A triplet spike-timing-dependent plasticity model generalizes the Bienenstock-Cooper-Munro rule to higher-order spatiotemporal correlations

Dual-Adaptive Heterojunction Synaptic Transistors for Efficient Machine Vision in Harsh Lighting Conditions

Photoadaptive synaptic devices enable in-sensor processing of complex illumination scenes, while second-order adaptive synaptic plasticity improves learning efficiency by modifying the learning rate in a given environment. The integration of above adaptations in one phototransistor device will provide opportunities for developing high-efficient machine vision system. Here, a dually adaptable organic heterojunction transistor as a working unit in the system, which facilitates precise contrast enhancement and improves convergence rate under harsh lighting conditions, is reported. The photoadaptive threshold sliding originates from the bidirectional photoconductivity caused by the light intensity-dependent photogating effect. Metaplasticity is successfully implemented owing to the combination of ambipolar behavior and charge trapping effect. By utilizing the transistor array in a machine vision system, the details and edges can be highlighted in the 0.4% low-contrast images, and a high recognition accuracy of 93.8% with a significantly promoted convergence rate by about 5 times are also achieved. These results open a strategy to fully implement metaplasticity in optoelectronic devices and suggest their vision processing applications in complex lighting scenes.

Astrocytes enhance plasticity response during reversal learning

Astrocytes play a key role in the regulation of synaptic strength and are thought to orchestrate synaptic plasticity and memory. Yet, how specifically astrocytes and their neuroactive transmitters control learning and memory is currently an open question. Recent experiments have uncovered an astrocyte-mediated feedback loop in CA1 pyramidal neurons which is started by the release of endocannabinoids by active neurons and closed by astrocytic regulation of the D-serine levels at the dendrites. D-serine is a co-agonist for the NMDA receptor regulating the strength and direction of synaptic plasticity. Activity-dependent D-serine release mediated by astrocytes is therefore a candidate for mediating between long-term synaptic depression (LTD) and potentiation (LTP) during learning. Here, we show that the mathematical description of this mechanism leads to a biophysical model of synaptic plasticity consistent with the phenomenological model known as the BCM model. The resulting mathematical framework can explain the learning deficit observed in mice upon disruption of the D-serine regulatory mechanism. It shows that D-serine enhances plasticity during reversal learning, ensuring fast responses to changes in the external environment. The model provides new testable predictions about the learning process, driving our understanding of the functional role of neuron-glia interaction in learning.

Anti-Hebbian plasticity drives sequence learning in striatum

Spatio-temporal activity patterns have been observed in a variety of brain areas in spontaneous activity, prior to or during action, or in response to stimuli. Biological mechanisms endowing neurons with the ability to distinguish between different sequences remain largely unknown. Learning sequences of spikes raises multiple challenges, such as maintaining in memory spike history and discriminating partially overlapping sequences. Here, we show that anti-Hebbian spike-timing dependent plasticity (STDP), as observed at cortico-striatal synapses, can naturally lead to learning spike sequences. We design a spiking model of the striatal output neuron receiving spike patterns defined as sequential input from a fixed set of cortical neurons. We use a simple synaptic plasticity rule that combines anti-Hebbian STDP and non-associative potentiation for a subset of the presented patterns called rewarded patterns. We study the ability of striatal output neurons to discriminate rewarded from non-rewarded patterns by firing only after the presentation of a rewarded pattern. In particular, we show that two biological properties of striatal networks, spiking latency and collateral inhibition, contribute to an increase in accuracy, by allowing a better discrimination of partially overlapping sequences. These results suggest that anti-Hebbian STDP may serve as a biological substrate for learning sequences of spikes.

A Hybrid CMOS-Memristor Spiking Neural Network Supporting Multiple Learning Rules

Artificial intelligence (AI) is changing the way computing is performed to cope with real-world, ill-defined tasks for which traditional algorithms fail. AI requires significant memory access, thus running into the von Neumann bottleneck when implemented in standard computing platforms. In this respect, low-latency energy-efficient in-memory computing can be achieved by exploiting emerging memristive devices, given their ability to emulate synaptic plasticity, which provides a path to design large-scale brain-inspired spiking neural networks (SNNs). Several plasticity rules have been described in the brain and their coexistence in the same network largely expands the computational capabilities of a given circuit. In this work, starting from the electrical characterization and modeling of the memristor device, we propose a neuro-synaptic architecture that co-integrates in a unique platform with a single type of synaptic device to implement two distinct learning rules, namely, the spike-timing-dependent plasticity (STDP) and the Bienenstock-Cooper-Munro (BCM). This architecture, by exploiting the aforementioned learning rules, successfully addressed two different tasks of unsupervised learning.

Learning what matters: Synaptic plasticity with invariance to second-order input correlations

Cortical populations of neurons develop sparse representations adapted to the statistics of the environment. To learn efficient population codes, synaptic plasticity mechanisms must differentiate relevant latent features from spurious input correlations, which are omnipresent in cortical networks. Here, we develop a theory for sparse coding and synaptic plasticity that is invariant to second-order correlations in the input. Going beyond classical Hebbian learning, our learning objective explains the functional form of observed excitatory plasticity mechanisms, showing how Hebbian long-term depression (LTD) cancels the sensitivity to second-order correlations so that receptive fields become aligned with features hidden in higher-order statistics. Invariance to second-order correlations enhances the versatility of biologically realistic learning models, supporting optimal decoding from noisy inputs and sparse population coding from spatially correlated stimuli. In a spiking model with triplet spike-timing-dependent plasticity (STDP), we show that individual neurons can learn localized oriented receptive fields, circumventing the need for input preprocessing, such as whitening, or population-level lateral inhibition. The theory advances our understanding of local unsupervised learning in cortical circuits, offers new interpretations of the Bienenstock-Cooper-Munro and triplet STDP models, and assigns a specific functional role to synaptic LTD mechanisms in pyramidal neurons.

Moiré synaptic transistor with room-temperature neuromorphic functionality

Moiré quantum materials host exotic electronic phenomena through enhanced internal Coulomb interactions in twisted two-dimensional heterostructures1-4. When combined with the exceptionally high electrostatic control in atomically thin materials5-8, moiré heterostructures have the potential to enable next-generation electronic devices with unprecedented functionality. However, despite extensive exploration, moiré electronic phenomena have thus far been limited to impractically low cryogenic temperatures9-14, thus precluding real-world applications of moiré quantum materials. Here we report the experimental realization and room-temperature operation of a low-power (20 pW) moiré synaptic transistor based on an asymmetric bilayer graphene/hexagonal boron nitride moiré heterostructure. The asymmetric moiré potential gives rise to robust electronic ratchet states, which enable hysteretic, non-volatile injection of charge carriers that control the conductance of the device. The asymmetric gating in dual-gated moiré heterostructures realizes diverse biorealistic neuromorphic functionalities, such as reconfigurable synaptic responses, spatiotemporal-based tempotrons and Bienenstock-Cooper-Munro input-specific adaptation. In this manner, the moiré synaptic transistor enables efficient compute-in-memory designs and edge hardware accelerators for artificial intelligence and machine learning.

