Chaos is ubiquitous in high-dimensional neural dynamics. A strong chaotic fluctuation may be harmful to information processing. A traditional way to mitigate this issue is to introduce Hebbian plasticity, which can stabilize the dynamics. Here, we introduce another distinct way without synaptic plasticity. An Onsager reaction term due to the feedback of the neuron itself is added to the vanilla recurrent dynamics, making the driving force a gradient form. The original unstable fixed points supporting the chaotic fluctuation can then be approached by further decreasing the kinetic energy of the dynamics. We show that this freezing effect also holds in more biologically realistic networks, such as those composed of excitatory and inhibitory neurons. The gradient dynamics are also useful for computational tasks such as recalling or predicting external time-dependent stimuli.
Short-term synaptic plasticity (STSP) affects the efficiency of synaptic transmission for persistent presynaptic activities. We consider attractor neural networks, for which the attractors are given, in the absence of STSP, by cell assemblies of excitatory cliques. We show that STSP may transform these attracting states into attractor relics, inducing ongoing transient-state dynamics in terms of sequences of transiently activated cell assemblies, the former attractors. Subsequent cell assemblies may be both disjoint or partially overlapping. It may hence be possible to use the resulting dynami…
Synaptic plasticity is vital for learning and memory in the brain. It consists of long-term potentiation (LTP) and long-term depression (LTD). Spike frequency is one of the major components of synaptic plasticity in the brain, a noisy environment. Recently, we mathematically analysed the frequency-dependent synaptic plasticity (FDP) in vivo and found that LTP is more likely to occur with an increase in the frequency of background synaptic activity. Previous studies suggest fluctuation in the amplitude of background synaptic activity. However, little is understood about the relationship between…
We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed.
Synaptic plasticity is the capacity of a preexisting connection between two neurons to change in strength as a function of neural activity. Because synaptic plasticity is the major candidate mechanism for learning and memory, the elucidation of its constituting mechanisms is of crucial importance in many aspects of normal and pathological brain function. In particular, a prominent aspect that remains debated is how the plasticity mechanisms, that encompass a broad spectrum of temporal and spatial scales, come to play together in a concerted fashion. Here we review and discuss evidence that pin…
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 syna…
Glutamatergic gliotransmission, that is the release of glutamate from perisynaptic astrocyte processes in an activity-dependent manner, has emerged as a potentially crucial signaling pathway for regulation of synaptic plasticity, yet its modes of expression and function in vivo remain unclear. Here, we focus on two experimentally well-identified gliotransmitter patwhays: (i)~modulations of synaptic release and (ii)~postynaptic slow inward currents mediated by glutamate released from astrocytes, and investigate their possible functional relevance on synaptic plasticity in a biophysical model of…
Synaptic plasticity or the ability of a brain to changes one or more of its functions or structures has generated and is sill generating a lot of interest from the scientific community especially neuroscientists. These interests especially went into high gear after empirical evidences were collected that challenged the established paradigm that human brain structures and functions are set from childhood and only modest changes were expected beyond. Early synaptic plasticity rules or laws to that regard include the basic Hebbian rule that proposed a mechanism for strengthening or weakening of s…
In this paper we present a biologically detailed mathematical model of tripartite synapses, where astrocytes modulate short-term synaptic plasticity. The model consists of a pre-synaptic bouton, a post-synaptic dendritic spine-head, a synaptic cleft and a peri-synaptic astrocyte controlling Ca2+ dynamics inside the synaptic bouton. This in turn controls glutamate release dynamics in the cleft. As a consequence of this, glutamate concentration in the cleft has been modeled, in which glutamate reuptake by astrocytes has also been incorporated. Finally, dendritic spine-head dynamics has been mode…
Controlling the flow and routing of data is a fundamental problem in many distributed networks, including transportation systems, integrated circuits, and the Internet. In the brain, synaptic plasticity rules have been discovered that regulate network activity in response to environmental inputs, which enable circuits to be stable yet flexible. Here, we develop a new neuro-inspired model for network flow control that only depends on modifying edge weights in an activity-dependent manner. We show how two fundamental plasticity rules (long-term potentiation and long-term depression) can be cast …
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 plas…
Brain plasticity refers to brain's ability to change neuronal connections, as a result of environmental stimuli, new experiences, or damage. In this work, we study the effects of the synaptic delay on both the coupling strengths and synchronisation in a neuronal network with synaptic plasticity. We build a network of Hodgkin-Huxley neurons, where the plasticity is given by the Hebbian rules. We verify that without time delay the excitatory synapses became stronger from the high frequency to low frequency neurons and the inhibitory synapses increases in the opposite way, when the delay is incre…
Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled oscillators have sparked the development of a new generation of neural mass models. Of notable interest are mean-field descriptions of all-to-all coupled quadratic integrate-and-fire (QIF) neurons, which have already seen numerous extensions and applications. These extensions include different forms of short-term adaptation (STA) considered to play an important rol…
Cortical populations of neurons develop sparse representations adapted to the statistics of the environment. While existing synaptic plasticity models reproduce some of the observed receptive-field properties, a major obstacle is the sensitivity of Hebbian learning to omnipresent spurious correlations in cortical networks which can overshadow relevant latent input features. Here we develop a theory for synaptic plasticity that is invariant to second-order correlations in the input. Going beyond classical Hebbian learning, we show how Hebbian long-term depression (LTD) cancels the sensitivity t…
School of Mathematical Sciences（数学科学学院）；School of Psychology, University of Nottingham（诺丁汉大学心理学院）
When training neural networks for classification tasks with backpropagation, parameters are updated on every trial, even if the sample is classified correctly. In contrast, humans concentrate their learning effort on errors. Inspired by human learning, we introduce lazy learning, which only learns on incorrect samples. Lazy learning can be implemented in a few lines of code and requires no hyperparameter tuning. Lazy learning achieves state-of-the-art performance and is particularly suited when datasets are large. For instance, it reaches 99.2% test accuracy on Extended MNIST using a single-la…
Objective: Hepatic encephalopathy (HE) is a potentially reversible brain dysfunction caused by liver failure. Altered synaptic plasticity is supposed to play a major role in the pathophysiology of HE. Here, we used paired associative stimulation with an inter-stimulus interval of 25 ms (PAS25), a transcranial magnetic stimulation (TMS) protocol, to test synaptic plasticity of the motor cortex in patients with manifest HE. Methods: 23 HE-patients and 23 healthy controls were enrolled in the study. Motor evoked potential (MEP) amplitudes were assessed as measure for cortical excitability. Time c…
Neuronal circuits internally regulate electrical signaling via a host of homeostatic mechanisms. Two prominent mechanisms, synaptic scaling and structural plasticity, are believed to maintain average activity within an operating range by modifying the strength and spatial extent of network connectivity using negative feedback. However, both mechanisms operate on relatively slow timescales and thus face fundamental limits due to delays. We show that these mechanisms fulfill complementary roles in maintaining stability in a large network. In particular, even relatively, slow growth dynamics impr…
We investigate the dynamical role of inhibitory and highly connected nodes (hub) in synchronization and input processing of leaky-integrate-and-fire neural networks with short term synaptic plasticity. We take advantage of a heterogeneous mean-field approximation to encode the role of network structure and we tune the fraction of inhibitory neurons $f_I$ and their connectivity level to investigate the cooperation between hub features and inhibition. We show that, depending on $f_I$, highly connected inhibitory nodes strongly drive the synchronization properties of the overall network through d…
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 does the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of…
Sparse coding algorithms trained on natural images can accurately predict the features that excite visual cortical neurons, but it is not known whether such codes can be learned using biologically realistic plasticity rules. We have developed a biophysically motivated spiking network, relying solely on synaptically local information, that can predict the full diversity of V1 simple cell receptive field shapes when trained on natural images. This represents the first demonstration that sparse coding principles, operating within the constraints imposed by cortical architecture, can successfully …
Learning and memory in the brain are implemented by complex, time-varying changes in neural circuitry. The computational rules according to which synaptic weights change over time are the subject of much research, and are not precisely understood. Until recently, limitations in experimental methods have made it challenging to test hypotheses about synaptic plasticity on a large scale. However, as such data become available and these barriers are lifted, it becomes necessary to develop analysis techniques to validate plasticity models. Here, we present a highly extensible framework for modeling…
In an all-to-all network of integrate-fire oscillators in which there is a disorder in the intrinsic firing rates of the neurons, we show that through spike timing-dependent plasticity the links which have the faster oscillators as presynaptic, tend to be strengthened while the links originated from the slow spiking neurons are weakened. The emergent effective flow of directed connections, introduces the faster neurons as the more influent elements in the network and facilitates synchronization by decreasing the synaptic cost for onset of synchronization.
