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<h2 id="usage-of-activations">Usage of activations</h2>
<p>Activations can either be used through an <code>Activation</code> layer, or through the <code>activation</code> argument supported by all forward layers:</p>
<pre><code class="python">from keras.layers import Activation, Dense
model.add(Dense(64))
model.add(Activation('tanh'))
</code></pre>
<p>This is equivalent to:</p>
<pre><code class="python">model.add(Dense(64, activation='tanh'))
</code></pre>
<p>You can also pass an element-wise TensorFlow/Theano/CNTK function as an activation:</p>
<pre><code class="python">from keras import backend as K
model.add(Dense(64, activation=K.tanh))
</code></pre>
<h2 id="available-activations">Available activations</h2>
<h3 id="elu">elu</h3>
<pre><code class="python">keras.activations.elu(x, alpha=1.0)
</code></pre>
<p>Exponential linear unit.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
<li><strong>alpha</strong>: A scalar, slope of negative section.</li>
</ul>
<p><strong>Returns</strong></p>
<p>The exponential linear activation: <code>x</code> if <code>x > 0</code> and
<code>alpha * (exp(x)-1)</code> if <code>x < 0</code>.</p>
<p><strong>References</strong></p>
<ul>
<li><a href="https://arxiv.org/abs/1511.07289">Fast and Accurate Deep Network Learning by Exponential
Linear Units (ELUs)</a></li>
</ul>
<hr />
<h3 id="softmax">softmax</h3>
<pre><code class="python">keras.activations.softmax(x, axis=-1)
</code></pre>
<p>Softmax activation function.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
<li><strong>axis</strong>: Integer, axis along which the softmax normalization is applied.</li>
</ul>
<p><strong>Returns</strong></p>
<p>Tensor, output of softmax transformation.</p>
<p><strong>Raises</strong></p>
<ul>
<li><strong>ValueError</strong>: In case <code>dim(x) == 1</code>.</li>
</ul>
<hr />
<h3 id="selu">selu</h3>
<pre><code class="python">keras.activations.selu(x)
</code></pre>
<p>Scaled Exponential Linear Unit (SELU).</p>
<p>SELU is equal to: <code>scale * elu(x, alpha)</code>, where alpha and scale
are predefined constants. The values of <code>alpha</code> and <code>scale</code> 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 <code>lecun_normal</code> initialization) and the number of inputs
is "large enough" (see references for more information).</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: A tensor or variable to compute the activation function for.</li>
</ul>
<p><strong>Returns</strong></p>
<p>The scaled exponential unit activation: <code>scale * elu(x, alpha)</code>.</p>
<p><strong>Note</strong></p>
<ul>
<li>To be used together with the initialization "lecun_normal".</li>
<li>To be used together with the dropout variant "AlphaDropout".</li>
</ul>
<p><strong>References</strong></p>
<ul>
<li><a href="https://arxiv.org/abs/1706.02515">Self-Normalizing Neural Networks</a></li>
</ul>
<hr />
<h3 id="softplus">softplus</h3>
<pre><code class="python">keras.activations.softplus(x)
</code></pre>
<p>Softplus activation function.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
</ul>
<p><strong>Returns</strong></p>
<p>The softplus activation: <code>log(exp(x) + 1)</code>.</p>
<hr />
<h3 id="softsign">softsign</h3>
<pre><code class="python">keras.activations.softsign(x)
</code></pre>
<p>Softsign activation function.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
</ul>
<p><strong>Returns</strong></p>
<p>The softsign activation: <code>x / (abs(x) + 1)</code>.</p>
<hr />
<h3 id="relu">relu</h3>
<pre><code class="python">keras.activations.relu(x, alpha=0.0, max_value=None, threshold=0.0)
</code></pre>
<p>Rectified Linear Unit.</p>
<p>With default values, it returns element-wise <code>max(x, 0)</code>.</p>
<p>Otherwise, it follows:
<code>f(x) = max_value</code> for <code>x >= max_value</code>,
<code>f(x) = x</code> for <code>threshold <= x < max_value</code>,
<code>f(x) = alpha * (x - threshold)</code> otherwise.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
<li><strong>alpha</strong>: float. Slope of the negative part. Defaults to zero.</li>
<li><strong>max_value</strong>: float. Saturation threshold.</li>
<li><strong>threshold</strong>: float. Threshold value for thresholded activation.</li>
</ul>
<p><strong>Returns</strong></p>
<p>A tensor.</p>
<hr />
<h3 id="tanh">tanh</h3>
<pre><code class="python">keras.activations.tanh(x)
</code></pre>
<p>Hyperbolic tangent activation function.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
</ul>
<p><strong>Returns</strong></p>
<p>The hyperbolic activation:
<code>tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))</code></p>
<hr />
<h3 id="sigmoid">sigmoid</h3>
<pre><code class="python">keras.activations.sigmoid(x)
</code></pre>
<p>Sigmoid activation function.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
</ul>
<p><strong>Returns</strong></p>
<p>The sigmoid activation: <code>1 / (1 + exp(-x))</code>.</p>
<hr />
<h3 id="hard_sigmoid">hard_sigmoid</h3>
<pre><code class="python">keras.activations.hard_sigmoid(x)
</code></pre>
<p>Hard sigmoid activation function.</p>
<p>Faster to compute than sigmoid activation.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
</ul>
<p><strong>Returns</strong></p>
<p>Hard sigmoid activation:</p>
<ul>
<li><code>0</code> if <code>x < -2.5</code></li>
<li><code>1</code> if <code>x > 2.5</code></li>
<li><code>0.2 * x + 0.5</code> if <code>-2.5 <= x <= 2.5</code>.</li>
</ul>
<hr />
<h3 id="exponential">exponential</h3>
<pre><code class="python">keras.activations.exponential(x)
</code></pre>
<p>Exponential (base e) activation function.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
</ul>
<p><strong>Returns</strong></p>
<p>Exponential activation: <code>exp(x)</code>.</p>
<hr />
<h3 id="linear">linear</h3>
<pre><code class="python">keras.activations.linear(x)
</code></pre>
<p>Linear (i.e. identity) activation function.</p>
<p><strong>Arguments</strong></p>
<ul>
<li><strong>x</strong>: Input tensor.</li>
</ul>
<p><strong>Returns</strong></p>
<p>Input tensor, unchanged.</p>
<h2 id="on-advanced-activations">On "Advanced Activations"</h2>
<p>Activations that are more complex than a simple TensorFlow/Theano/CNTK function (eg. learnable activations, which maintain a state) are available as <a href="../layers/advanced-activations/">Advanced Activation layers</a>, and can be found in the module <code>keras.layers.advanced_activations</code>. These include <code>PReLU</code> and <code>LeakyReLU</code>.</p>
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