Computational consequences of experimentally derived spike-time and weight dependent plasticity rules

Spontaneous dynamics of synaptic weights in stochastic models with pair-based spike-timing-dependent plasticity

We investigate spike-timing dependent plasticity (STPD) in the case of a synapse connecting two neuronal cells. We develop a theoretical analysis of several STDP rules using Markovian theory. In this context there are two different timescales, fast neuronal activity and slower synaptic weight updates. Exploiting this timescale separation, we derive the long-time limits of a single synaptic weight subject to STDP. We show that the pairing model of presynaptic and postsynaptic spikes controls the synaptic weight dynamics for small external input on an excitatory synapse. This result implies in particular that mean-field analysis of plasticity may miss some important properties of STDP. Anti-Hebbian STDP favors the emergence of a stable synaptic weight. In the case of an inhibitory synapse the pairing schemes matter less, and we observe convergence of the synaptic weight to a nonnull value only for Hebbian STDP. We extensively study different asymptotic regimes for STDP rules, raising interesting questions for future work on adaptative neuronal networks and, more generally, on adaptative systems.

Synaptic refinement during development and its effect on slow-wave activity: a computational study

Recent evidence suggests that synaptic refinement, the reorganization of synapses and connections without significant change in their number or strength, is important for the development of the visual system of juvenile rodents. Other evidence in rodents and humans shows that there is a marked drop in sleep slow-wave activity (SWA) during adolescence. Slow waves reflect synchronous transitions of neuronal populations between active and inactive states, and the amount of SWA is influenced by the connection strength and organization of cortical neurons. In this study, we investigated whether synaptic refinement could account for the observed developmental drop in SWA. To this end, we employed a large-scale neural model of primary visual cortex and sections of the thalamus, capable of producing realistic slow waves. In this model, we reorganized intralaminar connections according to experimental data on synaptic refinement: during prerefinement, local connections between neurons were homogenous, whereas in postrefinement, neurons connected preferentially to neurons with similar receptive fields and preferred orientations. Synaptic refinement led to a drop in SWA and to changes in slow-wave morphology, consistent with experimental data. To test whether learning can induce synaptic refinement, intralaminar connections were equipped with spike timing-dependent plasticity. Oriented stimuli were presented during a learning period, followed by homeostatic synaptic renormalization. This led to activity-dependent refinement accompanied again by a decline in SWA. Together, these modeling results show that synaptic refinement can account for developmental changes in SWA. Thus sleep SWA may be used to track noninvasively the reorganization of cortical connections during development.

The effect of STDP temporal kernel structure on the learning dynamics of single excitatory and inhibitory synapses

Spike-Timing Dependent Plasticity (STDP) is characterized by a wide range of temporal kernels. However, much of the theoretical work has focused on a specific kernel – the “temporally asymmetric Hebbian” learning rules. Previous studies linked excitatory STDP to positive feedback that can account for the emergence of response selectivity. Inhibitory plasticity was associated with negative feedback that can balance the excitatory and inhibitory inputs. Here we study the possible computational role of the temporal structure of the STDP. We represent the STDP as a superposition of two processes: potentiation and depression. This allows us to model a wide range of experimentally observed STDP kernels, from Hebbian to anti-Hebbian, by varying a single parameter. We investigate STDP dynamics of a single excitatory or inhibitory synapse in purely feed-forward architecture. We derive a mean-field-Fokker-Planck dynamics for the synaptic weight and analyze the effect of STDP structure on the fixed points of the mean field dynamics. We find a phase transition along the Hebbian to anti-Hebbian parameter from a phase that is characterized by a unimodal distribution of the synaptic weight, in which the STDP dynamics is governed by negative feedback, to a phase with positive feedback characterized by a bimodal distribution. The critical point of this transition depends on general properties of the STDP dynamics and not on the fine details. Namely, the dynamics is affected by the pre-post correlations only via a single number that quantifies its overlap with the STDP kernel. We find that by manipulating the STDP temporal kernel, negative feedback can be induced in excitatory synapses and positive feedback in inhibitory. Moreover, there is an exact symmetry between inhibitory and excitatory plasticity, i.e., for every STDP rule of inhibitory synapse there exists an STDP rule for excitatory synapse, such that their dynamics is identical.