Latency reduction of postsynaptic spikes is a well-known effect of Synaptic Time-Dependent Plasticity. We expand this notion for long postsynaptic spike trains, 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 of postsynaptic latencies can lead to the emergence …
Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Heuristic models of this process of synaptic plasticity can provide excellent fits to results from in-vitro experiments in which pre- and post-synaptic spiking is varied in a controlled fashion. However, the plasticity rules inferred from fitting such data are inevitably unstable, in that given constant pre- and post-synaptic activity the synapse will either fully potentiate or depress. This instability can be held in check by adding additional mechanisms, such as homeostasis. Here we consider a…
Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there …
Excitatory synaptic connections in the adult neocortex consist of multiple synaptic contacts, almost exclusively formed on dendritic spines. Changes of dendritic spine shape and volume, a correlate of synaptic strength, can be tracked in vivo for weeks. Here, we present a combined model of spike-timing dependent dendritic spine plasticity and turnover that explains the steady state multi-contact configuration of synapses in adult neocortical networks. In this model, many presynaptic neurons compete to make strong synaptic connections onto postsynaptic neurons, while the synaptic contacts compr…
We present an effective model for timing-dependent synaptic plasticity (STDP) in terms of two interacting traces, corresponding to the fraction of activated NMDA receptors and the Ca2+ concentration in the dendritic spine of the postsynaptic neuron. This model intends to bridge the worlds of existing simplistic phenomenological rules and highly detailed models, constituting thus a practical tool for the study of the interplay between neural activity and synaptic plasticity in extended spiking neural networks. For isolated pairs of pre- and postsynaptic spikes the standard pairwise STDP rule is…
We are concerned about burst synchronization (BS), related to neural information processes in health and disease, in the Barabási-Albert scale-free network (SFN) composed of inhibitory bursting Hindmarsh-Rose neurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without considering iSTDP, BS was found to appear in a range of noise intensities for fixed synaptic inhibition strengths. In contrast, in our present work, we take into consideration iSTDP and investigate its effect o…
Recently spike timing dependent plasticity was observed in inhibitory synapse in the layer II of entorhinal cortex. The rule provides an interesting zero in the region of $Δt=t_{post}-t_{pre}=0$ and in addition the dynamic range of the rule lie in gamma frequency band. We propose a robust mechanism based on this observed synaptic plasticity rule for inhibitory synapses for two mutually coupled interneurons to phase lock in synchrony in the presence of intrisic heterogeneity in firing. We study the stability of the phase locked solution by defining a map for spike times dependent on the phase r…
Spiking networks that perform probabilistic inference have been proposed both as models of cortical computation and as candidates for solving problems in machine learning. However, the evidence for spike-based computation being in any way superior to non-spiking alternatives remains scarce. We propose that short-term plasticity can provide spiking networks with distinct computational advantages compared to their classical counterparts. In this work, we use networks of leaky integrate-and-fire neurons that are trained to perform both discriminative and generative tasks in their forward and back…
Experimental observations on synaptic plasticity at individual glutamatergic synapses from the CA3 Shaffer collateral pathway onto CA1 pyramidal cells in the hippocampus suggest that the transitions in synaptic strength occur among discrete levels at individual synapses (~\cite{Peter} and S. S.-H. Wang, unpublished data used with the authors' permission). This happens for both long term potentiation (LTP) and long term depression (LTD) induction protocols. O'Connor, Wittenberg, and Wang have argued that three states would account for their observations on individual synapses in the CA3-CA1 pat…
In neuroscience, learning and memory are usually associated to long-term changes of neuronal connectivity. In this context, synaptic plasticity refers to the set of mechanisms driving the dynamics of neuronal connections, called {\em synapses} and represented by a scalar value, the synaptic weight. Spike-Timing Dependent Plasticity (STDP) is a biologically-based model representing the time evolution of the synaptic weight as a functional of the past spiking activity of adjacent neurons. If numerous models of neuronal cells have been proposed in the mathematical literature, few of them include …
Neuropeptides, members of a large and evolutionarily ancient family of proteinaceous cell-cell signaling molecules, are widely recognized as extremely potent regulators of brain function and behavior. At the cellular level, neuropeptides are known to act mainly via modulation of ion channel and synapse function, but functional impacts emerging at the level of complex cortical synaptic networks have resisted mechanistic analysis. New findings from single-cell RNA-seq transcriptomics now illuminate intricate patterns of cortical neuropeptide signaling gene expression and new tools now offer powe…
Neuronal mechanisms underlying addiction have been attracting attention in neurobiology, economics, neuropsychiatry, and neuroeconomics. This paper proposes a possible link between economic theory of addiction (Becker and Murphy, 1988) and neurobiological theory of bidirectional synaptic plasticity (Bienenstock, Cooper, Munro, 1982) based on recent findings in neuroeconomics and neurobiology of addiction. Furthermore, it is suggested that several neurobiological substrates such as cortisol (a stress hormone), NMDA and AMPA receptors/subunits and intracellular calcium in the postsynaptic neuron…
We show that the local Spike Timing-Dependent Plasticity (STDP) rule has the effect of regulating the trans-synaptic weights of loops of any length within a simulated network of neurons. We show that depending on STDP's polarity, functional loops are formed or eliminated in networks driven to normal spiking conditions by random, partially correlated inputs, where functional loops comprise weights that exceed a non-zero threshold. We further prove that STDP is a form of loop-regulating plasticity for the case of a linear network comprising random weights drawn from certain distributions. Thus a…
