Synaptic plasticity rules with physiological calcium levels

Since the discovery of place cells – single pyramidal neurons that encode spatial location – it has been hypothesized that the hippocampus may act as a cognitive map of known environments. This putative function has been extensively modeled using auto-associative networks, which utilize rate-coded synaptic plasticity rules in order to generate strong bi-directional connections between concurrently active place cells that encode for neighboring place fields. However, empirical studies using hippocampal cultures have demonstrated that the magnitude and direction of changes in synaptic strength can also be dictated by the relative timing of pre- and post-synaptic firing according to a spike-timing dependent plasticity (STDP) rule. Furthermore, electrophysiology studies have identified persistent “theta-coded” temporal correlations in place cell activity in vivo, characterized by phase precession of firing as the corresponding place field is traversed. It is not yet clear if STDP and theta-coded neural dynamics are compatible with cognitive map theory and previous rate-coded models of spatial learning in the hippocampus. Here, we demonstrate that an STDP rule based on empirical data obtained from the hippocampus can mediate rate-coded Hebbian learning when pre- and post-synaptic activity is stochastic and has no persistent sequence bias. We subsequently demonstrate that a spiking recurrent neural network that utilizes this STDP rule, alongside theta-coded neural activity, allows the rapid development of a cognitive map during directed or random exploration of an environment of overlapping place fields. Hence, we establish that STDP and phase precession are compatible with rate-coded models of cognitive map development.

GENERAL COMMENTARY article Front. Synaptic Neurosci., 22 November 2010 Volume 2 - 2010 | https://doi.org/10.3389/fnsyn.2010.00150

A forecast-based STDP rule suitable for neuromorphic implementation

Recent development of neuromorphic hardware offers great potential to speed up simulations of neural networks. SpiNNaker is a neuromorphic hardware and software system designed to be scalable and flexible enough to implement a variety of different types of simulations of neural systems, including spiking simulations with plasticity and learning. Spike-timing dependent plasticity (STDP) rules are the most common form of learning used in spiking networks. However, to date very few such rules have been implemented on SpiNNaker, in part because implementations must be designed to fit the specialized nature of the hardware. Here we explain how general STDP rules can be efficiently implemented in the SpiNNaker system. We give two examples of applications of the implemented rule: learning of a temporal sequence, and balancing inhibition and excitation of a neural network. Comparing the results from the SpiNNaker system to a conventional double-precision simulation, we find that the network behavior is comparable, and the final weights differ by less than 3% between the two simulations, while the SpiNNaker simulation runs much faster, since it runs in real time, independent of network size.

Spike-timing dependent plasticity (STDP), a synaptic modification depending on a relative timing of presynaptic and postsynaptic spikes, has fascinated researchers in the fields of neurophysiology and computational neuroscience, because it is not only conceptually simple or biologically reasonable but is also versatile in neural network simulations. The STDP rule may be valid only under specific conditions, however. We propose herein a method that could find more natural and potent rules of synaptic plasticity.

Spike Timing Dependent Plasticity (STDP) is a time-based synaptic plasticity rule that has generated significant interest in the area of neuromorphic engineering and Very Large Scale Integration (VLSI) circuit design. During the last decade, STDP and STDP-like learning mechanisms have shown promising solutions for various real world applications, ranging from pattern recognition to robotics. This paper presents a novel analog VLSI model for STDP that possesses advantages compared to previously published VLSI STDP designs. The presented STDP circuit is capable of reproducing the outcomes of several well known experiments using various plasticity rules inducing STDP protocols that utilise pairs, triplets, and quadruplets of spike patterns. When the circuit is compared to state-of-the-art VLSI STDP circuits, it shows a compact and symmetric design that makes the proposed circuit a powerful component for use in designing STDP or time-based Hebbian learning experiments and applications.

Rats and mice use their whiskers to probe the environment. By rhythmically swiping their whiskers back and forth they can detect the existence of an object, locate it, and identify its texture. Localization can be accomplished by inferring the whisker’s position. Rhythmic neurons that track the phase of the whisking cycle encode information about the azimuthal location of the whisker. These neurons are characterized by preferred phases of firing that are narrowly distributed. Consequently, pooling the rhythmic signal from several upstream neurons is expected to result in a much narrower distribution of preferred phases in the downstream population, which however has not been observed empirically. Here, we show how spike timing dependent plasticity (STDP) can provide a solution to this conundrum. We investigated the effect of STDP on the utility of a neural population to transmit rhythmic information downstream using the framework of a modeling study. We found that under a wide range of parameters, STDP facilitated the transfer of rhythmic information despite the fact that all the synaptic weights remained dynamic. As a result, the preferred phase of the downstream neuron was not fixed, but rather drifted in time at a drift velocity that depended on the preferred phase, thus inducing a distribution of preferred phases. We further analyzed how the STDP rule governs the distribution of preferred phases in the downstream population. This link between the STDP rule and the distribution of preferred phases constitutes a natural test for our theory.

