Weight-dependent Spike-timing-dependent Plasticity Research Articles

Photonic implementation of spike timing dependent plasticity with weight-dependent learning window based on VCSOA

Based on the well-known Fabry–Pérot approach, after taking into account the variation of bias current of the vertical-cavity semiconductor optical amplifier (VCSOA) according to the present synapse weight, we implement the optical spike timing dependent plasticity (STDP) with weight-dependent learning window in a VCSOA with double optical spike injections, and numerically investigate the corresponding weight-dependent STDP characteristics. The simulation results show that, the bias current of VCSOA has significant effect on the optical STDP curve. After introducing an adaptive variation of the bias current according to the present synapse weight, the optical weight-dependent STDP based on VCSOA can be realized. Moreover, the weight training based on the optical weight-dependent STDP can be effectively controlled by adjusting some typical external or intrinsic parameters and the excessive adjusting of synaptic weight is avoided, which can be used to balance the stability and competition among synapses and pave a way for the future large-scale energy efficient optical spiking neural networks based on the weight-dependent STDP learning mechanism.

STDP Based Unsupervised Multimodal Learning With Cross-Modal Processing in Spiking Neural Networks

Spiking neural networks perform reasonably well in recognition applications for single modality (e.g., images, audio, or text). In this paper, we propose a multimodal spiking neural network that combines two modalities (image and audio). The two unimodal ensembles are connected with cross-modal connections and the entire network is trained with unsupervised learning. The network receives inputs in both modalities for the same class and predicts the class label. The excitatory connections in the unimodal ensemble and the cross-modal connections are trained with power-law weight-dependent spike timing dependent plasticity learning rule. The cross-modal connections capture the correlation between neurons of different modalities. The multimodal network learns features of both modalities and improves the classification accuracy compared to unimodal topology, even when one of the modality is distorted by noise. The cross-modal connections suppress the effect of noise on classification accuracy. The well-learned cross-modal connections invoke additional spiking activity in neurons of the correct label. The cross-modal connections are only excitatory and do not inhibit the normal activity of the unimodal ensembles. We evaluated our multimodal network on images from MNIST dataset and utterances of digits from TI46 speech corpus. The multimodal network achieved a classification accuracy of 98% on the combined MNIST and TI46 dataset.

Theoretical investigation of weight-dependent optical spike timing dependent plasticity based on VCSOA

We propose an implement scheme of the weight-dependent optical spike timing dependent plasticity (STDP) based on the vertical-cavity semiconductor optical amplifiers (VCSOAs) subject to double optical spike injections, and numerically investigate the effects of the internal and external parameters of VCSOAs on the optical STDP curve by the well-known Fabry-Pérot approach. Additionally, the optical weight-dependent STDP is realized by introducing the various bias current according to the feedback signal. The simulation results show that, the width and height of the optical STDP curve window can be effectively controlled by adjusting the relevant parameters of VCSOAs. Moreover, the optical weight-dependent STDP is analogous to the biological STDP synapses and can be used to balance the stability and competition among synapses. These results can offer great potential for constructing a large-scale energy efficient optical spiking neural networks (SNNs).

STDP-Based Pruning of Connections and Weight Quantization in Spiking Neural Networks for Energy-Efficient Recognition

Spiking neural networks (SNNs) with a large number of weights and varied weight distribution can be difficult to implement in emerging in-memory computing hardware due to the limitations on crossbar size (implementing dot product), the constrained number of conductance states in non-CMOS devices and the power budget. We present a sparse SNN topology where noncritical connections are pruned to reduce the network size, and the remaining critical synapses are weight quantized to accommodate for limited conductance states. Pruning is based on the power law weight-dependent spike timing dependent plasticity model; synapses between pre- and post-neuron with high spike correlation are retained, whereas synapses with low correlation or uncorrelated spiking activity are pruned. The weights of the retained connections are quantized to the available number of conductance states. The process of pruning noncritical connections and quantizing the weights of critical synapses is performed at regular intervals during training. We evaluated our sparse and quantized network on MNIST dataset and on a subset of images from Caltech-101 dataset. The compressed topology achieved a classification accuracy of 90.1% (91.6%) on the MNIST (Caltech-101) dataset with 3.1X (2.2X) and 4X (2.6X) improvement in energy and area, respectively. The compressed topology is energy and area efficient while maintaining the same classification accuracy of a 2-layer fully connected SNN topology.

