Layer activation functions

Usage of activations

Activations can either be used through an Activation layer, or through the activation argument supported by all forward layers:

model.add(layers.Dense(64, activation=activations.relu))

This is equivalent to:

from keras import layers
from keras import activations

model.add(layers.Dense(64))
model.add(layers.Activation(activations.relu))

All built-in activations may also be passed via their string identifier:

model.add(layers.Dense(64, activation='relu'))

Available activations

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relu function

keras.activations.relu(x, negative_slope=0.0, max_value=None, threshold=0.0)

Applies the rectified linear unit activation function.

With default values, this returns the standard ReLU activation: max(x, 0), the element-wise maximum of 0 and the input tensor.

Modifying default parameters allows you to use non-zero thresholds, change the max value of the activation, and to use a non-zero multiple of the input for values below the threshold.

Examples

>>> x = [-10, -5, 0.0, 5, 10]
>>> keras.activations.relu(x)
[ 0.,  0.,  0.,  5., 10.]
>>> keras.activations.relu(x, negative_slope=0.5)
[-5. , -2.5,  0. ,  5. , 10. ]
>>> keras.activations.relu(x, max_value=5.)
[0., 0., 0., 5., 5.]
>>> keras.activations.relu(x, threshold=5.)
[-0., -0.,  0.,  0., 10.]

Arguments

• x: Input tensor.
• negative_slope: A float that controls the slope for values lower than the threshold.
• max_value: A float that sets the saturation threshold (the largest value the function will return).
• threshold: A float giving the threshold value of the activation function below which values will be damped or set to zero.

Returns

A tensor with the same shape and dtype as input x.

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sigmoid function

keras.activations.sigmoid(x)

Sigmoid activation function.

It is defined as: sigmoid(x) = 1 / (1 + exp(-x)).

For small values (<-5), sigmoid returns a value close to zero, and for large values (>5) the result of the function gets close to 1.

Sigmoid is equivalent to a 2-element softmax, where the second element is assumed to be zero. The sigmoid function always returns a value between 0 and 1.

Arguments

• x: Input tensor.

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softmax function

keras.activations.softmax(x, axis=-1)

Softmax converts a vector of values to a probability distribution.

The elements of the output vector are in range [0, 1] and sum to 1.

Each input vector is handled independently. The axis argument sets which axis of the input the function is applied along.

Softmax is often used as the activation for the last layer of a classification network because the result could be interpreted as a probability distribution.

The softmax of each vector x is computed as exp(x) / sum(exp(x)).

The input values in are the log-odds of the resulting probability.

Arguments

• x: Input tensor.
• axis: Integer, axis along which the softmax is applied.

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softplus function

keras.activations.softplus(x)

Softplus activation function.

It is defined as: softplus(x) = log(exp(x) + 1).

Arguments

• x: Input tensor.

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softsign function

keras.activations.softsign(x)

Softsign activation function.

Softsign is defined as: softsign(x) = x / (abs(x) + 1).

Arguments

• x: Input tensor.

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tanh function

keras.activations.tanh(x)

Hyperbolic tangent activation function.

It is defined as: tanh(x) = sinh(x) / cosh(x), i.e. tanh(x) = ((exp(x) - exp(-x)) / (exp(x) + exp(-x))).

Arguments

• x: Input tensor.

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selu function

keras.activations.selu(x)

Scaled Exponential Linear Unit (SELU).

The Scaled Exponential Linear Unit (SELU) activation function is defined as:

• scale * x if x > 0
• scale * alpha * (exp(x) - 1) if x < 0

where alpha and scale are pre-defined constants (alpha=1.67326324 and scale=1.05070098).

Basically, the SELU activation function multiplies scale (> 1) with the output of the keras.activations.elu function to ensure a slope larger than one for positive inputs.

The values of alpha and scale are chosen so that the mean and variance of the inputs are preserved between two consecutive layers as long as the weights are initialized correctly (see keras.initializers.LecunNormal initializer) and the number of input units is "large enough" (see reference paper for more information).

Arguments

• x: Input tensor.