The variation of individual synaptic transmission impacts the dynamics of complex neural circuits. We performed whole-cell recordings from monosynaptically connected hippocampal neurons in rat organotypic slice cultures using a synapse mapping method. The amplitude of unitary excitatory postsynaptic current (uEPSC) varied from trial to trial and was independent of the physical distance between cell pairs. To investigate the source of the transmission variability, we obtained patch-clamp recordings from intact axons. Axonal action potentials (APs) were reliably transmitted throughout the axonal arbour and showed modest changes in width. In contrast, calcium imaging from presynaptic boutons revealed that the amplitude of AP-evoked calcium transients exhibited large variations both among different boutons at a given trial and among trials in a given bouton. These results suggest that a factor contributing to the uEPSC fluctuations is the variability in calcium dynamics at presynaptic terminals. Finally, we acquired triple whole-cell recordings from divergent circuit motifs with one presynaptic neuron projecting to two postsynaptic neurons. Consistent with the independency of calcium dynamics among axonal boutons, a series of uEPSC fluctuations was not correlated between the two postsynaptic cells, indicating that different synapses even from the same neuron act independently.We conclude that the intra-bouton and inter-bouton variability in AP-induced calcium dynamics determine the heterogeneity and independency of uEPSCs.

We present a compact mixed-signal implementation of synaptic plasticity for both Spike Timing Dependent Plasticity (STDP) and Spike Timing Dependent Delay Plasticity (STDDP). The proposed mixed-signal implementation consists of an a VLSI time window generator and a digital adaptor. The weight and delay values are stored in a digital memory, and the adaptor will send these values to the time window generator using a digital spike of which the duration is modulated according to these values. The analogue time window generator will then generate a time window, which is required for the implementation of STDP and STDDP. The digital adaptor will carry out the weight/delay adaption using this time window. The aVLSI time window generator is compact (50 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in IBM 130nm process) and we use a time multiplexing approach to achieve up to 65536 (64k) virtual digital adaptors with one physical adaptor, consuming only a fraction of the hardware resource on a Virtex 6 FPGA. Since the digital adaptor has been implemented on an FPGA, it can be easily reconfigured for different adaptation algorithms, which leaves it open for future development. Our mixed-signal implementation is therefore practical for implementing the synaptic plasticity in large-scale spiking neural networks running in real time. We show circuit simulation results illustrating both weight and delay adaptation.

The influence of a weight-dependent spike-timing dependent plasticity (STDP) rule on the temporal evolution and equilibrium state of a certain synapse is investigated. We show that under certain conditions, a spike-induced rate-learning scheme could be achieved. Through studying the situation when a single Hodgkin-Huxley neuron is driven by a large ensemble of input neurons, we find that synchronized firing of a sub population of input neurons may be important to information processing in the nervous system. Using simulations, we show that the temporal structure of the spike trains of these synchronized input neurons can be transmitted reliably; further, synapses from these neurons will increase stably due to the STDP rule and this may provide a mechanism for learning and information storage in biologically plausible network models.

Gamma rhythms have been the focus of significant research interest within the neuroscience community in recent years [1]. Earlier theoretical studies focused on the question: how can a network of GABA containing neurons generate gamma oscillations? The findings suggest that for non-instantaneous synaptic events, inhibition rather than excitation is a better synchronizing mechanism for the generation of gamma rhythms [2]. Synchrony in inhibitory neural networks however is extremely sensitive to intrinsic heterogeneity in the network [3]. Based on the evidence for spike timing dependent plasticity (STDP) in inhibitory neurons [4,5], we hypothesize that STDP of inhibitory synapses can promote robust neural synchrony in inhibitory neuronal networks in the presence of heterogeneity. We investigate our hypothesis in a computational (Figure ​(Figure1a)1a) and a hybrid (Figure ​(Figure1b)1b) uni-directionally coupled network (UCI) of two fast-spiking inhibitory neurons. In the computational model, each neuron is modeled using the Hodgkin-Huxley (HH) framework [4]. Heterogeneity (H) is modeled by the difference in the intrinsic firing activity of the coupled neurons resulting from different DC current input. In the presence of STDP, the strength of synaptic coupling between the coupled neurons is modeled using a linear additive rule as: gs(t) = gs(t – 1) + ΔgSTDP(Δt), where Δt = tA – tB is the time interval between successive spikes of the post-synaptic and the pre-synaptic neurons and ΔgSTDP is the STDP rule adapted from [4]. In Figure ​Figure1a,1a, we demonstrate the effect of STDP on synchrony between coupled neurons in the presence of and the absence of STDP for network heterogeneity H=12%. Theoretical analysis using the concept of spike time response curves and Arnold tongue revealed that STDP induced 1:1 synchrony in the UCI network is (i) robust against a large range of heterogeneity in the intrinsic firing activity of coupled neurons, and (ii) in-phase i.e., Δt ≈ 0. Furthermore, the time to in-phase synchronization increases with increasing heterogeneity. Figure 1 a) Theoretical model of UCI. Autaptic synapse is introduced to mimic spike frequency adaptation in neuronal firing activity. b) Hybrid UCI network. Dynamic clamp experimental results for experimental protocol with fixed static-synaptic strength gs(0)=0.5 ... We used the dynamic clamp technique to construct a hybrid UCI network consisting of an HH based model of a inhibitory neuron coupled to a living inhibitory neuron in the stratum oriens of area CA1 of the hippocampus. Whole cell patch clamp recordings were obtained from the live cell under the following experimental protocols: (i) Fix H, vary the static synapse coupling strength gs(0) and (ii) Fix static synapse coupling strength gs(0) and vary H. In Figure ​Figure1b,1b, we present results from the second experimental protocol. We see that as predicted by our theoretical model, the time to in phase neural synchrony in the hybrid UCI network increases with increasing heterogeneity. We conclude that STDP of inhibitory synapses is a putative mechanism for robust neural synchrony in inhibitory neuronal networks.