Calcium-dependent calcium decay explains STDP in a dynamic model of hippocampal synapses

It is widely accepted that the direction and magnitude of synaptic plasticity depends on post-synaptic calcium flux, where high levels of calcium lead to long-term potentiation and moderate levels lead to long-term depression. At synapses onto neurons in region CA1 of the hippocampus (and many other synapses), NMDA receptors provide the relevant source of calcium. In this regard, post-synaptic calcium captures the coincidence of pre- and post-synaptic activity, due to the blockage of these receptors at low voltage. Previous studies show that under spike timing dependent plasticity (STDP) protocols, potentiation at CA1 synapses requires post-synaptic bursting and an inter-pairing frequency in the range of the hippocampal theta rhythm. We hypothesize that these requirements reflect the saturation of the mechanisms of calcium extrusion from the post-synaptic spine. We test this hypothesis with a minimal model of NMDA receptor-dependent plasticity, simulating slow extrusion with a calcium-dependent calcium time constant. In simulations of STDP experiments, the model accounts for latency-dependent depression with either post-synaptic bursting or theta-frequency pairing (or neither) and accounts for latency-dependent potentiation when both of these requirements are met. The model makes testable predictions for STDP experiments and our simple implementation is tractable at the network level, demonstrating associative learning in a biophysical network model with realistic synaptic dynamics.

A neuromorphic architecture for object recognition and motion anticipation using burst-STDP

In this work we investigate the possibilities offered by a minimal framework of artificial spiking neurons to be deployed in silico. Here we introduce a hierarchical network architecture of spiking neurons which learns to recognize moving objects in a visual environment and determine the correct motor output for each object. These tasks are learned through both supervised and unsupervised spike timing dependent plasticity (STDP). STDP is responsible for the strengthening (or weakening) of synapses in relation to pre- and post-synaptic spike times and has been described as a Hebbian paradigm taking place both in vitro and in vivo. We utilize a variation of STDP learning, called burst-STDP, which is based on the notion that, since spikes are expensive in terms of energy consumption, then strong bursting activity carries more information than single (sparse) spikes. Furthermore, this learning algorithm takes advantage of homeostatic renormalization, which has been hypothesized to promote memory consolidation during NREM sleep. Using this learning rule, we design a spiking neural network architecture capable of object recognition, motion detection, attention towards important objects, and motor control outputs. We demonstrate the abilities of our design in a simple environment with distractor objects, multiple objects moving concurrently, and in the presence of noise. Most importantly, we show how this neural network is capable of performing these tasks using a simple leaky-integrate-and-fire (LIF) neuron model with binary synapses, making it fully compatible with state-of-the-art digital neuromorphic hardware designs. As such, the building blocks and learning rules presented in this paper appear promising for scalable fully neuromorphic systems to be implemented in hardware chips.

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.

Reconciling the STDP and BCM models of synaptic plasticity in a spiking recurrent neural network

Rate-coded Hebbian learning, as characterized by the BCM formulation, is an established computational model of synaptic plasticity. Recently it has been demonstrated that changes in the strength of synapses in vivo can also depend explicitly on the relative timing of pre- and postsynaptic firing. Computational modeling of this spike-timing-dependent plasticity (STDP) has demonstrated that it can provide inherent stability or competition based on local synaptic variables. However, it has also been demonstrated that these properties rely on synaptic weights being either depressed or unchanged by an increase in mean stochastic firing rates, which directly contradicts empirical data. Several analytical studies have addressed this apparent dichotomy and identified conditions under which distinct and disparate STDP rules can be reconciled with rate-coded Hebbian learning. The aim of this research is to verify, unify, and expand on these previous findings by manipulating each element of a standard computational STDP model in turn. This allows us to identify the conditions under which this plasticity rule can replicate experimental data obtained using both rate and temporal stimulation protocols in a spiking recurrent neural network. Our results describe how the relative scale of mean synaptic weights and their dependence on stochastic pre- or postsynaptic firing rates can be manipulated by adjusting the exact profile of the asymmetric learning window and temporal restrictions on spike pair interactions respectively. These findings imply that previously disparate models of rate-coded autoassociative learning and temporally coded heteroassociative learning, mediated by symmetric and asymmetric connections respectively, can be implemented in a single network using a single plasticity rule. However, we also demonstrate that forms of STDP that can be reconciled with rate-coded Hebbian learning do not generate inherent synaptic competition, and thus some additional mechanism is required to guarantee long-term input-output selectivity.

