Stability versus Neuronal Specialization for STDP: Long-Tail Weight Distributions Solve the Dilemma

Abstract

Spike-timing-dependent plasticity (STDP) modifies the weight (or strength) of synaptic connections between neurons and is considered to be crucial for generating network structure. It has been observed in physiology that, in addition to spike timing, the weight update also depends on the current value of the weight. The functional implications of this feature are still largely unclear. Additive STDP gives rise to strong competition among synapses, but due to the absence of weight dependence, it requires hard boundaries to secure the stability of weight dynamics. Multiplicative STDP with linear weight dependence for depression ensures stability, but it lacks sufficiently strong competition required to obtain a clear synaptic specialization. A solution to this stability-versus-function dilemma can be found with an intermediate parametrization between additive and multiplicative STDP. Here we propose a novel solution to the dilemma, named log-STDP, whose key feature is a sublinear weight dependence for depression. Due to its specific weight dependence, this new model can produce significantly broad weight distributions with no hard upper bound, similar to those recently observed in experiments. Log-STDP induces graded competition between synapses, such that synapses receiving stronger input correlations are pushed further in the tail of (very) large weights. Strong weights are functionally important to enhance the neuronal response to synchronous spike volleys. Depending on the input configuration, multiple groups of correlated synaptic inputs exhibit either winner-share-all or winner-take-all behavior. When the configuration of input correlations changes, individual synapses quickly and robustly readapt to represent the new configuration. We also demonstrate the advantages of log-STDP for generating a stable structure of strong weights in a recurrently connected network. These properties of log-STDP are compared with those of previous models. Through long-tail weight distributions, log-STDP achieves both stable dynamics for and robust competition of synapses, which are crucial for spike-based information processing.

A Lognormal Recurrent Network Model for Burst Generation during Hippocampal Sharp Waves

“…The average interevent interval was ϳ1.25 Hz, which approximately coincides with the intervals of spontaneous sharp waves measured in area CA3 in vitro (ϳ1.1-1.6 Hz) (Ellender et al, 2010;Hájos et al, 2013) and in vivo (0.01-2.0 Hz) (Buzsáki, 1986). The SWR events in CA1, which reflect the population synchrony in CA3, occur at average frequencies of 0.3-1.0 Hz during sleep (Eschenko et al, 2008;Girardeau et al, 2014). These values were also consistent with the prediction of our model.…”

“…We show that the low-frequency spontaneous activity in our network model well replicates the lognormal features of hippocampal activity. Moreover, the bursting activity exhibited by our model resembles the complex spike bursts of hippocampal pyramidal neurons (Harris et al, 2001) observed frequently, but not always, during sharp-wave ripples (SWRs) (Buzsáki et al, 2002;Lee and Wilson, 2002;Foster and Wilson, 2006), which are transient oscillatory activities in CA1 and play a crucial role in memory consolidation (Girardeau et al, 2009;Ego-Stengel and Wilson, 2010;Carr et al, 2011). The SWRs originate from the activation of CA3 neural ensembles and typically occur when sensory influences on the hippocampus decrease during slow-wave sleep and immobility.…”

Excitatory and inhibitory STDP jointly tune feedforward neural circuits to selectively propagate correlated spiking activity

“…The eSTDP update includes log-STDP weight dependence, which produces a long-tailed distribution of weights (Gilson and Fukai, 2011). For every pair of a pre- and a postsynaptic spikes, the weight w e is modified by a quantity that depends on the current value of w e and the spike-time difference Δ t = t pre − t post :…”

Heterosynaptic Plasticity Prevents Runaway Synaptic Dynamics

“…These include weight dependence, so that weaker synapses potentiate more while stronger synapses express less potentiation, and in the limit even depress (Bi and Poo, 1998;van Rossum et al, 2000;Hardingham et al, 2007), and/or precise balancing of STDP rules for potentiation and depression (Abbott and Nelson, 2000;van Rossum et al, 2000;Kempter et al, 2001;Gütig et al, 2003;Morrison et al, 2007;Babadi and Abbott, 2010;Delgado et al, 2010;Gilson and Fukai, 2011). It was rigorously shown that STDP can lead to stabilization of the mean firing rate of the postsynaptic neuron if the integral of the learning window is negative (Kempter et al, 2001).…”