|
In computational networks, the activation function of a node defines the output of that node given an input or set of inputs. A standard computer chip circuit can be seen as a digital network of activation functions that can be "ON" (1) or "OFF" (0), depending on input. This is similar to the behavior of the linear perceptron in neural networks. However, it is the ''nonlinear'' activation function that allows such networks to compute nontrivial problems using only a small number of nodes. In artificial neural networks this function is also called transfer function (not to be confused with a linear system’s transfer function). == Functions == In biologically inspired neural networks, the activation function is usually an abstraction representing the rate of action potential firing in the cell. In its simplest form, this function is binary—that is, either the neuron is firing or not. The function looks like , where is the Heaviside step function. In this case a large number of neurons must be used in computation beyond linear separation of categories. A line of positive slope may also be used to reflect the increase in firing rate that occurs as input current increases. The function would then be of the form , where is the slope. This activation function is linear, and therefore has the same problems as the binary function. In addition, networks constructed using this model have unstable convergence because neuron inputs along favored paths tend to increase without bound, as this function is not normalizable. All problems mentioned above can be handled by using a normalizable sigmoid activation function. One realistic model stays at zero until input current is received, at which point the firing frequency increases quickly at first, but gradually approaches an asymptote at 100% firing rate. Mathematically, this looks like , where the hyperbolic tangent function can also be replaced by any sigmoid function. This behavior is realistically reflected in the neuron, as neurons cannot physically fire faster than a certain rate. This model runs into problems, however, in computational networks as it is not differentiable, a requirement in order to calculate backpropagation. The final model, then, that is used in multilayer perceptrons is a sigmoidal activation function in the form of a hyperbolic tangent. Two forms of this function are commonly used: whose range is normalized from -1 to 1, and is vertically translated to normalize from 0 to 1. The latter model is often considered more biologically realistic, but it runs into theoretical and experimental difficulties with certain types of computational problems. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「activation function」の詳細全文を読む スポンサード リンク
|