Scalable excitatory synaptic circuit design using floating gate based leaky integrators

We propose a scalable synaptic circuit realizing spike timing dependent plasticity (STDP)—compatible with randomly spiking neurons. The feasible working of the circuit was examined by circuit simulation using the BSIM 4.6.0 model. A distinguishable feature of the circuit is the use of floating-gate integrators that provide the compact implementation of biologically plausible relaxation time scale. This relaxation occurs on the basis of charge tunneling that mainly relies upon area-independent tunnel barrier properties (e.g. barrier width and height) rather than capacitance. The circuit simulations feature (i) weight-dependent STDP that spontaneously limits the synaptic weight growth, (ii) competitive synaptic adaptation within both unsupervised and supervised frameworks with randomly spiking neurons. The estimated power consumption is merely 34 pW, perhaps meeting one of the most crucial principles (power-efficiency) of neuromorphic engineering. Finally, a means of fine-tuning the STDP behavior is provided.

Optical spike-timing-dependent plasticity with weight-dependent learning window and reward modulation.

Optical spike-timing-dependent plasticity (STDP) synapses form the basis of learning in photonic neuromorphic system. In biological neural systems, STDP synapses generally have multiplicative boundary mechanisms, and can be modulated by a third factor such as dopamine. Analogously, we introduce a third factor into optical STDP: The current-injection of semiconductor optical amplifiers can be modified in an adaptive way according to local or global feedback signals. The local one is present synaptic weight, which elicits an optical weight-dependent STDP, while the global one is a reward signal. We demonstrate that the optical weight-dependent STDP can emulate the behavior of biological STDP synapses more closely, and can be seen as an intermediate configuration between additive and multiplicative STDP, which balances stability and competition among synapses. Simulation studies with scalable photonic neurons further show that optical STDP with reward modulation enables reward-based reinforcement learning.

Spectral Analysis of Input Spike Trains by Spike-Timing-Dependent Plasticity

Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron “sees” the input correlations. We thus denote this unsupervised learning scheme as ‘kernel spectral component analysis’ (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a “linear” response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP.

Interplay between dendritic non-linearities and STDP

Recent results about dendritic computation of responses to presynaptic stimulations have raised a lot of interest. In particular, the integration of postsynaptic potentials (PSPs) exhibits non-linearities depending on their location on dendrites, even before it reaches the soma [1]. This implies important implications for spike processing at the scale of the whole neuron, when stimulated by many input spike trains via distributed synapses. Here we examine a specific aspect of dendritic non-linearities related to spike-timing-dependent plasticity (STDP). Under STDP, synapses are strengthened or weakened depending on the relative timing of pre- and postsynaptic spikes at the scale of milliseconds. The resulting learning dynamics can dramatically shape the distribution of synaptic weights, which in turn modifies the neuronal response to its inputs [2]. We investigate the interplay between dendritic non-linearities, weight distributions and STDP-based learning, in order to evaluate whether their combined effects can be useful in terms of spiking computation. We develop a mathematical analysis using the Poisson neuron model (spiking neuron) and a phenomenological model of STDP that describes the weight update using a learning window function [3]. The synaptic competition depends on properties of the STDP learning window, non-linear PSP integration, and stimulating inputs (in particular, the input spike-time correlations). As a first step, we constrain the present study to a configuration where pools of input spike trains with (narrow) temporal correlations excite certain groups of synapses. In addition, we assume linearity in the summation of PSPs for proximal (basal) synapses, whereas PSPs on distal (apical) synapses experience a supralinear summation when they belong to the same branch [1]. Using our mathematical framework, we show how distinct STDP rules applied to proximal and distal synapses can “match” their different PSP properties. Because of the corresponding supralinearity, a small increase of the weights for distal synapses will be felt stronger at the soma, as compared to proximal synapses. In this sense, a Gaussian-like distribution for the former is equivalent to a long-tail weight distribution for the latter. For linear PSP summation, such distributions can be produced by multiplicative STDP [2] and a new weight-dependent STDP model that we proposed recently (submitted work), respectively. Here we discuss how these distributions are affected by the dendritic non-linearities. Then we investigate how some synapses are potentiated at the expense of others for various input configurations, in particular, the possibility of jointly selecting correlated inputs even though they excite different dendritic sites. A previous study [4] used additive (weight-independent) STDP with a realistic neuron model in order to examine the competition between basal and apical synapses. It was found in this configuration that, in most cases, either basal or apical synapses take over, and a balance between them is difficult to obtain. Our results suggest that non-additive STDP models can partly solve this problem by adjusting their weight dependence to the dendritic non-linearity, and realize a “fair” synaptic competition. This means that the emerging connectivity can reflect the stimulating input properties despite the constraint of being located on different dendritic branches. A future step consists in incorporating more physiological details in our model (e.g., compartmental neuron model as in [4]) to verify that our results still hold. Eventually, we aim to understand how the diversity of STDP and PSP properties observed in the biology contributes to the computational power of neurons in terms of spike processing.