The combination of Hebbian and predictive plasticity learns invariant object representations in deep sensory networks

Recognition of objects from sensory stimuli is essential for survival. To that end, sensory networks in the brain must form object representations invariant to stimulus changes, such as size, orientation and context. Although Hebbian plasticity is known to shape sensory networks, it fails to create invariant object representations in computational models, raising the question of how the brain achieves such processing. In the present study, we show that combining Hebbian plasticity with a predictive form of plasticity leads to invariant representations in deep neural network models. We derive a local learning rule that generalizes to spiking neural networks and naturally accounts for several experimentally observed properties of synaptic plasticity, including metaplasticity and spike-timing-dependent plasticity. Finally, our model accurately captures neuronal selectivity changes observed in the primate inferotemporal cortex in response to altered visual experience. Thus, we provide a plausible normative theory emphasizing the importance of predictive plasticity mechanisms for successful representational learning.

How to incorporate biological insights into network models and why it matters

Due to the staggering complexity of the brain and its neural circuitry, neuroscientists rely on the analysis of mathematical models to elucidate its function. From Hodgkin and Huxley's detailed description of the action potential in 1952 to today, new theories and increasing computational power have opened up novel avenues to study how neural circuits implement the computations that underlie behaviour. Computational neuroscientists have developed many models of neural circuits that differ in complexity, biological realism or emergent network properties. With recent advances in experimental techniques for detailed anatomical reconstructions or large-scale activity recordings, rich biological data have become more available. The challenge when building network models is to reflect experimental results, either through a high level of detail or by finding an appropriate level of abstraction. Meanwhile, machine learning has facilitated the development of artificial neural networks, which are trained to perform specific tasks. While they have proven successful at achieving task-oriented behaviour, they are often abstract constructs that differ in many features from the physiology of brain circuits. Thus, it is unclear whether the mechanisms underlying computation in biological circuits can be investigated by analysing artificial networks that accomplish the same function but differ in their mechanisms. Here, we argue that building biologically realistic network models is crucial to establishing causal relationships between neurons, synapses, circuits and behaviour. More specifically, we advocate for network models that consider the connectivity structure and the recorded activity dynamics while evaluating task performance.

Meta-SpikePropamine: learning to learn with synaptic plasticity in spiking neural networks

We propose that in order to harness our understanding of neuroscience toward machine learning, we must first have powerful tools for training brain-like models of learning. Although substantial progress has been made toward understanding the dynamics of learning in the brain, neuroscience-derived models of learning have yet to demonstrate the same performance capabilities as methods in deep learning such as gradient descent. Inspired by the successes of machine learning using gradient descent, we introduce a bi-level optimization framework that seeks to both solve online learning tasks and improve the ability to learn online using models of plasticity from neuroscience. We demonstrate that models of three-factor learning with synaptic plasticity taken from the neuroscience literature can be trained in Spiking Neural Networks (SNNs) with gradient descent via a framework of learning-to-learn to address challenging online learning problems. This framework opens a new path toward developing neuroscience inspired online learning algorithms.

Doppler Frequency-Shift Information Processing in WOx -Based Memristive Synapse for Auditory Motion Perception

Auditory motion perception is one crucial capability to decode and discriminate the spatiotemporal information for neuromorphic auditory systems. Doppler frequency-shift feature and interaural time difference (ITD) are two fundamental cues of auditory information processing. In this work, the functions of azimuth detection and velocity detection, as the typical auditory motion perception, are demonstrated in a WO_x -based memristive synapse. The WO_x memristor presents both the volatile mode (M1) and semi-nonvolatile mode (M2), which are capable of implementing the high-pass filtering and processing the spike trains with a relative timing and frequency shift. In particular, the Doppler frequency-shift information processing for velocity detection is emulated in the WO_x memristor based auditory system for the first time, which relies on a scheme of triplet spike-timing-dependent-plasticity in the memristor. These results provide new opportunities for the mimicry of auditory motion perception and enable the auditory sensory system to be applied in future neuromorphic sensing.

A SmNiO3 memristor with artificial synapse function properties and the implementation of Boolean logic circuits

Recently, with the improvement of the requirements for fast and efficient data processing in the era of artificial intelligence, new forms of computing have come into being. Developing memristor devices that can simulate the brain's computing neutral network is particularly important for applications in the field of artificial intelligence. However, there are still some challenges in their biological function simulation and related circuit design. In this work, a memristor based on perovskite rare earth nickelates (RNiO₃) is presented with excellent electrical performance, including three orders of magnitude higher current switching ratio and good repeatability, and can achieve bidirectional conductance regulation like weight modulation in bio-synapse. Furthermore, the synaptic like characteristics of the device have been mimicked successfully, such as excitatory postsynaptic current (EPSC), paired pulse facilitation (PPF), classical double pulse spike time-dependent plasticity (classical pair-STDP), triplet spike time-dependent plasticity (triplet-STDP), short-term plasticity (STP), long-term plasticity (LTP), the refractory period phenomenon and learning and forgetting rules. In particular, two synaptic devices and a leaky integrate-and-fire (LIF) neuron device are used to achieve a logic gate circuit to realize "AND", "OR", and "NOT" functions. The device paves the way for the application of high-density circuits in artificial intelligence.

Mammalian-brain-inspired neuromorphic motion-cognition nerve achieves cross-modal perceptual enhancement

Perceptual enhancement of neural and behavioral response due to combinations of multisensory stimuli are found in many animal species across different sensory modalities. By mimicking the multisensory integration of ocular-vestibular cues for enhanced spatial perception in macaques, a bioinspired motion-cognition nerve based on a flexible multisensory neuromorphic device is demonstrated. A fast, scalable and solution-processed fabrication strategy is developed to prepare a nanoparticle-doped two-dimensional (2D)-nanoflake thin film, exhibiting superior electrostatic gating capability and charge-carrier mobility. The multi-input neuromorphic device fabricated using this thin film shows history-dependent plasticity, stable linear modulation, and spatiotemporal integration capability. These characteristics ensure parallel, efficient processing of bimodal motion signals encoded as spikes and assigned with different perceptual weights. Motion-cognition function is realized by classifying the motion types using mean firing rates of encoded spikes and postsynaptic current of the device. Demonstrations of recognition of human activity types and drone flight modes reveal that the motion-cognition performance match the bio-plausible principles of perceptual enhancement by multisensory integration. Our system can be potentially applied in sensory robotics and smart wearables.

