neurons. However, it can be computationally expensive to simulate large networks with BCPNN learning since it requires multiple state variables for each synapse, each of which needs to be updated every simulation time-step. We discuss the trade-offs in efficiency and accuracy involved in developing an event-based BCPNN implementation for SpiNNaker based on an analytical solution to the BCPNN equations, and detail the steps taken to fit this within the limited computational and memory resources of the SpiNNaker architecture. We demonstrate this learning rule by learning temporal sequences of neural activity within a recurrent attractor network which we simulate at scales of up to 2.0 × 104 neurons and 5.1 × 107 plastic synapses: the largest plastic neural network ever to be simulated on neuromorphic hardware. We also run a comparable simulation on a Cray XC-30 supercomputer system and find that, if it is to match the run-time of our SpiNNaker simulation, the super computer system uses approximately 45× more power. This suggests that cheaper, more power efficient neuromorphic systems are becoming useful discovery tools in the study of plasticity in large-scale brain models.

Learning of Chunking Sequences in Cognition and Behavior

We often learn and recall long sequences in smaller segments, such as a phone number 858 534 22 30 memorized as four segments. Behavioral experiments suggest that humans and some animals employ this strategy of breaking down cognitive or behavioral sequences into chunks in a wide variety of tasks, but the dynamical principles of how this is achieved remains unknown. Here, we study the temporal dynamics of chunking for learning cognitive sequences in a chunking representation using a dynamical model of competing modes arranged to evoke hierarchical Winnerless Competition (WLC) dynamics. Sequential memory is represented as trajectories along a chain of metastable fixed points at each level of the hierarchy, and bistable Hebbian dynamics enables the learning of such trajectories in an unsupervised fashion. Using computer simulations, we demonstrate the learning of a chunking representation of sequences and their robust recall. During learning, the dynamics associates a set of modes to each information-carrying item in the sequence and encodes their relative order. During recall, hierarchical WLC guarantees the robustness of the sequence order when the sequence is not too long. The resulting patterns of activities share several features observed in behavioral experiments, such as the pauses between boundaries of chunks, their size and their duration. Failures in learning chunking sequences provide new insights into the dynamical causes of neurological disorders such as Parkinson’s disease and Schizophrenia.

Because chunking is a hallmark of the brain’s organization, efforts to understand its dynamics can provide valuable insights into the brain and its disorders. For identifying the dynamical principles of chunking learning, we hypothesize that perceptual sequences can be learned and stored as a chain of metastable fixed points in a low-dimensional dynamical system, similar to the trajectory of a ball rolling down a pinball machine. During a learning phase, the interactions in the network evolve such that the network learns a chunking representation of the sequence, as when memorizing a phone number in segments. In the example of the pinball machine, learning can be identified with the gradual placement of the pins. After learning, the pins are placed in a way that, at each run, the ball follows the same trajectory (recall of the same sequence) that encodes the perceptual sequence. Simulations show that the dynamics are endowed with the hallmarks of chunking observed in behavioral experiments, such as increased delays observed before loading new chunks.

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.

The dependence of neuronal encoding efficiency on Hebbian plasticity and homeostatic regulation of neurotransmitter release

Synapses act as information filters by different molecular mechanisms including retrograde messenger that affect neuronal spiking activity. One of the well-known effects of retrograde messenger in presynaptic neurons is a change of the probability of neurotransmitter release. Hebbian learning describe a strengthening of a synapse between a presynaptic input onto a postsynaptic neuron when both pre- and postsynaptic neurons are coactive. In this work, a theory of homeostatic regulation of neurotransmitter release by retrograde messenger and Hebbian plasticity in neuronal encoding is presented. Encoding efficiency was measured for different synaptic conditions. In order to gain high encoding efficiency, the spiking pattern of a neuron should be dependent on the intensity of the input and show low levels of noise. In this work, we represent spiking trains as zeros and ones (corresponding to non-spike or spike in a time bin, respectively) as words with length equal to three. Then the frequency of each word (here eight words) is measured using spiking trains. These frequencies are used to measure neuronal efficiency in different conditions and for different parameter values. Results show that neurons that have synapses acting as band-pass filters show the highest efficiency to encode their input when both Hebbian mechanism and homeostatic regulation of neurotransmitter release exist in synapses. Specifically, the integration of homeostatic regulation of feedback inhibition with Hebbian mechanism and homeostatic regulation of neurotransmitter release in the synapses leads to even higher efficiency when high stimulus intensity is presented to the neurons. However, neurons with synapses acting as high-pass filters show no remarkable increase in encoding efficiency for all simulated synaptic plasticity mechanisms. This study demonstrates the importance of cooperation of Hebbian mechanism with regulation of neurotransmitter release induced by rapid diffused retrograde messenger in neurons with synapses as low and band-pass filters to obtain high encoding efficiency in different environmental and physiological conditions.

Reducing the computational footprint for real-time BCPNN learning

The implementation of synaptic plasticity in neural simulation or neuromorphic hardware is usually very resource-intensive, often requiring a compromise between efficiency and flexibility. A versatile, but computationally-expensive plasticity mechanism is provided by the Bayesian Confidence Propagation Neural Network (BCPNN) paradigm. Building upon Bayesian statistics, and having clear links to biological plasticity processes, the BCPNN learning rule has been applied in many fields, ranging from data classification, associative memory, reward-based learning, probabilistic inference to cortical attractor memory networks. In the spike-based version of this learning rule the pre-, postsynaptic and coincident activity is traced in three low-pass-filtering stages, requiring a total of eight state variables, whose dynamics are typically simulated with the fixed step size Euler method. We derive analytic solutions allowing an efficient event-driven implementation of this learning rule. Further speedup is achieved by first rewriting the model which reduces the number of basic arithmetic operations per update to one half, and second by using look-up tables for the frequently calculated exponential decay. Ultimately, in a typical use case, the simulation using our approach is more than one order of magnitude faster than with the fixed step size Euler method. Aiming for a small memory footprint per BCPNN synapse, we also evaluate the use of fixed-point numbers for the state variables, and assess the number of bits required to achieve same or better accuracy than with the conventional explicit Euler method. All of this will allow a real-time simulation of a reduced cortex model based on BCPNN in high performance computing. More important, with the analytic solution at hand and due to the reduced memory bandwidth, the learning rule can be efficiently implemented in dedicated or existing digital neuromorphic hardware.

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.