Syntax, synfire, and synaptic plasticity: Modeling the generation of structure in birdsong and neuronal networks

Event Abstract Back to Event Syntax, synfire, and synaptic plasticity: Modeling the generation of structure in birdsong and neuronal networks Abigail Morrison1, 2* 1 Bernstein Center Freiburg, Germany 2 University of Freiburg, Faculty of Biology, Germany Adult Bengalese finches generate a variable song that obeys a distinct and individual syntax. The syntax is gradually lost over a period of days after deafening and is recovered when hearing is restored. In the first part of this talk I will present a spiking neuronal network model of the song syntax generation and its loss, based on the assumption that the syntax is stored in reafferent connections from the auditory to the motor control area. Propagating synfire activity in the HVC (high vocal center) codes for individual syllables of the song and priming signals from the auditory network reduce the competition between syllables to allow only those transitions that are permitted by the syntax. Both imprinting of song syntax within HVC and the interaction of the reafferent signal with an efference copy of the motor command are sufficient to explain the gradual loss of syntax in the absence of auditory feedback. In the second part of this talk I will consider how the synfire chains assumed in the first part could develop. It has long been though that spike-timing dependent plasticity (STDP) provides an answer to the question of how the brain can develop functional structure in response to repeated stimuli. However, convincing demonstrations of this capacity in large, initially random networks have not been forthcoming; such demonstrations as there are typically rely on constraining the problem artificially. I will present a theoretical analysis based on a mean field approach of the development of feed-forward structure in random networks. An unstable fixed point in the recruitment dynamics prevents the stable propagation of structure in recurrent networks with weight-dependent STDP. The key theoretical predictions can be confirmed in large-scale simulations. The theory provides insight into the reasons why such development does not take place in unconstrained systems and enables the identification of candidate biologically motivated adaptations to the balanced random network model that might resolve the issue. Keywords: Plasticity and Learning Conference: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011. Presentation Type: Keynote Topic: other Citation: Morrison A (2011). Syntax, synfire, and synaptic plasticity: Modeling the generation of structure in birdsong and neuronal networks. Front. Comput. Neurosci. Conference Abstract: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011. doi: 10.3389/conf.fncom.2011.53.00021 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 26 Sep 2011; Published Online: 04 Oct 2011. * Correspondence: Prof. Abigail Morrison, Bernstein Center Freiburg, Freiburg, Germany, morrison@fz-juelich.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Abigail Morrison Google Abigail Morrison Google Scholar Abigail Morrison PubMed Abigail Morrison Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks V: self-organization schemes and weight dependence

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity on a (much) slower time scale. This paper examines the effect of STDP in a recurrently connected network stimulated by external pools of input spike trains, where both input and recurrent synapses are plastic. Our previously developed theoretical framework is extended to incorporate weight-dependent STDP and dendritic delays. The weight dynamics is determined by an interplay between the neuronal activation mechanisms, the input spike-time correlations, and the learning parameters. For the case of two external input pools, the resulting learning scheme can exhibit a symmetry breaking of the input connections such that two neuronal groups emerge, each specialized to one input pool only. In addition, we show how the recurrent connections within each neuronal group can be strengthened by STDP at the expense of those between the two groups. This neuronal self-organization can be seen as a basic dynamical ingredient for the emergence of neuronal maps induced by activity-dependent plasticity.

Representation of input structure in synaptic weights by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) has been shown to generate a synaptic weight structure that is determined by the timing of the pre- and postsynaptic spikes at the synapse. In this paper it is shown under what conditions a neuron stimulated by several pools of delta-correlated inputs encodes this input structure in its resulting weight structure. The analysis is carried out using Poisson neurons with weight-dependent STDP. The learning dynamics induced by STDP leads to both stabilization of the input weights and competition between the weights for a broad range of learning parameters. The results demonstrate how weight-dependent STDP can generate multimodal stable asymptotic distributions of the synaptic weights.