Adaptive control of synaptic plasticity integrates micro- and macroscopic network function

Synaptic plasticity configures interactions between neurons and is therefore likely to be a primary driver of behavioral learning and development. How this microscopic-macroscopic interaction occurs is poorly understood, as researchers frequently examine models within particular ranges of abstraction and scale. Computational neuroscience and machine learning models offer theoretically powerful analyses of plasticity in neural networks, but results are often siloed and only coarsely linked to biology. In this review, we examine connections between these areas, asking how network computations change as a function of diverse features of plasticity and vice versa. We review how plasticity can be controlled at synapses by calcium dynamics and neuromodulatory signals, the manifestation of these changes in networks, and their impacts in specialized circuits. We conclude that metaplasticity-defined broadly as the adaptive control of plasticity-forges connections across scales by governing what groups of synapses can and can't learn about, when, and to what ends. The metaplasticity we discuss acts by co-opting Hebbian mechanisms, shifting network properties, and routing activity within and across brain systems. Asking how these operations can go awry should also be useful for understanding pathology, which we address in the context of autism, schizophrenia and Parkinson's disease.

Ionic-electronic halide perovskite memdiodes enabling neuromorphic computing with a second-order complexity

With increasing computing demands, serial processing in von Neumann architectures built with zeroth-order complexity digital circuits is saturating in computational capacity and power, entailing research into alternative paradigms. Brain-inspired systems built with memristors are attractive owing to their large parallelism, low energy consumption, and high error tolerance. However, most demonstrations have thus far only mimicked primitive lower-order biological complexities using devices with first-order dynamics. Memristors with higher-order complexities are predicted to solve problems that would otherwise require increasingly elaborate circuits, but no generic design rules exist. Here, we present second-order dynamics in halide perovskite memristive diodes (memdiodes) that enable Bienenstock-Cooper-Munro learning rules capturing both timing- and rate-based plasticity. A triplet spike timing-dependent plasticity scheme exploiting ion migration, back diffusion, and modulable Schottky barriers establishes general design rules for realizing higher-order memristors. This higher order enables complex binocular orientation selectivity in neural networks exploiting the intrinsic physics of the devices, without the need for complicated circuitry.

Stability and learning in excitatory synapses by nonlinear inhibitory plasticity

Synaptic changes are hypothesized to underlie learning and memory formation in the brain. But Hebbian synaptic plasticity of excitatory synapses on its own is unstable, leading to either unlimited growth of synaptic strengths or silencing of neuronal activity without additional homeostatic mechanisms. To control excitatory synaptic strengths, we propose a novel form of synaptic plasticity at inhibitory synapses. Using computational modeling, we suggest two key features of inhibitory plasticity, dominance of inhibition over excitation and a nonlinear dependence on the firing rate of postsynaptic excitatory neurons whereby inhibitory synaptic strengths change with the same sign (potentiate or depress) as excitatory synaptic strengths. We demonstrate that the stable synaptic strengths realized by this novel inhibitory plasticity model affects excitatory/inhibitory weight ratios in agreement with experimental results. Applying a disinhibitory signal can gate plasticity and lead to the generation of receptive fields and strong bidirectional connectivity in a recurrent network. Hence, a novel form of nonlinear inhibitory plasticity can simultaneously stabilize excitatory synaptic strengths and enable learning upon disinhibition.

An overview of brain-like computing: Architecture, applications, and future trends

With the development of technology, Moore's law will come to an end, and scientists are trying to find a new way out in brain-like computing. But we still know very little about how the brain works. At the present stage of research, brain-like models are all structured to mimic the brain in order to achieve some of the brain's functions, and then continue to improve the theories and models. This article summarizes the important progress and status of brain-like computing, summarizes the generally accepted and feasible brain-like computing models, introduces, analyzes, and compares the more mature brain-like computing chips, outlines the attempts and challenges of brain-like computing applications at this stage, and looks forward to the future development of brain-like computing. It is hoped that the summarized results will help relevant researchers and practitioners to quickly grasp the research progress in the field of brain-like computing and acquire the application methods and related knowledge in this field.

Spike-Timing-Dependent Plasticity With Activation-Dependent Scaling for Receptive Fields Development

Spike-timing-dependent plasticity (STDP) is one of the most popular and deeply biologically motivated forms of unsupervised Hebbian-type learning. In this article, we propose a variant of STDP extended by an additional activation-dependent scale factor. The consequent learning rule is an efficient algorithm, which is simple to implement and applicable to spiking neural networks (SNNs). It is demonstrated that the proposed plasticity mechanism combined with competitive learning can serve as an effective mechanism for the unsupervised development of receptive fields (RFs). Furthermore, the relationship between synaptic scaling and lateral inhibition is explored in the context of the successful development of RFs. Specifically, we demonstrate that maintaining a high level of synaptic scaling followed by its rapid increase is crucial for the development of neuronal mechanisms of selectivity. The strength of the proposed solution is assessed in classification tasks performed on the Modified National Institute of Standards and Technology (MNIST) data set with an accuracy level of 94.65% (a single network) and 95.17% (a network committee)-comparable to the state-of-the-art results of single-layer SNN architectures trained in an unsupervised manner. Furthermore, the training process leads to sparse data representation and the developed RFs have the potential to serve as local feature detectors in multilayered spiking networks. We also prove theoretically that when applied to linear Poisson neurons, our rule conserves total synaptic strength, guaranteeing the convergence of the learning process.

Spike Timing-Dependent Plasticity with Enhanced Long-Term Depression Leads to an Increase of Statistical Complexity

Synaptic plasticity is characterized by remodeling of existing synapses caused by strengthening and/or weakening of connections. This is represented by long-term potentiation (LTP) and long-term depression (LTD). The occurrence of a presynaptic spike (or action potential) followed by a temporally nearby postsynaptic spike induces LTP; conversely, if the postsynaptic spike precedes the presynaptic spike, it induces LTD. This form of synaptic plasticity induction depends on the order and timing of the pre- and postsynaptic action potential, and has been termed spike time-dependent plasticity (STDP). After an epileptic seizure, LTD plays an important role as a depressor of synapses, which may lead to their complete disappearance together with that of their neighboring connections until days after the event. Added to the fact that after an epileptic seizure the network seeks to regulate the excess activity through two key mechanisms: depressed connections and neuronal death (eliminating excitatory neurons from the network), LTD becomes of great interest in our study. To investigate this phenomenon, we develop a biologically plausible model that privileges LTD at the triplet level while maintaining the pairwise structure in the STPD and study how network dynamics are affected as neuronal damage increases. We find that the statistical complexity is significantly higher for the network where LTD presented both types of interactions. While in the case where the STPD is defined with purely pairwise interactions an increase is observed as damage becomes higher for both Shannon Entropy and Fisher information.