Neuromorphic engineering has a wide range of applications in the fields of machine learning, pattern recognition, adaptive control, etc. Photonics, characterized by its high speed, wide bandwidth, low power consumption and massive parallelism, is an ideal way to realize ultrafast spiking neural networks (SNNs). Synaptic plasticity is believed to be critical for learning, memory and development in neural circuits. Experimental results have shown that changes of synapse are highly dependent on the relative timing of pre- and postsynaptic spikes. Synaptic plasticity in which presynaptic spikes preceding postsynaptic spikes results in strengthening, while the opposite timing results in weakening is called antisymmetric spike-timing-dependent plasticity (STDP) learning rule. And synaptic plasticity has the opposite effect under the same conditions is called antisymmetric anti-STDP learning rule. We proposed and experimentally demonstrated an optical implementation of neural learning algorithms, which can achieve both of antisymmetric STDP and anti-STDP learning rule, based on the cross-gain modulation (XGM) within a single semiconductor optical amplifier (SOA). The weight and height of the potentitation and depression window can be controlled by adjusting the injection current of the SOA, to mimic the biological antisymmetric STDP and anti-STDP learning rule more realistically. As the injection current increases, the width of depression and potentitation window decreases and height increases, due to the decreasing of recovery time and increasing of gain under a stronger injection current. Based on the demonstrated optical STDP circuit, ultrafast learning in optical SNNs can be realized.

Emerging nonvolatile memory technologies have been much studied to realize massively interconnected Spiking Neural Networks (SNNs) due to its high density, and energy efficiency. Nevertheless, most of the previous studies on utilizing such technologies have focused on implementing a traditional pair-based Spike Timing Dependent Plasticity (STDP) rule, which turned out to fail to reproduce multiple physiological experimental results. In this paper, we present a neuromorphic circuit for a three-terminal spintronic synapse with a triplet-based STDP rule, which is a higher order of learning mechanism. Simulation results indicate that the proposed learning circuit for the triplet-based STDP rule significantly improves learning capability in mimicking the various biological experimental data. We introduce a normalized mean-square error $\boldsymbol{E}$ value to evaluate the performance of each of the learning circuits quantitatively. The proposed learning circuit achieves $\boldsymbol{E}$ value of 1.77, which is far better than the conventional one that achieves $\boldsymbol{E}$ value of 12.2.

Neuromorphic computing is emerging as a promising Beyond Moore computing paradigm that employs event-triggered computation and non-von Neumann hardware. Spike Timing Dependent Plasticity (STDP) is a well-known bio-inspired learning rule that relies on activities of locally connected neurons to adjust the weights of their respective synapses. In this work, we analyze a basic STDP rule and its sensitivity on the different hyperparameters for training spiking neural networks (SNNs) with supervision, customized for a neuromorphic hardware implementation with integer weights. We compare the classification performance on four UCI datasets (iris, wine, breast cancer and digits) that depict varying levels of complexity. We perform a search for optimal set of hyperparameters using both grid search and Bayesian optimization. Through the use of Bayesian optimization, we show the general trends in hyperparameter sensitivity in SNN classification problem. With the best sets of hyperparameters, we achieve accuracies comparable to some of the best performing SNNs on these four datasets. With a highly optimized supervised STDP rule we show that these accuracies can be achieved with just 20 epochs of training.

Synaptic plasticity is widely thought to support memory storage in the brain, but the rules determining impactful synaptic changes in vivo are not known. We considered the trial-by-trial shifting dynamics of hippocampal place fields (PF) as an indicator of ongoing plasticity during memory formation and familiarization. By implementing different plasticity rules in computational models of spiking place cells and comparing them to experimentally measured PFs from mice navigating familiar and new environments, we found that behavioral timescale synaptic plasticity (BTSP), rather than Hebbian spike-timing-dependent plasticity (STDP), best explains PF shifting dynamics. BTSP-triggering events are rare, but more frequent during new experiences. During exploration, their probability is dynamic-it decays after PF onset, but continually drives a population-level representational drift. Additionally, our results show that BTSP occurs in CA3 but is less frequent and phenomenologically different than in CA1. Overall, our study provides a new framework to understand how synaptic plasticity continuously shapes neuronal representations during learning.