We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation speeds) and network plasticity (via dynamic coupling constants) inspired by the Hebbian learning rule in neuroscience. When time-delay and learning effects combine, novel synchronization phenomena are observed. We investigate the formation of spatio-temporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment…
Learning, especially rapid learning, is critical for survival. However, learning is hard: a large number of synaptic weights must be set based on noisy, often ambiguous, sensory information. In such a high-noise regime, keeping track of probability distributions over weights is the optimal strategy. Here we hypothesize that synapses take that strategy; in essence, when they estimate weights, they include error bars. They then use that uncertainty to adjust their learning rates, with more uncertain weights having higher learning rates. We also make a second, independent, hypothesis: synapses co…
We consider a noise driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system to obtain the mean activity level for the system as a function of the mean synaptic weight, which predicts a first-order transition and hysteresis between a noise-dominated regime and a regime of persistent neural activity. Assuming Poisson firing statistics for the neurons, the plasticity dynamics of a synapse under the influence of the mean-field environmen…
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasi-synchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a doubling-period transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaot…
IBM Research – Zurich（IBM苏黎世研究院）；Huawei – Zurich Research Center（华为苏黎世研究中心）
Biological neurons and their in-silico emulations for neuromorphic artificial intelligence (AI) use extraordinarily energy-efficient mechanisms, such as spike-based communication and local synaptic plasticity. It remains unclear whether these neuronal mechanisms only offer efficiency or also underlie the superiority of biological intelligence. Here, we prove rigorously that, indeed, the Bayes-optimal prediction and inference of randomly but continuously transforming environments, a common natural setting, relies on short-term spike-timing-dependent plasticity, a hallmark of biological synapses…
Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting short-term plasticity (STP). Under the assumption that spike arrivals at synapses have Poisson statistics, we derive analytically stochastic mean-field dynamics for the effective synaptic coupling between finite-size populations undergoing Tsodyks-Markram STP. The novel mean-field equations a…
Self-organized criticality has been proposed to be a universal mechanism for the emergence of scale-free dynamics in many complex systems, and possibly in the brain. While such scale-free patterns were identified experimentally in many different types of neural recordings, the biological principles behind their emergence remained unknown. Utilizing different network models and motivated by experimental observations, synaptic plasticity was proposed as a possible mechanism to self-organize brain dynamics towards a critical point. In this review, we discuss how various biologically plausible pla…
Membrane receptors for neuromodulators (NM) are highly regulated in their distribution and efficacy - a phenomenon which influences the individual cell's response to central signals of NM release. Even though NM receptor regulation is implicated in the pharmacological action of many drugs, and is also known to be influenced by various environmental factors, its functional consequences and modes of action are not well understood. In this paper we summarize relevant experimental evidence on NM receptor regulation (specifically dopamine D1 and D2 receptors) in order to explore its significance fo…
We consider the Watts-Strogatz small-world network consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities through competition between the constructive and the destructive roles of noise. Here, we investigate the effect of additive STDP on the SSS by varying the noise inte…
Traveling waves are commonly observed across the brain. While previous studies have suggested the role of traveling waves in learning, the mechanism is still unclear. We adopted a computational approach to investigate the effect of traveling waves on synaptic plasticity. Our results indicate that traveling waves facilitate the learning of poly-synaptic network-paths when combined with a reward-dependent local synaptic plasticity rule. We also demonstrate that traveling waves expedite finding the shortest paths and learning nonlinear input/output-mapping, such as exclusive or (XOR) function.
In this work we study the detection of weak stimuli by spiking neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level…
Working memory (WM) has been intensively used to enable the temporary storing of information for processing purposes, playing an important role in the execution of various cognitive tasks. Recent studies have shown that information in WM is not only maintained through persistent recurrent activity but also can be stored in activity-silent states such as in short-term synaptic plasticity (STSP). Motivated by important applications of the STSP mechanisms in WM, the main focus of the present work is on the analysis of the effects of random inputs on a leaky integrate-and-fire (LIF) synaptic condu…
Short-Term Synaptic Plasticity (STSP) strongly affects the neural dynamics of cortical networks. The Tsodyks and Markram (TM) model for STSP accurately accounts for a wide range of physiological responses at different types of cortical synapses. Here, we report for the first time a route to chaotic behavior via a Shilnikov homoclinic bifurcation that dynamically organises some of the responses in the TM model. In particular, the presence of such a homoclinic bifurcation strongly affects the shape of the trajectories in the phase space and induces highly irregular transient dynamics; indeed, in…
Large-scale neuromorphic hardware systems typically bear the trade-off between detail level and required chip resources. Especially when implementing spike-timing-dependent plasticity, reduction in resources leads to limitations as compared to floating point precision. By design, a natural modification that saves resources would be reducing synaptic weight resolution. In this study, we give an estimate for the impact of synaptic weight discretization on different levels, ranging from random walks of individual weights to computer simulations of spiking neural networks. The FACETS wafer-scale h…
