Convergence mechanism of learning on backpropagation and new high speed method

Summary form only given, as follows. A neural network consists of three layers (input, hidden, and output). The connection of the layers is used by the I/O function as a sigmoid function. However, as the number of training cycles depends on the function, it is necessary to devise the function. Applying the new function, the convergent mechanism should be studied until the learning finishes. When the input data of each layer are processed by the sigmoid function, its sensitivity is different from the operating point. The sensitive region is named the active region. The signals in active regions are amended effectively towards the supervised signals. Managing and controlling the active region, the new I/O function for high-speed learning can be obtained using a neural network with back-propagation