Research on Sparsity of Output Synapses in Echo State Networks

Figure 4

The variation of predicted steps for ESN with the increment of silent synapse. In each subgraph, there are five curves which represent different connection states of output synapses, where is the weight matrix of output connections when ESN has the maximal energy efficiency after redundant output synapses are removed, is the weight matrix of output connections when output synapses are all activated, is the weight matrix of output connections when ESN has the minimal energy efficiency after redundant output synapses are removed, is the weight matrix of output connections when we randomly select an output synapse and silence it, and is the weight matrix of output connections when we silence redundant output synapses corresponding to the neurons with the minimal energy contribution. The horizontal line in each subgraph denotes that output synapses are all activated, and is the weight matrix of output connections. (a) Prediction results of Mackey-Glass system. (b) Prediction results of Lorenz system. (c) Prediction results of Rössler system. (d) Prediction results of Chen system.

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