The representation of input correlation structure from multiple pools in the synaptic weights by STDP

Spike-timing-dependent plasticity (STDP) has been shown to generate a synaptic weight structure by the strengthening (potentiation) or weakening (depression) of synapses depending on the timing of the pre- and post-synaptic spikes at the synapse at the scale of milliseconds [1,2]. Mathematical studies of STDP have shown how it generates competition between individual weights that can lead to effective neuronal specialization relying on spike-time correlations [3,4]. In addition, the change in the synaptic weight induced by STDP is affected by its current value, which modulates the resulting competition [5]. It was shown for the case of a single neuron stimulated by two identical input pools that the asymptotic weight distribution can be either unimodal or bimodal, depending on the strength of the weight dependence for STDP [6]; the transition (bifurcation) between these two classes of STDP also depends upon the input correlation level. Stronger input correlations and almost-additive STDP lead to effective weight specialization, namely an asymptotic bimodal distribution. For the case of several pools with identical properties, the weight dependence can also lead to the selection of a subset of the pools [7]. In this paper it is shown under what conditions a neuron stimulated by several pools that have within-pool (but no between-pool) correlations with distinct strengths encodes this input structure in its resulting weight structure. The analysis is carried out using the Poisson neuron model [3] with pair-wise weight-dependent STDP [6]. The learning dynamics induced by STDP leads to both stabilization of the input weights and competition between the weights for a broad range of learning parameters. While weak weight dependence is synonymous with strong competition between individual weights, there is a qualitative difference between the weight dynamics generated by additive and almost-additive STDP. For additive STDP, only the bounds of the weights are stable, whereas intermediate values can be stable even for weakly weight-dependent STDP. In the latter case, a stable multimodal asymptotic distribution can emerge, where the weights are sorted in increasing order with respect to the correlation strength of the corresponding pool they come from. When the strength of weight dependence is increased, the spreading of the asymptotic distribution diminishes, eventually becoming unimodal. The results demonstrate how weakly weight-dependent STDP can generate a multimodal stable asymptotic distribution of the synaptic weights, providing a further step towards a better understanding of how STDP can represent the input (spike-time correlation) structure in the resulting weight structure.

Limits to the development of feed-forward structures in large recurrent neuronal networks

Spike-timing dependent plasticity (STDP) has traditionally been of great interest to theoreticians, as it seems to provide an answer to the question of how the brain can develop functional structure in response to repeated stimuli. However, despite this high level of interest, convincing demonstrations of this capacity in large, initially random networks have not been forthcoming. Such demonstrations as there are typically rely on constraining the problem artificially. Techniques include employing additional pruning mechanisms or STDP rules that enhance symmetry breaking, simulating networks with low connectivity that magnify competition between synapses, or combinations of the above. In this paper, we first review modeling choices that carry particularly high risks of producing non-generalizable results in the context of STDP in recurrent networks. We then develop a theory for the development of feed-forward structure in random networks and conclude that an unstable fixed point in the dynamics prevents the stable propagation of structure in recurrent networks with weight-dependent STDP. We demonstrate that the key predictions of the theory hold in large-scale simulations. The theory provides insight into the reasons why such development does not take place in unconstrained systems and enables us to identify biologically motivated candidate adaptations to the balanced random network model that might enable it.

STDP in Adaptive Neurons Gives Close-To-Optimal Information Transmission

Spike-frequency adaptation is known to enhance the transmission of information in sensory spiking neurons by rescaling the dynamic range for input processing, matching it to the temporal statistics of the sensory stimulus. Achieving maximal information transmission has also been recently postulated as a role for spike-timing-dependent plasticity (STDP). However, the link between optimal plasticity and STDP in cortex remains loose, as does the relationship between STDP and adaptation processes. We investigate how STDP, as described by recent minimal models derived from experimental data, influences the quality of information transmission in an adapting neuron. We show that a phenomenological model based on triplets of spikes yields almost the same information rate as an optimal model specially designed to this end. In contrast, the standard pair-based model of STDP does not improve information transmission as much. This result holds not only for additive STDP with hard weight bounds, known to produce bimodal distributions of synaptic weights, but also for weight-dependent STDP in the context of unimodal but skewed weight distributions. We analyze the similarities between the triplet model and the optimal learning rule, and find that the triplet effect is an important feature of the optimal model when the neuron is adaptive. If STDP is optimized for information transmission, it must take into account the dynamical properties of the postsynaptic cell, which might explain the target-cell specificity of STDP. In particular, it accounts for the differences found in vitro between STDP at excitatory synapses onto principal cells and those onto fast-spiking interneurons.

Input synchrony and spike-timing dependent plasticity

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.