Notes:

• To be used together with the keras.initializers.LecunNormal initializer.
• To be used together with the dropout variant keras.layers.AlphaDropout (rather than regular dropout).

Reference

• Klambauer et al., 2017

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elu function

keras.activations.elu(x, alpha=1.0)

Exponential Linear Unit.

The exponential linear unit (ELU) with alpha > 0 is defined as:

• x if x > 0
• alpha * exp(x) - 1 if x < 0

ELUs have negative values which pushes the mean of the activations closer to zero.

Mean activations that are closer to zero enable faster learning as they bring the gradient closer to the natural gradient. ELUs saturate to a negative value when the argument gets smaller. Saturation means a small derivative which decreases the variation and the information that is propagated to the next layer.

Arguments

• x: Input tensor.

Reference

• Clevert et al., 2016

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exponential function

keras.activations.exponential(x)

Exponential activation function.

Arguments

• x: Input tensor.

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leaky_relu function

keras.activations.leaky_relu(x, negative_slope=0.2)

Leaky relu activation function.

Arguments

• x: Input tensor.
• negative_slope: A float that controls the slope for values lower than the threshold.

[source]

relu6 function

keras.activations.relu6(x)

Relu6 activation function.

It's the ReLU function, but truncated to a maximum value of 6.

Arguments

• x: Input tensor.

[source]

silu function

keras.activations.silu(x)

Swish (or Silu) activation function.

It is defined as: swish(x) = x * sigmoid(x).

The Swish (or Silu) activation function is a smooth, non-monotonic function that is unbounded above and bounded below.

Arguments

• x: Input tensor.

Reference

• Ramachandran et al., 2017

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hard_silu function

keras.activations.hard_silu(x)

Hard SiLU activation function, also known as Hard Swish.

It is defined as:

• 0 if if x < -3
• x if x > 3
• x * (x + 3) / 6 if -3 <= x <= 3

It's a faster, piecewise linear approximation of the silu activation.

Arguments

• x: Input tensor.

Reference

• A Howard, 2019

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gelu function

keras.activations.gelu(x, approximate=False)

Gaussian error linear unit (GELU) activation function.

The Gaussian error linear unit (GELU) is defined as:

gelu(x) = x * P(X <= x) where P(X) ~ N(0, 1), i.e. gelu(x) = 0.5 * x * (1 + erf(x / sqrt(2))).

GELU weights inputs by their value, rather than gating inputs by their sign as in ReLU.

Arguments

• x: Input tensor.
• approximate: A bool, whether to enable approximation.

Reference

• Hendrycks et al., 2016

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hard_sigmoid function

keras.activations.hard_sigmoid(x)

Hard sigmoid activation function.

The hard sigmoid activation is defined as:

• 0 if if x <= -3
• 1 if x >= 3
• (x/6) + 0.5 if -3 < x < 3

It's a faster, piecewise linear approximation of the sigmoid activation.

Arguments

• x: Input tensor.

Reference

• Wikipedia "Hard sigmoid"

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linear function

keras.activations.linear(x)

Linear activation function (pass-through).

A "linear" activation is an identity function: it returns the input, unmodified.

Arguments

• x: Input tensor.

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mish function

keras.activations.mish(x)

Mish activation function.

It is defined as:

mish(x) = x * tanh(softplus(x))

where softplus is defined as:

softplus(x) = log(exp(x) + 1)

Arguments

• x: Input tensor.

Reference

• Misra, 2019

[source]

log_softmax function

keras.activations.log_softmax(x, axis=-1)

Log-Softmax activation function.

Each input vector is handled independently. The axis argument sets which axis of the input the function is applied along.

Arguments

• x: Input tensor.
• axis: Integer, axis along which the softmax is applied.

Creating custom activations

You can also use a callable as an activation (in this case it should take a tensor and return a tensor of the same shape and dtype):

model.add(layers.Dense(64, activation=keras.ops.tanh))

About "advanced activation" layers

Activations that are more complex than a simple function (eg. learnable activations, which maintain a state) are available as Advanced Activation layers.