Synaptic plasticity in self-powered artificial striate cortex for binocular orientation selectivity

Get in-depth understanding of each part of visual pathway yields insights to conquer the challenges that classic computer vision is facing. Here, we first report the bioinspired striate cortex with binocular and orientation selective receptive field based on the crossbar array of self-powered memristors which is solution-processed monolithic all-perovskite system with each cross-point containing one CsFAPbI₃ solar cell directly stacking on the CsPbBr₂I memristor. The plasticity of self-powered memristor can be modulated by optical stimuli following triplet-STDP rules. Furthermore, plasticity of 3 × 3 flexible crossbar array of self-powered memristors has been successfully modulated based on generalized BCM learning rule for optical-encoded pattern recognition. Finally, we implemented artificial striate cortex with binocularity and orientation selectivity based on two simulated 9 × 9 self-powered memristors networks. The emulation of striate cortex with binocular and orientation selectivity will facilitate the brisk edge and corner detection for machine vision in the future applications.

Designing efficient bio-inspired vision systems remains a challenge. Here, the authors report a bio-inspired striate visual cortex with binocular and orientation selective receptive field based on self-powered memristor to enable machine vision with brisk edge and corner detection in the future applications.

Formation and computational implications of assemblies in neural circuits

In the brain, patterns of neural activity represent sensory information and store it in non-random synaptic connectivity. A prominent theoretical hypothesis states that assemblies, groups of neurons that are strongly connected to each other, are the key computational units underlying perception and memory formation. Compatible with these hypothesised assemblies, experiments have revealed groups of neurons that display synchronous activity, either spontaneously or upon stimulus presentation, and exhibit behavioural relevance. While it remains unclear how assemblies form in the brain, theoretical work has vastly contributed to the understanding of various interacting mechanisms in this process. Here, we review the recent theoretical literature on assembly formation by categorising the involved mechanisms into four components: synaptic plasticity, symmetry breaking, competition and stability. We highlight different approaches and assumptions behind assembly formation and discuss recent ideas of assemblies as the key computational unit in the brain. Abstract figure legend Assembly Formation. Assemblies are groups of strongly connected neurons formed by the interaction of multiple mechanisms and with vast computational implications. Four interacting components are thought to drive assembly formation: synaptic plasticity, symmetry breaking, competition and stability. This article is protected by copyright. All rights reserved.

Weight dependence in BCM leads to adjustable synaptic competition

Models of synaptic plasticity have been used to better understand neural development as well as learning and memory. One prominent classic model is the Bienenstock-Cooper-Munro (BCM) model that has been particularly successful in explaining plasticity of the visual cortex. Here, in an effort to include more biophysical detail in the BCM model, we incorporate 1) feedforward inhibition, and 2) the experimental observation that large synapses are relatively harder to potentiate than weak ones, while synaptic depression is proportional to the synaptic strength. These modifications change the outcome of unsupervised plasticity under the BCM model. The amount of feed-forward inhibition adds a parameter to BCM that turns out to determine the strength of competition. In the limit of strong inhibition the learning outcome is identical to standard BCM and the neuron becomes selective to one stimulus only (winner-take-all). For smaller values of inhibition, competition is weaker and the receptive fields are less selective. However, both BCM variants can yield realistic receptive fields.

A Hebbian Approach to Non-Spatial Prelinguistic Reasoning

This research integrates key concepts of Computational Neuroscience, including the Bienestock-CooperMunro (BCM) rule, Spike Timing-Dependent Plasticity Rules (STDP), and the Temporal Difference Learning algorithm, with an important structure of Deep Learning (Convolutional Networks) to create an architecture with the potential of replicating observations of some cognitive experiments (particularly, those that provided some basis for sequential reasoning) while sharing the advantages already achieved by the previous proposals. In particular, we present Ring Model B, which is capable of associating visual with auditory stimulus, performing sequential predictions, and predicting reward from experience. Despite its simplicity, we considered such abilities to be a first step towards the formulation of more general models of prelinguistic reasoning.

The generation of cortical novelty responses through inhibitory plasticity

Animals depend on fast and reliable detection of novel stimuli in their environment. Neurons in multiple sensory areas respond more strongly to novel in comparison to familiar stimuli. Yet, it remains unclear which circuit, cellular, and synaptic mechanisms underlie those responses. Here, we show that spike-timing-dependent plasticity of inhibitory-to-excitatory synapses generates novelty responses in a recurrent spiking network model. Inhibitory plasticity increases the inhibition onto excitatory neurons tuned to familiar stimuli, while inhibition for novel stimuli remains low, leading to a network novelty response. The generation of novelty responses does not depend on the periodicity but rather on the distribution of presented stimuli. By including tuning of inhibitory neurons, the network further captures stimulus-specific adaptation. Finally, we suggest that disinhibition can control the amplification of novelty responses. Therefore, inhibitory plasticity provides a flexible, biologically plausible mechanism to detect the novelty of bottom-up stimuli, enabling us to make experimentally testable predictions.

Boost of the Bio-memristor Performance for Artificial Electronic Synapses by Surface Reconstruction

Biomaterial-based memristors (bio-memristors) are often adopted to emulate biological synapse functions and applied to construct neural computing networks in brain-inspired chip systems. However, the randomness of conductive filament formation in bio-memristors inhibits their switching performance by causing the dispersion of the device-switching parameters. In this case, a facile porous silk fibroin (p-SF) memristor was obtained through a protein surface reconstruction strategy, in which the size of the hole can be adjusted by the density of hybrid nanoseeds. The porous SF memristors exhibit greatly enhanced electrical characteristics, including uniform I-V cycles, centralized distribution of the switching voltages, and both high and low resistances, compared to devices without pores. The results of three-dimensional (3D) simulations based on classical density functional theory (cDFT) suggest that the reconstructed pores in the SF layers guide the formation and fracture of Ag filaments under an electric field and enhance the overall conductivity by separating Ag⁺ ion and electron diffusion pathways. Ag⁺ ions are predicted to preferentially diffuse through pores, whereas electrons diffuse through the SF network. Interestingly, the device conductance can be bidirectionally modulated gradually by positive and negative voltages, can faithfully simulate short-term and long-term plasticity, and can even realize the triplet-spike-timing-dependent plasticity (triplet-STDP) rule, which can be used for pattern recognition in biological systems. The simulation results reveal that a memristor network of this type has an accuracy of ∼95.78% in memory learning and the capability of pattern learning. This work provides a facile technology route to improve the performance of bionic-material memristors.

Heterogeneity across neural populations: Its significance for the dynamics and functions of neural circuits

Neural populations show patterns of synchronous activity, as they share common correlated inputs. Neurons in the cortex that are connected by strong synapses cause rapid firing explosions. In addition, areas that are connected by weaker synapses have a slower dynamics and they can contribute to asymmetries in the input distributions. The aim of this work is to develop a neural model to investigate how the heterogeneities in the synaptic input distributions affect different levels of organizational activity in the brain dynamics. We analytically show how small changes in the correlation inputs can cause large changes in the interactions of the outputs that lead to a phase transition, demonstrating that a simple variation in the direction of a biased skewed distribution in the neuronal inputs can generate a transition of states in the firing rate, passing from spontaneous silence ("down state") to an absolute spiking activity ("up state"). We present an exact quantification of the dynamics of the output variables, showing that when considering a biased skewed distribution in the inputs of neuronal population, the critical point is not in an asynchronous or synchronous state but rather at an intermediate value.