Sleep and synaptic renormalization: a computational study

Recent evidence indicates that net synaptic strength in cortical and other networks increases during wakefulness and returns to a baseline level during sleep. These homeostatic changes in synaptic strength are accompanied by corresponding changes in sleep slow wave activity (SWA) and in neuronal firing rates and synchrony. Other evidence indicates that sleep is associated with an initial reactivation of learned firing patterns that decreases over time. Finally, sleep can enhance performance of learned tasks, aid memory consolidation, and desaturate the ability to learn. Using a large-scale model of the corticothalamic system equipped with a spike-timing dependent learning rule, in agreement with experimental results, we demonstrate a net increase in synaptic strength in the waking mode associated with an increase in neuronal firing rates and synchrony. In the sleep mode, net synaptic strength decreases accompanied by a decline in SWA. We show that the interplay of activity and plasticity changes implements a control loop yielding an exponential, self-limiting renormalization of synaptic strength. Moreover, when the model "learns" a sequence of activation during waking, the learned sequence is preferentially reactivated during sleep, and reactivation declines over time. Finally, sleep-dependent synaptic renormalization leads to increased signal-to-noise ratios, increased resistance to interference, and desaturation of learning capabilities. Although the specific mechanisms implemented in the model cannot capture the variety and complexity of biological substrates, and will need modifications in line with future evidence, the present simulations provide a unified, parsimonious account for diverse experimental findings coming from molecular, electrophysiological, and behavioral approaches.

STDP in Recurrent Neuronal Networks

Recent results about spike-timing-dependent plasticity (STDP) in recurrently connected neurons are reviewed, with a focus on the relationship between the weight dynamics and the emergence of network structure. In particular, the evolution of synaptic weights in the two cases of incoming connections for a single neuron and recurrent connections are compared and contrasted. A theoretical framework is used that is based upon Poisson neurons with a temporally inhomogeneous firing rate and the asymptotic distribution of weights generated by the learning dynamics. Different network configurations examined in recent studies are discussed and an overview of the current understanding of STDP in recurrently connected neuronal networks is presented.

Rate and pulse based plasticity governed by local synaptic state variables

Classically, action-potential-based learning paradigms such as the Bienenstock–Cooper–Munroe (BCM) rule for pulse rates or spike timing-dependent plasticity for pulse pairings have been experimentally demonstrated to evoke long-lasting synaptic weight changes (i.e., plasticity). However, several recent experiments have shown that plasticity also depends on the local dynamics at the synapse, such as membrane voltage, Calcium time course and level, or dendritic spikes. In this paper, we introduce a formulation of the BCM rule which is based on the instantaneous postsynaptic membrane potential as well as the transmission profile of the presynaptic spike. While this rule incorporates only simple local voltage- and current dynamics and is thus neither directly rate nor timing based, it can replicate a range of experiments, such as various rate and spike pairing protocols, combinations of the two, as well as voltage-dependent plasticity. A detailed comparison of current plasticity models with respect to this range of experiments also demonstrates the efficacy of the new plasticity rule. All experiments can be replicated with a limited set of parameters, avoiding the overfitting problem of more involved plasticity rules.

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.

Inhibition, not excitation, is the key to multimodal sensory integration

Multimodal neuronal maps, combining input from two or more sensory systems, play a key role in the processing of sensory and motor information. For such maps to be of any use, the input from all participating modalities must be calibrated so that a stimulus at a specific spatial location is represented at an unambiguous position in the multimodal map. Here we discuss two methods based on supervised spike-timing-dependent plasticity (STDP) to gauge input from different sensory modalities so as to ensure a proper map alignment. The first uses an excitatory teacher input. It is therefore called excitation-mediated learning. The second method is based on an inhibitory teacher signal, as found in the barn owl, and is called inhibition-mediated learning. Using detailed analytical calculations and numerical simulations, we demonstrate that inhibitory teacher input is essential if high-quality multimodal integration is to be learned rapidly. Furthermore, we show that the quality of the resulting map is not so much limited by the quality of the teacher signal but rather by the accuracy of the input from other sensory modalities.

Phenomenological models of synaptic plasticity based on spike timing

Synaptic plasticity is considered to be the biological substrate of learning and memory. In this document we review phenomenological models of short-term and long-term synaptic plasticity, in particular spike-timing dependent plasticity (STDP). The aim of the document is to provide a framework for classifying and evaluating different models of plasticity. We focus on phenomenological synaptic models that are compatible with integrate-and-fire type neuron models where each neuron is described by a small number of variables. This implies that synaptic update rules for short-term or long-term plasticity can only depend on spike timing and, potentially, on membrane potential, as well as on the value of the synaptic weight, or on low-pass filtered (temporally averaged) versions of the above variables. We examine the ability of the models to account for experimental data and to fulfill expectations derived from theoretical considerations. We further discuss their relations to teacher-based rules (supervised learning) and reward-based rules (reinforcement learning). All models discussed in this paper are suitable for large-scale network simulations.