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

Abstract

Synaptic strength depresses for low and potentiates for high activation of the postsynaptic neuron. This feature is a key property of the Bienenstock-Cooper-Munro (BCM) synaptic learning rule, which has been shown to maximize the selectivity of the postsynaptic neuron, and thereby offers a possible explanation for experience-dependent cortical plasticity such as orientation selectivity. However, the BCM framework is rate-based and a significant amount of recent work has shown that synaptic plasticity also depends on the precise timing of presynaptic and postsynaptic spikes. Here we consider a triplet model of spike-timing-dependent plasticity (STDP) that depends on the interactions of three precisely timed spikes. Triplet STDP has been shown to describe plasticity experiments that the classical STDP rule, based on pairs of spikes, has failed to capture. In the case of ratebased patterns, we show a tight correspondence between the triplet STDP rule and the BCM rule. We analytically demonstrate the selectivity property of the triplet STDP rule for orthogonal inputs and perform numerical simulations for nonorthogonal inputs. Moreover, in contrast to BCM, we show that triplet STDP can also induce selectivity for input patterns consisting of higher-order spatiotemporal correlations, which exist in natural stimuli and have been measured in the brain. We show that this sensitivity to higher-order correlations can be used to develop direction and speed selectivity. S ynaptic plasticity depends on the activity of presynaptic and postsynaptic neurons and is believed to provide the basis for learning and memory (1, 2). It has been shown that low-frequency stimulation (1-3 Hz) (3) or stimulation paired with low postsynaptic depolarization (4) induces synaptic long-term depression (LTD), whereas synapses undergo long-term potentiation (LTP) after high-frequency stimulation (100 Hz) (5). Such findings are consistent with the well-known Bienenstock-Cooper-Munro (BCM) learning rule (6). This BCM model has been shown to elicit orientation selectivity and other aspects of experience-dependent cortical plasticity (6, 7). Furthermore, in this model the modification threshold between LTP and LTD varies as a function of the history of postsynaptic activity, a prediction that has been confirmed experimentally (8).Despite its consistency with experimental data and its functional relevance, the BCM framework is still limited experimentally and functionally. Experimentally, because the learning rule is expressed in terms of firing rates, it cannot predict synaptic modification on the basis of the timing of pre-and postsynaptic spikes (9, 10). This form of plasticity, called spike-timing-dependent plasticity (STDP), uses the timing of spike pairs to induce synaptic modification (11,12). The presynaptic spike is required to shortly precede the postsynaptic spike to elicit LTP, whereas the reverse timing of pre-and postsynaptic spikes leads to LTD (9, 10). Functionally, the BCM model cannot segregate input patterns that are characterized by...

Networks that learn the precise timing of event sequences

“…Variables symbol description I j external stimulus for excitatory population j u j non-dimensional firing rate of excitatory population j (maximum u j = 1) v non-dimensional firing rate of global inhibitory population (maximum v = 1) p j level of facilitation of synapses from population j (baseline p j = 1) w jk , w strength of excitation from population k to excitatory population j T j , T duration of stimulus Similar assumptions have been used in previous rate-based models of LTP/LTD (von der Malsburg, 1973;Bienenstock et al, 1982;Oja, 1982;Miller, 1994), and it has been shown that calciumbased (Graupner and Brunel, 2012) and spike-time dependent (Clopath et al, 2010;Gjorgjieva et al, 2011) plasticity rules can be reduced to such ratebased rules (Pfister and Gerstner, 2006). Furthermore, the fact that pre-synaptic activity is necessary to initiate either LTP or LTD is supported by experimental observations that plasticity depends on calcium influx through NMDA receptors (Malenka and Bear, 2004).…”

A neuromorphic VLSI design for spike timing and rate based synaptic plasticity

“…The proposed circuit, hence, can be utilized in the implementation of a VLSI synapse which possesses timing-and rate-based plasticity features, simultaneously. This synapse then can be employed in various neuromorphic systems aiming for different applications ranging from classifying complex patterns Mitra et al (2009), to a TSTDP circuit which generalizes the BCM rule to higher order spatio-temporal correlations Gjorgjieva et al (2011). All These features make the proposed circuit a valued and interesting contribution to the silicon based synaptic neural systems and pave the way for a realistic neuromorphic engineering implementation.…”

“…This variation aware design technique exploits source degeneration and negative feedback methods to increase the dynamic range of input voltages of transistors and make them robust against mismatch errors that happen majorly because of the low input voltage dynamic range in traditional subthreshold current mode circuits . A direction for future research is to use the source degeneration and negative feedback design technique and build a network of neurons with TSTDP synapses which is capable of pattern selection as described in Gjorgjieva et al (2011).…”

Two dimensional model of learning in spiking neural networks with homeostasis and reward

“…Для хебівської форми використано правило триплетної спайк-часовозалежної пластичності [15], яке може бути зведено до розширеного правила BCM [16].…”