Synaptic plasticity is widely accepted to be the mechanism behind learning in the brain's neural networks. A central question is how synapses, with access to only local information about the network, can still organize collectively and perform circuit-wide learning in an efficient manner. In single-layered and all-to-all connected neural networks, local plasticity has been shown to implement gradient-based learning on a class of cost functions that contain a term that aligns the similarity of outputs to the similarity of inputs. Whether such cost functions exist for networks with other architectures is not known. In this paper, we introduce structured and deep similarity matching cost functions, and show how they can be optimized in a gradient-based manner by neural networks with local learning rules.
Spike timing plasticity (STDP) is a special form of synaptic plasticity where the relative timing of post-and presynaptic activity determines the change of the synaptic weight. On the postsynaptic side, active backpropagating spikesin dendrites seem to play a crucial role in the induction of spike timing dependent plasticity. We argue that postsynaptically the temporal change of the membrane potential determines the weight change. Coming from the presynaptic side induction of STDP is closely related to the activation of NMDA channels. Therefore, we will calculate analytically the change of the synaptic weight by correlating the derivative ofthe membrane potential with the activity of the NMDA channel.
This paper explores the computational consequences of simultaneous intrinsic andsynaptic plasticity in individual model neurons. It proposes a new intrinsic plasticity mechanism for a continuous activation model neuron based on low order moments of the neuron's firing rate distribution. Thegoal of the intrinsic plasticity mechanism is to enforce a sparse distribution of the neuron's activity level. In conjunction with Hebbian learning at the neuron's synapses, the neuron is shown to discover sparse directions in the input.
When stimulated with complex action potential sequences synapses exhibit spike timing-dependent plasticity (STDP) with attenuated and enhanced pre- and postsynaptic contributions to long-term synaptic modifications. In order to investigate the functional consequences of these contribution dynamics (CD) we propose a minimal model formulated in terms of differential equations. We find that our model reproduces a wide range of experimental results with a small number of biophysically interpretable parameters. The model allows to investigate the susceptibility of STDP to arbitrary time courses of pre- and postsynaptic activities, i.e. its nonlinear filter properties. We demonstrate this for the simple example of small periodic modulations of pre- and postsynaptic firing rates for which our model can be solved. It predicts synaptic strengthening for synchronous rate modulations. For low baseline rates modifications are dominant in the theta frequency range, a result which underlines the well known relevance of theta activities in hippocampus and cortex for learning. We also find emphasis of low baseline spike rates and suppression for high baseline rates. The latter suggests a mechanism of network activity regulation inherent in STDP. Furthermore, our novel formulation provides a general framework for investigating the joint dynamics of neuronal activity and the CD of STDP in both spike-based as well as rate-based neuronal network models.
Recent biological experimental findings have shown that the synaptic plasticitydepends on the relative timing of the pre-and postsynaptic spikeswhich determines whether Long Term Potentiation (LTP) occurs or Long Term Depression (LTD) does. The synaptic plasticity has been called "Temporally Asymmetric Hebbian plasticity (TAH)".Many authors have numerically shown that spatiotemporal patternscan be stored in neural networks.