Balanced networks under spike-time dependent plasticity

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike–timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity–induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.

Animals are able to learn complex tasks through changes in individual synapses between cells. Such changes lead to the coevolution of neural activity patterns and the structure of neural connectivity, but the consequences of these interactions are not fully understood. We consider plasticity in model neural networks which achieve an average balance between the excitatory and inhibitory synaptic inputs to different cells, and display cortical–like, irregular activity. We extend the theory of balanced networks to account for synaptic plasticity and show which rules can maintain balance, and which will drive the network into a different state. This theory of plasticity can provide insights into the relationship between stimuli, network dynamics, and synaptic circuitry.

Unsupervised AER Object Recognition Based on Multiscale Spatio-Temporal Features and Spiking Neurons

This article proposes an unsupervised address event representation (AER) object recognition approach. The proposed approach consists of a novel multiscale spatio-temporal feature (MuST) representation of input AER events and a spiking neural network (SNN) using spike-timing-dependent plasticity (STDP) for object recognition with MuST. MuST extracts the features contained in both the spatial and temporal information of AER event flow, and forms an informative and compact feature spike representation. We show not only how MuST exploits spikes to convey information more effectively, but also how it benefits the recognition using SNN. The recognition process is performed in an unsupervised manner, which does not need to specify the desired status of every single neuron of SNN, and thus can be flexibly applied in real-world recognition tasks. The experiments are performed on five AER datasets including a new one named GESTURE-DVS. Extensive experimental results show the effectiveness and advantages of the proposed approach.

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.

Bienenstock-Cooper-Munro Learning Rule Realized in Polysaccharide-Gated Synaptic Transistors with Tunable Threshold

With reference to the organization of the human brain nervous system, a hardware-based approach that builds massively parallel neuromorphic circuits is of great significance to neuromorphic computing. The Bienenstock-Cooper-Munro (BCM) learning rule, which describes that the synaptic weight modulation exhibits frequency-dependent and tunable frequency threshold characteristics, is more compatible with the working principle of neuromorphic computing systems than spike-timing-dependent plasticity. Therefore, it is interesting to simulate the BCM learning rule on solid-state synaptic devices. Here, we have prepared λ-carrageenan (λ-car) electrolyte-gated oxide synaptic transistors, which exhibit good transistor performances, including a low subthreshold swing of 125 mV/dec, an on/off ratio larger than 10⁶, and a mobility of 9.5 cm² V^-1 s^-1. By modulating the initial channel current and spike frequency, the simulation of the BCM rule was successfully realized. The competitive relationship between the drift of protons under an electric field and the spontaneous diffusion of protons can explain this mechanism. The proposed λ-car-gated synaptic transistor has a great significance to neuromorphic computing.

Homeostatic mechanisms regulate distinct aspects of cortical circuit dynamics

Homeostasis is indispensable to counteract the destabilizing effects of Hebbian plasticity. Although it is commonly assumed that homeostasis modulates synaptic strength, membrane excitability, and firing rates, its role at the neural circuit and network level is unknown. Here, we identify changes in higher-order network properties of freely behaving rodents during prolonged visual deprivation. Strikingly, our data reveal that functional pairwise correlations and their structure are subject to homeostatic regulation. Using a computational model, we demonstrate that the interplay of different plasticity and homeostatic mechanisms can capture the initial drop and delayed recovery of firing rates and correlations observed experimentally. Moreover, our model indicates that synaptic scaling is crucial for the recovery of correlations and network structure, while intrinsic plasticity is essential for the rebound of firing rates, suggesting that synaptic scaling and intrinsic plasticity can serve distinct functions in homeostatically regulating network dynamics.

Induction of LTD-like corticospinal plasticity by low-frequency rTMS depends on pre-stimulus phase of sensorimotor μ-rhythm

Background

Neural oscillations reflect rapidly changing brain excitability states. We have demonstrated previously with EEG-triggered transcranial magnetic stimulation (TMS) of human motor cortex that the positive vs. negative peak of the sensorimotor μ-oscillation reflect corticospinal low-vs. high-excitability states. In vitro experiments showed that induction of long-term depression (LTD) by low-frequency stimulation depends on the postsynaptic excitability state.

Objective/Hypothesis: We tested the hypothesis that induction of LTD-like corticospinal plasticity in humans by 1 Hz repetitive TMS (rTMS) is enhanced when rTMS is synchronized with the low-excitability state, but decreased or even shifted towards long-term (LTP)-like plasticity when synchronized with the high-excitability state.

Methods

We applied real-time EEG-triggered 1-Hz-rTMS (900 pulses) to the hand area of motor cortex in healthy subjects. In a randomized double-blind three-condition crossover design, pulses were synchronized to either the positive or negative peak of the sensorimotor μ-oscillation, or were applied at random phase (control). The amplitude of motor evoked potentials was recorded as an index of corticospinal excitability before and after 1-Hz-rTMS.

Results

1-Hz-rTMS at random phase resulted in a trend towards LTD-like corticospinal plasticity. RTMS in the positive peak condition (i.e., the low-excitability state) induced significant LTD-like plasticity. RTMS in the negative peak condition (i.e., the high-excitability state) showed a trend towards LTP-like plasticity, which was significantly different from the other two conditions.

Conclusion

The level of corticospinal depolarization reflected by phase of the μ-oscillation determines the degree of corticospinal plasticity induced by low-frequency rTMS, a finding that may guide future personalized therapeutic stimulation.

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Positive vs. negative phase of μ-rhythm are states of low vs. high excitability.

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1-Hz-rTMS coupled to positive but not negative phase results in LTD-like plasticity.

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Phase of μ-rhythm determines effect size of 1-Hz-rTMS induced plasticity.

Multicoding in neural information transfer suggested by mathematical analysis of the frequency-dependent synaptic plasticity in vivo

Two elements of neural information processing have primarily been proposed: firing rate and spike timing of neurons. In the case of synaptic plasticity, although spike-timing-dependent plasticity (STDP) depending on presynaptic and postsynaptic spike times had been considered the most common rule, recent studies have shown the inhibitory nature of the brain in vivo for precise spike timing, which is key to the STDP. Thus, the importance of the firing frequency in synaptic plasticity in vivo has been recognized again. However, little is understood about how the frequency-dependent synaptic plasticity (FDP) is regulated in vivo. Here, we focused on the presynaptic input pattern, the intracellular calcium decay time constants, and the background synaptic activity, which vary depending on neuron types and the anatomical and physiological environment in the brain. By analyzing a calcium-based model, we found that the synaptic weight differs depending on these factors characteristic in vivo, even if neurons receive the same input rate. This finding suggests the involvement of multifaceted factors other than input frequency in FDP and even neural coding in vivo.

