Mathematical formulations of Hebbian learning

By Wulfram Gerstner, Werner M. Kistler. 2002

453 citations recorded by the source corpus.

Abstract. Several formulations of correlation-based Hebbian learning are reviewed. On the presynaptic side, activity is described either by a firing rate or by presynaptic spike arrival. The state of the postsynaptic neuron can be described by its membrane potential, its firing rate, or the timing of backpropagating action potentials (BPAPs). It is shown that all of the above formulations can be derived from the point of view of an expansion. In the absence of BPAPs, it is natural to correlate presynaptic spikes with the postsynaptic membrane potential. Time windows of spike-time-dependent plasticity arise naturally if the timing of postsynaptic spikes is available at the site of the synapse, as is the case in the presence of BPAPs. With an appropriate choice of parameters, Hebbian synaptic plasticity has intrinsic normalization properties that stabilizes postsynaptic firing rates and leads to subtractive weight normalization.

Subfields: Cellular and Molecular Neuroscience, Cognitive Neuroscience, Electrical and Electronic Engineering

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Citations in the corpus

Born to Learn: the Inspiration, Progress, and Future of Evolved Plastic Artificial Neural Networks (2017, methodology): “…learning is implemented in neural networks with self-Organising Maps (SOM) (Kohonen, 1982, 1990), auto-encoders (Bourlard and Kamp, 1988), restricted Boltzmann machines (RBM) (Hinton and Salakhutdinov, 2006), and Hebbian plasticity (Hebb, 1949; Gerstner and Kistler, 2002a; Cooper, 2005).”
A Constructive Mean-Field Analysis of Multi-Population Neural Networks with Random Synaptic Weights and Stochastic Inputs (2008, neutral): “Bifurcation analysis of Jansen’s neural mass model.”
Simulation of networks of spiking neurons: A review of tools and strategies (2006, unknown): “In many cases, the spike response model (Gerstner and Kistler 2002) is also the integral expression of a hybrid system.”
GRAIL: A Goal-Discovering Robotic Architecture for Intrinsically-Motivated Learning (2016, methodology): “The connection weight vji connecting IR-V unit i to ER-M unit j is updated through a Hebbian rule (with decay and postsynaptic gating [28])”
Introduction to spiking neural networks: Information processing, learning and applications. (2011, methodology): “…of the self-organizing maps (Ruf and Schmitt 1998, Ruf 1998), temporal sequence recognition based on the subspaces clustering (Natschlaeger and Ruf 1998a), formation of associative memories (Knoblauch 2003), or extraction of principal components from spike trains (Gerstner and Kistler 2002b).”
Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules (2016, background): “Equation (1) then indicates that changes of the synaptic weight depend on coincidences between the spikes of the pre- and postsynaptic neuron (Kempter et al., 1999; Song et al., 2000; Gerstner and Kistler, 2002; Morrison et al., 2008).”
From modulated Hebbian plasticity to simple behavior learning through noise and weight saturation (2012, methodology): “The reconfigure-and-saturate Hebbian dynamics hold equally with a simple spiking neuron model (Wilson, 1999; Maass and Bishop, 1999; Gerstner and Kistler, 2002b).”
Copying and Evolution of Neuronal Topology (2008, result): “The capacity of STDP to capture temporal relations consistent with causality rather than just correlations has been described by several authors [65,87,88,89].”