keras代码阅读-relu函数

概述

relu是激活函数的一种。很多地方说relu函数的公式就是：

f(x)=max(0,x)

阅读了theano的代码

def relu(x, alpha=0):
    """
    Compute the element-wise rectified linear activation function.

    .. versionadded:: 0.7.1

    Parameters
    ----------
    x : symbolic tensor
        Tensor to compute the activation function for.
    alpha : scalar or tensor, optional
        Slope for negative input, usually between 0 and 1. The default value
        of 0 will lead to the standard rectifier, 1 will lead to
        a linear activation function, and any value in between will give a
        leaky rectifier. A shared variable (broadcastable against `x`) will
        result in a parameterized rectifier with learnable slope(s).

    Returns
    -------
    symbolic tensor
        Element-wise rectifier applied to `x`.

    Notes
    -----
    This is numerically equivalent to ``T.switch(x > 0, x, alpha * x)``
    (or ``T.maximum(x, alpha * x)`` for ``alpha < 1``), but uses a faster
    formulation or an optimized Op, so we encourage to use this function.

    """
    # This is probably the fastest implementation for GPUs. Both the forward
    # pass and the gradient get compiled into a single GpuElemwise call.
    # TODO: Check if it's optimal for CPU as well; add an "if" clause if not.
    # TODO: Check if there's a faster way for the gradient; create an Op if so.
    if alpha == 0:
        return 0.5 * (x + abs(x))
    else:
        f1 = 0.5 * (1 + alpha)
        f2 = 0.5 * (1 - alpha)
        return f1 * x + f2 * abs(x)

发现这个代码中用了以下方法，当alpha为0的时候

f(x)=x+|x|2

当alpha不等于0时。是这样的：

f(x)=1+α2x+1−α2|x|