Presynaptic inhibition rapidly stabilises recurrent excitation in the face of plasticity

Hebbian plasticity, a mechanism believed to be the substrate of learning and memory, detects and further enhances correlated neural activity. Because this constitutes an unstable positive feedback loop, it requires additional homeostatic control. Computational work suggests that in recurrent networks, the homeostatic mechanisms observed in experiments are too slow to compensate instabilities arising from Hebbian plasticity and need to be complemented by rapid compensatory processes. We suggest presynaptic inhibition as a candidate that rapidly provides stability by compensating recurrent excitation induced by Hebbian changes. Presynaptic inhibition is mediated by presynaptic GABA receptors that effectively and reversibly attenuate transmitter release. Activation of these receptors can be triggered by excess network activity, hence providing a stabilising negative feedback loop that weakens recurrent interactions on sub-second timescales. We study the stabilising effect of presynaptic inhibition in recurrent networks, in which presynaptic inhibition is implemented as a multiplicative reduction of recurrent synaptic weights in response to increasing inhibitory activity. We show that networks with presynaptic inhibition display a gradual increase of firing rates with growing excitatory weights, in contrast to traditional excitatory-inhibitory networks. This alleviates the positive feedback loop between Hebbian plasticity and network activity and thereby allows homeostasis to act on timescales similar to those observed in experiments. Our results generalise to spiking networks with a biophysically more detailed implementation of the presynaptic inhibition mechanism. In conclusion, presynaptic inhibition provides a powerful compensatory mechanism that rapidly reduces effective recurrent interactions and thereby stabilises Hebbian learning.

Synapses between neurons change during learning and memory formation, a process termed synaptic plasticity. Established models of plasticity rely on strengthening synapses of co-active neurons. In recurrent networks, mutually connected neurons tend to be co-active. The emerging positive feedback loop is believed to be counteracted by homeostatic mechanisms that aim to keep neural activity at a given set point. However, theoretical work indicates that experimentally observed forms of homeostasis are too slow to maintain stable network activity. In this article, we suggest that presynaptic inhibition can alleviate this problem. Presynaptic inhibition is an inhibitory mechanism that weakens synapses rather than suppressing neural activity. Using mathematical analyses and computer simulations, we show that presynaptic inhibition can compensate the strengthening of recurrent connections and thus stabilises neural networks subject to synaptic plasticity, even if homeostasis acts on biologically plausible timescales.

Autonomous emergence of connectivity assemblies via spike triplet interactions

Non-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP), which depends on the interactions of three precisely-timed spikes, and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We derive synaptic changes arising from correlations up to third-order and describe them as the sum of structural motifs, which determine how any spike in the network influences a given synaptic connection through possible connectivity paths. This motif expansion framework reveals novel structural motifs under the triplet STDP rule, which support the formation of bidirectional connections and ultimately the spontaneous emergence of global network structure in the form of self-connected groups of neurons, or assemblies. We propose that under triplet STDP assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule common in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of the triplet STDP rule or the synaptic transmission function differentially promote structural motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures.

Emergent non-random connectivity structures in different brain regions are tightly related to specific patterns of neural activity and support diverse brain functions. For instance, self-connected groups of neurons, known as assemblies, have been proposed to represent functional units in brain circuits and can emerge even without patterned external instruction. Here we investigate the emergence of non-random connectivity in recurrent networks using a particular plasticity rule, triplet STDP, which relies on the interaction of spike triplets and can capture higher-order statistical dependencies in neural activity. We derive the evolution of the synaptic strengths in the network and explore the conditions for the self-organization of connectivity into assemblies. We demonstrate key differences of the triplet STDP rule compared to the classical pair-based rule in terms of how assemblies are formed, including the realistic asymmetric shape and influence of novel connectivity motifs on network plasticity driven by higher-order correlations. Assembly formation depends on the specific shape of the STDP window and synaptic transmission function, pointing towards an important role of neuromodulatory signals on formation of intrinsically generated assemblies.

Toward a generalized Bienenstock-Cooper-Munro rule for spatiotemporal learning via triplet-STDP in memristive devices

The close replication of synaptic functions is an important objective for achieving a highly realistic memristor-based cognitive computation. The emulation of neurobiological learning rules may allow the development of neuromorphic systems that continuously learn without supervision. In this work, the Bienenstock-Cooper-Munro learning rule, as a typical case of spike-rate-dependent plasticity, is mimicked using a generalized triplet-spike-timing-dependent plasticity scheme in a WO3-x memristive synapse. It demonstrates both presynaptic and postsynaptic activities and remedies the absence of the enhanced depression effect in the depression region, allowing a better description of the biological counterpart. The threshold sliding effect of Bienenstock-Cooper-Munro rule is realized using a history-dependent property of the second-order memristor. Rate-based orientation selectivity is demonstrated in a simulated feedforward memristive network with this generalized Bienenstock-Cooper-Munro framework. These findings provide a feasible approach for mimicking Bienenstock-Cooper-Munro learning rules in memristors, and support the applications of spatiotemporal coding and learning using memristive networks.

Emerging neuromorphic devices

Artificial intelligence (AI) has the ability of revolutionizing our lives and society in a radical way, by enabling machine learning in the industry, business, health, transportation, and many other fields. The ability to recognize objects, faces, and speech, requires, however, exceptional computational power and time, which is conflicting with the current difficulties in transistor scaling due to physical and architectural limitations. As a result, to accelerate the progress of AI, it is necessary to develop materials, devices, and systems that closely mimic the human brain. In this work, we review the current status and challenges on the emerging neuromorphic devices for brain-inspired computing. First, we provide an overview of the memory device technologies which have been proposed for synapse and neuron circuits in neuromorphic systems. Then, we describe the implementation of synaptic learning in the two main types of neural networks, namely the deep neural network and the spiking neural network (SNN). Bio-inspired learning, such as the spike-timing dependent plasticity scheme, is shown to enable unsupervised learning processes which are typical of the human brain. Hardware implementations of SNNs for the recognition of spatial and spatio-temporal patterns are also shown to support the cognitive computation in silico. Finally, we explore the recent advances in reproducing bio-neural processes via device physics, such as insulating-metal transitions, nanoionics drift/diffusion, and magnetization flipping in spintronic devices. By harnessing the device physics in emerging materials, neuromorphic engineering with advanced functionality, higher density and better energy efficiency can be developed.

