6.5. Custom Layers
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One factor behind deep learning’s success is the availability of a wide range of layers that can be composed in creative ways to design architectures suitable for a wide variety of tasks. For instance, researchers have invented layers specifically for handling images, text, looping over sequential data, and performing dynamic programming. Sooner or later, you will need a layer that does not exist yet in the deep learning framework. In these cases, you must build a custom layer. In this section, we show you how.

import torch
from torch import nn
from torch.nn import functional as F
from d2l import torch as d2l
from mxnet import np, npx
from mxnet.gluon import nn
from d2l import mxnet as d2l

import jax
from flax import linen as nn
from jax import numpy as jnp
from d2l import jax as d2l
No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)
import tensorflow as tf
from d2l import tensorflow as d2l

6.5.1. Layers without Parameters

To start, we construct a custom layer that does not have any parameters of its own. This should look familiar if you recall our introduction to modules in Section 6.1. The following CenteredLayer class simply subtracts the mean from its input. To build it, we simply need to inherit from the base layer class and implement the forward propagation function.

class CenteredLayer(nn.Module):
    def __init__(self):

    def forward(self, X):
        return X - X.mean()
class CenteredLayer(nn.Block):
    def __init__(self, **kwargs):

    def forward(self, X):
        return X - X.mean()
class CenteredLayer(nn.Module):
    def __call__(self, X):
        return X - X.mean()
class CenteredLayer(tf.keras.Model):
    def __init__(self):

    def call(self, X):
        return X - tf.reduce_mean(X)

Let’s verify that our layer works as intended by feeding some data through it.

layer = CenteredLayer()
layer(torch.tensor([1.0, 2, 3, 4, 5]))
tensor([-2., -1.,  0.,  1.,  2.])
layer = CenteredLayer()
layer(np.array([1.0, 2, 3, 4, 5]))
[21:49:18] ../src/storage/storage.cc:196: Using Pooled (Naive) StorageManager for CPU
array([-2., -1.,  0.,  1.,  2.])
layer = CenteredLayer()
layer(jnp.array([1.0, 2, 3, 4, 5]))
Array([-2., -1.,  0.,  1.,  2.], dtype=float32)
layer = CenteredLayer()
layer(tf.constant([1.0, 2, 3, 4, 5]))
<tf.Tensor: shape=(5,), dtype=float32, numpy=array([-2., -1.,  0.,  1.,  2.], dtype=float32)>

We can now incorporate our layer as a component in constructing more complex models.

net = nn.Sequential(nn.LazyLinear(128), CenteredLayer())
net = nn.Sequential()
net.add(nn.Dense(128), CenteredLayer())
net = nn.Sequential([nn.Dense(128), CenteredLayer()])
net = tf.keras.Sequential([tf.keras.layers.Dense(128), CenteredLayer()])

As an extra sanity check, we can send random data through the network and check that the mean is in fact 0. Because we are dealing with floating point numbers, we may still see a very small nonzero number due to quantization.

Y = net(torch.rand(4, 8))
tensor(-6.5193e-09, grad_fn=<MeanBackward0>)
Y = net(np.random.rand(4, 8))

Here we utilize the init_with_output method which returns both the output of the network as well as the parameters. In this case we only focus on the output.

Y, _ = net.init_with_output(d2l.get_key(), jax.random.uniform(d2l.get_key(),
                                                              (4, 8)))
Array(-3.7252903e-09, dtype=float32)
Y = net(tf.random.uniform((4, 8)))
<tf.Tensor: shape=(), dtype=float32, numpy=-1.8626451e-09>

6.5.2. Layers with Parameters

Now that we know how to define simple layers, let’s move on to defining layers with parameters that can be adjusted through training. We can use built-in functions to create parameters, which provide some basic housekeeping functionality. In particular, they govern access, initialization, sharing, saving, and loading model parameters. This way, among other benefits, we will not need to write custom serialization routines for every custom layer.

Now let’s implement our own version of the fully connected layer. Recall that this layer requires two parameters, one to represent the weight and the other for the bias. In this implementation, we bake in the ReLU activation as a default. This layer requires two input arguments: in_units and units, which denote the number of inputs and outputs, respectively.

class MyLinear(nn.Module):
    def __init__(self, in_units, units):
        self.weight = nn.Parameter(torch.randn(in_units, units))
        self.bias = nn.Parameter(torch.randn(units,))

    def forward(self, X):
        linear = torch.matmul(X, self.weight.data) + self.bias.data
        return F.relu(linear)

Next, we instantiate the MyLinear class and access its model parameters.

