Self-regulation mechanism of Temporally Asymmetric Hebbian plasticity

Recent biological experimental findings have shown that the synaptic plasticity depends on the relative timing of the pre- and postsynaptic spikes which 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 spatio-temporal patterns can be stored in neural networks. However, the mathematical mechanism for storage of the spatio-temporal patterns is still unknown, especially the effects of LTD. In this paper, we employ a simple neural network model and show that interference of LTP and LTD disappears in a sparse coding scheme. On the other hand, it is known that the covariance learning is indispensable for storing sparse patterns. We also show that TAH qualitatively has the same effect as the covariance learning when spatio-temporal patterns are embedded in the network.