Spiking time-dependent plasticity leads to efficient coding of predictions

Latency reduction in postsynaptic spikes is a well-known effect of spiking time-dependent plasticity. We expand this notion for long postsynaptic spike trains on single neurons, showing that, for a fixed input spike train, STDP reduces the number of postsynaptic spikes and concentrates the remaining ones. Then, we study the consequences of this phenomena in terms of coding, finding that this mechanism improves the neural code by increasing the signal-to-noise ratio and lowering the metabolic costs of frequent stimuli. Finally, we illustrate that the reduction in postsynaptic latencies can lead to the emergence of predictions.

Memristive and CMOS Devices for Neuromorphic Computing

Neuromorphic computing has emerged as one of the most promising paradigms to overcome the limitations of von Neumann architecture of conventional digital processors. The aim of neuromorphic computing is to faithfully reproduce the computing processes in the human brain, thus paralleling its outstanding energy efficiency and compactness. Toward this goal, however, some major challenges have to be faced. Since the brain processes information by high-density neural networks with ultra-low power consumption, novel device concepts combining high scalability, low-power operation, and advanced computing functionality must be developed. This work provides an overview of the most promising device concepts in neuromorphic computing including complementary metal-oxide semiconductor (CMOS) and memristive technologies. First, the physics and operation of CMOS-based floating-gate memory devices in artificial neural networks will be addressed. Then, several memristive concepts will be reviewed and discussed for applications in deep neural network and spiking neural network architectures. Finally, the main technology challenges and perspectives of neuromorphic computing will be discussed.

Simplified calcium signaling cascade for synaptic plasticity

We propose a model for synaptic plasticity based on a calcium signaling cascade. The model simplifies the full signaling pathways from a calcium influx to the phosphorylation (potentiation) and dephosphorylation (depression) of glutamate receptors that are gated by fictive C1 and C2 catalysts, respectively. This model is based on tangible chemical reactions, including fictive catalysts, for long-term plasticity rather than the conceptual theories commonplace in various models, such as preset thresholds of calcium concentration. Our simplified model successfully reproduced the experimental synaptic plasticity induced by different protocols such as (i) a synchronous pairing protocol and (ii) correlated presynaptic and postsynaptic action potentials (APs). Further, the ocular dominance plasticity (or the experimental verification of the celebrated Bienenstock-Cooper-Munro theory) was reproduced by two model synapses that compete by means of back-propagating APs (bAPs). The key to this competition is synapse-specific bAPs with reference to bAP-boosting on the physiological grounds.

Optimal Stimulation Protocol in a Bistable Synaptic Consolidation Model

Synaptic changes induced by neural activity need to be consolidated to maintain memory over a timescale of hours. In experiments, synaptic consolidation can be induced by repeating a stimulation protocol several times and the effectiveness of consolidation depends crucially on the repetition frequency of the stimulations. We address the question: is there an understandable reason why induction protocols with repetitions at some frequency work better than sustained protocols—even though the accumulated stimulation strength might be exactly the same in both cases? In real synapses, plasticity occurs on multiple time scales from seconds (induction), to several minutes (early phase of long-term potentiation) to hours and days (late phase of synaptic consolidation). We use a simplified mathematical model of just two times scales to elucidate the above question in a purified setting. Our mathematical results show that, even in such a simple model, the repetition frequency of stimulation plays an important role for the successful induction, and stabilization, of potentiation.

Time and rate dependent synaptic learning in neuro-mimicking resistive memories

Memristors have demonstrated immense potential as building blocks in future adaptive neuromorphic architectures. Recently, there has been focus on emulating specific synaptic functions of the mammalian nervous system by either tailoring the functional oxides or engineering the external programming hardware. However, high device-to-device variability in memristors induced by the electroforming process and complicated programming hardware are among the key challenges that hinder achieving biomimetic neuromorphic networks. Here, a simple hybrid complementary metal oxide semiconductor (CMOS)-memristor approach is reported to implement different synaptic learning rules by utilizing a CMOS-compatible memristor based on oxygen-deficient SrTiO3-x (STOx). The potential of such hybrid CMOS-memristor approach is demonstrated by successfully imitating time-dependent (pair and triplet spike-time-dependent-plasticity) and rate-dependent (Bienenstosk-Cooper-Munro) synaptic learning rules. Experimental results are benchmarked against in-vitro measurements from hippocampal and visual cortices with good agreement. The scalability of synaptic devices and their programming through a CMOS drive circuitry elaborates the potential of such an approach in realizing adaptive neuromorphic computation and networks.

Asymmetric ON-OFF processing of visual motion cancels variability induced by the structure of natural scenes

Animals detect motion using a variety of visual cues that reflect regularities in the natural world. Experiments in animals across phyla have shown that motion percepts incorporate both pairwise and triplet spatiotemporal correlations that could theoretically benefit motion computation. However, it remains unclear how visual systems assemble these cues to build accurate motion estimates. Here, we used systematic behavioral measurements of fruit fly motion perception to show how flies combine local pairwise and triplet correlations to reduce variability in motion estimates across natural scenes. By generating synthetic images with statistics controlled by maximum entropy distributions, we show that the triplet correlations are useful only when images have light-dark asymmetries that mimic natural ones. This suggests that asymmetric ON-OFF processing is tuned to the particular statistics of natural scenes. Since all animals encounter the world's light-dark asymmetries, many visual systems are likely to use asymmetric ON-OFF processing to improve motion estimation.

Extended memory lifetime in spiking neural networks employing memristive synapses with nonlinear conductance dynamics

Spiking neural networks (SNNs) employing memristive synapses are capable of life-long online learning. Because of their ability to process and classify large amounts of data in real-time using compact and low-power electronic systems, they promise a substantial technology breakthrough. However, the critical issue that memristor-based SNNs have to face is the fundamental limitation in their memory capacity due to finite resolution of the synaptic elements, which leads to the replacement of old memories with new ones and to a finite memory lifetime. In this study we demonstrate that the nonlinear conductance dynamics of memristive devices can be exploited to improve the memory lifetime of a network. The network is simulated on the basis of a spiking neuron model of mixed-signal digital-analogue sub-threshold neuromorphic CMOS circuits, and on memristive synapse models derived from the experimental nonlinear conductance dynamics of resistive memory devices when stimulated by trains of identical pulses. The network learning circuits implement a spike-based plasticity rule compatible with both spike-timing and rate-based learning rules. In order to get an insight on the memory lifetime of the network, we analyse the learning dynamics in the context of a classical benchmark of neural network learning, that is hand-written digit classification. In the proposed architecture, the memory lifetime and the performance of the network are improved for memristive synapses with nonlinear dynamics with respect to linear synapses with similar resolution. These results demonstrate the importance of following holistic approaches that combine the study of theoretical learning models with the development of neuromorphic CMOS SNNs with memristive devices used to implement life-long on-chip learning.

