Activations

Special algorithms for gradient descent.

What are activations?

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.

Usage

The recommended method to use activations is to add an activation layer in your neural network, and configure your desired activation:

GraphBuilder graphBuilder = new NeuralNetConfiguration.Builder()
// add hyperparameters and other layers
.addLayer("softmax", new ActivationLayer(Activation.SOFTMAX), "previous_input")
// add more layers and output
.build();

Available activations

ActivationRectifiedTanh

[source]

Rectified tanh

Essentially max(0, tanh(x))

Underlying implementation is in native code

ActivationELU

[source]

f(x) = alpha (exp(x) - 1.0); x < 0 = x ; x>= 0

alpha defaults to 1, if not specified

ActivationReLU

[source]

f(x) = max(0, x)

ActivationRationalTanh

[source]

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

ActivationThresholdedReLU

[source]

Thresholded RELU

f(x) = x for x > theta, f(x) = 0 otherwise. theta defaults to 1.0

ActivationReLU6

[source]

f(x) = min(max(input, cutoff), 6)

ActivationHardTanH

[source]

1, if x > 1
f(x) =-1, if x < -1
⎩ x, otherwise

ActivationSigmoid

[source]

f(x) = 1 / (1 + exp(-x))

ActivationGELU

[source]

GELU activation function - Gaussian Error Linear Units

ActivationPReLU

[source]

/ 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.

ActivationIdentity

[source]

f(x) = x

ActivationSoftSign

[source]

f_i(x) = x_i / (1+

x_i

)

ActivationHardSigmoid

[source]

f(x) = min(1, max(0, 0.2x + 0.5))

ActivationSoftmax

[source]

f_i(x) = exp(x_i - shift) / sum_j exp(x_j - shift) where shift = max_i(x_i)

ActivationCube

[source]

f(x) = x^3

ActivationRReLU

[source]

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

Empirical Evaluation of Rectified Activations in Convolutional Network

ActivationTanH

[source]

f(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))

ActivationSELU

[source]

https://arxiv.org/pdf/1706.02515.pdf

ActivationLReLU

[source]

Leaky RELU f(x) = max(0, x) + alpha min(0, x) alpha defaults to 0.01

ActivationSwish

[source]

f(x) = x sigmoid(x)

ActivationSoftPlus

[source]

f(x) = log(1+e^x)