Activations
Special algorithms for gradient descent.
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Special algorithms for gradient descent.
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At a simple level, activation functions help decide whether a neuron should be activated. This helps determine whether the information that the neuron is receiving is relevant for the input. The activation function is a non-linear transformation that happens over an input signal, and the transformed output is sent to the next neuron.
The recommended method to use activations is to add an activation layer in your neural network, and configure your desired activation:
Rectified tanh
Essentially max(0, tanh(x))
Underlying implementation is in native code
f(x) = alpha (exp(x) - 1.0); x < 0 = x ; x>= 0
alpha defaults to 1, if not specified
f(x) = max(0, x)
Rational tanh approximation From https://arxiv.org/pdf/1508.01292v3
f(x) = 1.7159 tanh(2x/3) where tanh is approximated as follows, tanh(y) ~ sgn(y) { 1 - 1/(1+|y|+y^2+1.41645y^4)}
Underlying implementation is in native code
Thresholded RELU
f(x) = x for x > theta, f(x) = 0 otherwise. theta defaults to 1.0
f(x) = min(max(input, cutoff), 6)
f(x) = 1 / (1 + exp(-x))
GELU activation function - Gaussian Error Linear Units
/ Parametrized Rectified Linear Unit (PReLU)
f(x) = alpha x for x < 0, f(x) = x for x >= 0
alpha has the same shape as x and is a learned parameter.
f(x) = x
f_i(x) = x_i / (1+
x_i
)
f(x) = min(1, max(0, 0.2x + 0.5))
f_i(x) = exp(x_i - shift) / sum_j exp(x_j - shift) where shift = max_i(x_i)
f(x) = x^3
f(x) = max(0,x) + alpha min(0, x)
alpha is drawn from uniform(l,u) during training and is set to l+u/2 during test l and u default to 1/8 and 1/3 respectively
f(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
https://arxiv.org/pdf/1706.02515.pdf
Leaky RELU f(x) = max(0, x) + alpha min(0, x) alpha defaults to 0.01
f(x) = x sigmoid(x)
f(x) = log(1+e^x)