Functional mechanisms underlie the emergence of a diverse range of plasticity phenomena

Diverse plasticity mechanisms are orchestrated to shape the spatiotemporal dynamics underlying brain functions. However, why these plasticity rules emerge and how their dynamics interact with neural activity to give rise to complex neural circuit dynamics remains largely unknown. Here we show that both Hebbian and homeostatic plasticity rules emerge from a functional perspective of neuronal dynamics whereby each neuron learns to encode its own activity in the population activity, so that the activity of the presynaptic neuron can be decoded from the activity of its postsynaptic neurons. We explain how a range of experimentally observed plasticity phenomena with widely separated time scales emerge from learning this encoding function, including STDP and its frequency dependence, and metaplasticity. We show that when implemented in neural circuits, these plasticity rules naturally give rise to essential neural response properties, including variable neural dynamics with balanced excitation and inhibition, and approximately log-normal distributions of synaptic strengths, while simultaneously encoding a complex real-world visual stimulus. These findings establish a novel function-based account of diverse plasticity mechanisms, providing a unifying framework relating plasticity, dynamics and neural computation.

Many experiments have documented a variety of ways in which the connectivity strengths between neurons change in response to the activity of neurons. These changes are an important part of learning. However, it is not understood how such a diverse range of observations can be understood as consequences of an underlying algorithm used by brains for learning. In order to understand such a learning algorithm it is also necessary to understand the neural computation that is being learned, that is, how the functions of the brain are encoded in the activity of its neurons and its connectivity. In this work we propose a simple way in which information can be encoded and decoded in a network of neurons for operating on real-world stimuli, and how this can be learned using two fundamental plasticity rules that change the strength of connections between neurons in response to neural activity. Surprisingly, many experimental observations result as consequences of this approach, indicating that studying the learning of function provides a novel framework for unifying plasticity, dynamics, and neural computation.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of NeoHebbian Three-Factor Learning Rules

Most elementary behaviors such as moving the arm to grasp an object or walking into the next room to explore a museum evolve on the time scale of seconds; in contrast, neuronal action potentials occur on the time scale of a few milliseconds. Learning rules of the brain must therefore bridge the gap between these two different time scales. Modern theories of synaptic plasticity have postulated that the co-activation of pre- and postsynaptic neurons sets a flag at the synapse, called an eligibility trace, that leads to a weight change only if an additional factor is present while the flag is set. This third factor, signaling reward, punishment, surprise, or novelty, could be implemented by the phasic activity of neuromodulators or specific neuronal inputs signaling special events. While the theoretical framework has been developed over the last decades, experimental evidence in support of eligibility traces on the time scale of seconds has been collected only during the last few years. Here we review, in the context of three-factor rules of synaptic plasticity, four key experiments that support the role of synaptic eligibility traces in combination with a third factor as a biological implementation of neoHebbian three-factor learning rules.

Modulation of Spike-Timing Dependent Plasticity: Towards the Inclusion of a Third Factor in Computational Models

In spike-timing dependent plasticity (STDP) change in synaptic strength depends on the timing of pre- vs. postsynaptic spiking activity. Since STDP is in compliance with Hebb's postulate, it is considered one of the major mechanisms of memory storage and recall. STDP comprises a system of two coincidence detectors with N-methyl-D-aspartate receptor (NMDAR) activation often posited as one of the main components. Numerous studies have unveiled a third component of this coincidence detection system, namely neuromodulation and glia activity shaping STDP. Even though dopaminergic control of STDP has most often been reported, acetylcholine, noradrenaline, nitric oxide (NO), brain-derived neurotrophic factor (BDNF) or gamma-aminobutyric acid (GABA) also has been shown to effectively modulate STDP. Furthermore, it has been demonstrated that astrocytes, via the release or uptake of glutamate, gate STDP expression. At the most fundamental level, the timing properties of STDP are expected to depend on the spatiotemporal dynamics of the underlying signaling pathways. However in most cases, due to technical limitations experiments grant only indirect access to these pathways. Computational models carefully constrained by experiments, allow for a better qualitative understanding of the molecular basis of STDP and its regulation by neuromodulators. Recently, computational models of calcium dynamics and signaling pathway molecules have started to explore STDP emergence in ex and in vivo-like conditions. These models are expected to reproduce better at least part of the complex modulation of STDP as an emergent property of the underlying molecular pathways. Elucidation of the mechanisms underlying STDP modulation and its consequences on network dynamics is of critical importance and will allow better understanding of the major mechanisms of memory storage and recall both in health and disease.

Effects of Firing Variability on Network Structures with Spike-Timing-Dependent Plasticity

Synaptic plasticity is believed to be the biological substrate underlying learning and memory. One of the most widespread forms of synaptic plasticity, spike-timing-dependent plasticity (STDP), uses the spike timing information of presynaptic and postsynaptic neurons to induce synaptic potentiation or depression. An open question is how STDP organizes the connectivity patterns in neuronal circuits. Previous studies have placed much emphasis on the role of firing rate in shaping connectivity patterns. Here, we go beyond the firing rate description to develop a self-consistent linear response theory that incorporates the information of both firing rate and firing variability. By decomposing the pairwise spike correlation into one component associated with local direct connections and the other associated with indirect connections, we identify two distinct regimes regarding the network structures learned through STDP. In one regime, the contribution of the direct-connection correlations dominates over that of the indirect-connection correlations in the learning dynamics; this gives rise to a network structure consistent with the firing rate description. In the other regime, the contribution of the indirect-connection correlations dominates in the learning dynamics, leading to a network structure different from the firing rate description. We demonstrate that the heterogeneity of firing variability across neuronal populations induces a temporally asymmetric structure of indirect-connection correlations. This temporally asymmetric structure underlies the emergence of the second regime. Our study provides a new perspective that emphasizes the role of high-order statistics of spiking activity in the spike-correlation-sensitive learning dynamics.

Emergent Dynamical Properties of the BCM Learning Rule

The Bienenstock-Cooper-Munro (BCM) learning rule provides a simple setup for synaptic modification that combines a Hebbian product rule with a homeostatic mechanism that keeps the weights bounded. The homeostatic part of the learning rule depends on the time average of the post-synaptic activity and provides a sliding threshold that distinguishes between increasing or decreasing weights. There are, thus, two essential time scales in the BCM rule: a homeostatic time scale, and a synaptic modification time scale. When the dynamics of the stimulus is rapid enough, it is possible to reduce the BCM rule to a simple averaged set of differential equations. In previous analyses of this model, the time scale of the sliding threshold is usually faster than that of the synaptic modification. In this paper, we study the dynamical properties of these averaged equations when the homeostatic time scale is close to the synaptic modification time scale. We show that instabilities arise leading to oscillations and in some cases chaos and other complex dynamics. We consider three cases: one neuron with two weights and two stimuli, one neuron with two weights and three stimuli, and finally a weakly interacting network of neurons.