# Layers¶

The lasagne.layers module provides various classes representing the layers of a neural network. All of them are subclasses of the lasagne.layers.Layer base class.

## Creating a layer¶

A layer can be created as an instance of a Layer subclass. For example, a dense layer can be created as follows:

>>> import lasagne
>>> l = lasagne.layers.DenseLayer(l_in, num_units=100)


This will create a dense layer with 100 units, connected to another layer l_in.

## Creating a network¶

Note that for almost all types of layers, you will have to specify one or more other layers that the layer you are creating gets its input from. The main exception is InputLayer, which can be used to represent the input of a network.

Chaining layer instances together like this will allow you to specify your desired network structure. Note that the same layer can be used as input to multiple other layers, allowing for arbitrary tree and directed acyclic graph (DAG) structures.

Here is an example of an MLP with a single hidden layer:

>>> import theano.tensor as T
>>> l_in = lasagne.layers.InputLayer((100, 50))
>>> l_hidden = lasagne.layers.DenseLayer(l_in, num_units=200)
>>> l_out = lasagne.layers.DenseLayer(l_hidden, num_units=10,
...                                   nonlinearity=T.nnet.softmax)


The first layer of the network is an InputLayer, which represents the input. When creating an input layer, you should specify the shape of the input data. In this example, the input is a matrix with shape (100, 50), representing a batch of 100 data points, where each data point is a vector of length 50. The first dimension of a tensor is usually the batch dimension, following the established Theano and scikit-learn conventions.

The hidden layer of the network is a dense layer with 200 units, taking its input from the input layer. Note that we did not specify the nonlinearity of the hidden layer. A layer with rectified linear units will be created by default.

The output layer of the network is a dense layer with 10 units and a softmax nonlinearity, allowing for 10-way classification of the input vectors.

Note also that we did not create any object representing the entire network. Instead, the output layer instance l_out is also used to refer to the entire network in Lasagne.

## Naming layers¶

For convenience, you can name a layer by specifying the name keyword argument:

>>> l_hidden = lasagne.layers.DenseLayer(l_in, num_units=200,
...                                      name="hidden_layer")


## Initializing parameters¶

Many types of layers, such as DenseLayer, have trainable parameters. These are referred to by short names that match the conventions used in modern deep learning literature. For example, a weight matrix will usually be called W, and a bias vector will usually be b.

When creating a layer with trainable parameters, Theano shared variables will be created for them and initialized automatically. You can optionally specify your own initialization strategy by using keyword arguments that match the parameter variable names. For example:

>>> l = lasagne.layers.DenseLayer(l_in, num_units=100,
...                               W=lasagne.init.Normal(0.01))


The weight matrix W of this dense layer will be initialized using samples from a normal distribution with standard deviation 0.01 (see lasagne.init for more information).

There are several ways to manually initialize parameters:

• Theano shared variable

If a shared variable instance is provided, this is used unchanged as the parameter variable. For example:

>>> import theano
>>> import numpy as np
>>> W = theano.shared(np.random.normal(0, 0.01, (50, 100)))
>>> l = lasagne.layers.DenseLayer(l_in, num_units=100, W=W)

• numpy array

If a numpy array is provided, a shared variable is created and initialized using the array. For example:

>>> W_init = np.random.normal(0, 0.01, (50, 100))
>>> l = lasagne.layers.DenseLayer(l_in, num_units=100, W=W_init)

• callable

If a callable is provided (e.g. a function or a lasagne.init.Initializer instance), a shared variable is created and the callable is called with the desired shape to generate suitable initial parameter values. The variable is then initialized with those values. For example:

>>> l = lasagne.layers.DenseLayer(l_in, num_units=100,
...                               W=lasagne.init.Normal(0.01))


Or, using a custom initialization function:

>>> def init_W(shape):
...     return np.random.normal(0, 0.01, shape)
>>> l = lasagne.layers.DenseLayer(l_in, num_units=100, W=init_W)


Some types of parameter variables can also be set to None at initialization (e.g. biases). In that case, the parameter variable will be omitted. For example, creating a dense layer without biases is done as follows:

>>> l = lasagne.layers.DenseLayer(l_in, num_units=100, b=None)


## Parameter sharing¶

Parameter sharing between multiple layers can be achieved by using the same Theano shared variable instance for their parameters. For example:

>>> l1 = lasagne.layers.DenseLayer(l_in, num_units=100)
>>> l2 = lasagne.layers.DenseLayer(l_in, num_units=100, W=l1.W)


These two layers will now share weights (but have separate biases).

## Propagating data through layers¶

To compute an expression for the output of a single layer given its input, the get_output_for() method can be used. To compute the output of a network, you should instead call lasagne.layers.get_output() on it. This will traverse the network graph.

You can call this function with the layer you want to compute the output expression for:

>>> y = lasagne.layers.get_output(l_out)


In that case, a Theano expression will be returned that represents the output in function of the input variables associated with the lasagne.layers.InputLayer instance (or instances) in the network, so given the example network from before, you could compile a Theano function to compute its output given an input as follows:

>>> f = theano.function([l_in.input_var], lasagne.layers.get_output(l_out))


You can also specify a Theano expression to use as input as a second argument to lasagne.layers.get_output():

>>> x = T.matrix('x')
>>> y = lasagne.layers.get_output(l_out, x)
>>> f = theano.function([x], y)


This only works when there is only a single InputLayer in the network. If there is more than one, you can specify input expressions in a dictionary. For example, in a network with two input layers l_in1 and l_in2 and an output layer l_out:

>>> x1 = T.matrix('x1')
>>> x2 = T.matrix('x2')
>>> y = lasagne.layers.get_output(l_out, { l_in1: x1, l_in2: x2 })


Any keyword arguments passed to get_output() are propagated to all layers. This makes it possible to control the behavior of the entire network. The main use case for this is the deterministic keyword argument, which disables stochastic behaviour such as dropout when set to True. This is useful because a deterministic output is desirable at evaluation time.

>>> y = lasagne.layers.get_output(l_out, deterministic=True)


Some networks may have multiple output layers - or you may just want to compute output expressions for intermediate layers in the network. In that case, you can pass a list of layers. For example, in a network with two output layers l_out1 and l_out2:

>>> y1, y2 = lasagne.layers.get_output([l_out1, l_out2])


You could also just call lasagne.layers.get_output() twice:

>>> y1 = lasagne.layers.get_output(l_out1)
>>> y2 = lasagne.layers.get_output(l_out2)


However, this is not recommended! Some network layers may have non-deterministic output, such as dropout layers. If you compute the network output expressions with separate calls to lasagne.layers.get_output(), they will not use the same samples. Furthermore, this may lead to unnecessary computation because Theano is not always able to merge identical computations properly. Calling get_output() only once prevents both of these issues.