linear = MyLinear(5, 3)
Parameter containing:
tensor([[ 0.4783,  0.4284, -0.0899],
        [-0.6347,  0.2913, -0.0822],
        [-0.4325, -0.1645, -0.3274],
        [ 1.1898,  0.6482, -1.2384],
        [-0.1479,  0.0264, -0.9597]], requires_grad=True)
class MyDense(nn.Block):
    def __init__(self, units, in_units, **kwargs):
        self.weight = self.params.get('weight', shape=(in_units, units))
        self.bias = self.params.get('bias', shape=(units,))

    def forward(self, x):
        linear = np.dot(x, self.weight.data(ctx=x.ctx)) + self.bias.data(
        return npx.relu(linear)

Next, we instantiate the MyDense class and access its model parameters.

dense = MyDense(units=3, in_units=5)
mydense0_ (
  Parameter mydense0_weight (shape=(5, 3), dtype=<class 'numpy.float32'>)
  Parameter mydense0_bias (shape=(3,), dtype=<class 'numpy.float32'>)
class MyDense(nn.Module):
    in_units: int
    units: int

    def setup(self):
        self.weight = self.param('weight', nn.initializers.normal(stddev=1),
                                 (self.in_units, self.units))
        self.bias = self.param('bias', nn.initializers.zeros, self.units)

    def __call__(self, X):
        linear = jnp.matmul(X, self.weight) + self.bias
        return nn.relu(linear)

Next, we instantiate the MyDense class and access its model parameters.

dense = MyDense(5, 3)
params = dense.init(d2l.get_key(), jnp.zeros((3, 5)))
    params: {
        weight: Array([[-0.23823419, -0.70915407,  0.72494346],
               [ 0.2568525 , -0.20872341, -0.8993567 ],
               [ 0.80883664,  0.16673394,  0.75610644],
               [-0.35652584,  0.13841456, -1.0971175 ],
               [ 0.3117082 ,  1.2280334 , -1.0946037 ]], dtype=float32),
        bias: Array([0., 0., 0.], dtype=float32),
class MyDense(tf.keras.Model):
    def __init__(self, units):
        self.units = units

    def build(self, X_shape):
        self.weight = self.add_weight(name='weight',
            shape=[X_shape[-1], self.units],
        self.bias = self.add_weight(
            name='bias', shape=[self.units],

    def call(self, X):
        linear = tf.matmul(X, self.weight) + self.bias
        return tf.nn.relu(linear)

Next, we instantiate the MyDense class and access its model parameters.

dense = MyDense(3)
dense(tf.random.uniform((2, 5)))
[array([[-0.01007051, -0.05935554,  0.03142897],
        [ 0.02453684, -0.01833588, -0.03096254],
        [-0.09680572, -0.01736571, -0.00858052],
        [-0.02245625,  0.02958351, -0.05780673],
        [ 0.03997313,  0.01949595, -0.00150928]], dtype=float32),
 array([0., 0., 0.], dtype=float32)]

We can directly carry out forward propagation calculations using custom layers.

linear(torch.rand(2, 5))
tensor([[0.0000, 0.9316, 0.0000],
        [0.1808, 1.4208, 0.0000]])
dense(np.random.uniform(size=(2, 5)))
array([[0.        , 0.01633355, 0.        ],
       [0.        , 0.01581812, 0.        ]])
dense.apply(params, jax.random.uniform(d2l.get_key(),
                                       (2, 5)))
Array([[0.3850514 , 0.        , 0.49188882],
       [0.46509624, 0.26056105, 0.        ]], dtype=float32)
dense(tf.random.uniform((2, 5)))
<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[0., 0., 0.],
       [0., 0., 0.]], dtype=float32)>

We can also construct models using custom layers. Once we have that we can use it just like the built-in fully connected layer.

net = nn.Sequential(MyLinear(64, 8), MyLinear(8, 1))
net(torch.rand(2, 64))
tensor([[ 0.0000],
net = nn.Sequential()
net.add(MyDense(8, in_units=64),
        MyDense(1, in_units=8))
net(np.random.uniform(size=(2, 64)))
       [0.0615553 ]])
net = nn.Sequential([MyDense(64, 8), MyDense(8, 1)])
Y, _ = net.init_with_output(d2l.get_key(), jax.random.uniform(d2l.get_key(),
                                                              (2, 64)))
       [0.]], dtype=float32)
net = tf.keras.models.Sequential([MyDense(8), MyDense(1)])
net(tf.random.uniform((2, 64)))
<tf.Tensor: shape=(2, 1), dtype=float32, numpy=
array([[0.        ],
       [0.00309976]], dtype=float32)>

6.5.3. Summary

We can design custom layers via the basic layer class. This allows us to define flexible new layers that behave differently from any existing layers in the library. Once defined, custom layers can be invoked in arbitrary contexts and architectures. Layers can have local parameters, which can be created through built-in functions.

6.5.4. Exercises

  1. Design a layer that takes an input and computes a tensor reduction, i.e., it returns \(y_k = \sum_{i, j} W_{ijk} x_i x_j\).

  2. Design a layer that returns the leading half of the Fourier coefficients of the data.