[python] How to initialize weights in PyTorch?

How to initialize the weights and biases (for example, with He or Xavier initialization) in a network in PyTorch?

Cuz I haven't had the enough reputation so far, I can't add a comment under

the answer posted by prosti in Jun 26 '19 at 13:16.

    def reset_parameters(self):
        init.kaiming_uniform_(self.weight, a=math.sqrt(3))
        if self.bias is not None:
            fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight)
            bound = 1 / math.sqrt(fan_in)
            init.uniform_(self.bias, -bound, bound)

But I wanna point out that actually we know some assumptions in the paper of Kaiming He, Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification, are not appropriate, though it looks like the deliberately designed initialization method makes a hit in practice.

E.g., within the subsection of Backward Propagation Case, they assume that $w_l$ and $\delta y_l$ are independent of each other. But as we all known, take the score map $\delta y^L_i$ as an instance, it often is $y_i-softmax(y^L_i)=y_i-softmax(w^L_ix^L_i)$ if we use a typical cross entropy loss function objective.

So I think the true underlying reason why He's Initialization works well remains to unravel. Cuz everyone has witnessed its power on boosting deep learning training.

To initialize layers you typically don't need to do anything.

PyTorch will do it for you. If you think about, this has lot of sense. Why should we initialize layers, when PyTorch can do that following the latest trends.

Check for instance the Linear layer.

In the __init__ method it will call Kaiming He init function.

    def reset_parameters(self):
        init.kaiming_uniform_(self.weight, a=math.sqrt(3))
        if self.bias is not None:
            fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight)
            bound = 1 / math.sqrt(fan_in)
            init.uniform_(self.bias, -bound, bound)

The similar is for other layers types. For conv2d for instance check here.

To note : The gain of proper initialization is the faster training speed. If your problem deserves special initialization you can do it afterwords.

Iterate over parameters

If you cannot use apply for instance if the model does not implement Sequential directly:

Same for all

# see UNet at https://github.com/milesial/Pytorch-UNet/tree/master/unet


def init_all(model, init_func, *params, **kwargs):
    for p in model.parameters():
        init_func(p, *params, **kwargs)

model = UNet(3, 10)
init_all(model, torch.nn.init.normal_, mean=0., std=1) 
# or
init_all(model, torch.nn.init.constant_, 1.) 

Depending on shape

def init_all(model, init_funcs):
    for p in model.parameters():
        init_func = init_funcs.get(len(p.shape), init_funcs["default"])
        init_func(p)

model = UNet(3, 10)
init_funcs = {
    1: lambda x: torch.nn.init.normal_(x, mean=0., std=1.), # can be bias
    2: lambda x: torch.nn.init.xavier_normal_(x, gain=1.), # can be weight
    3: lambda x: torch.nn.init.xavier_uniform_(x, gain=1.), # can be conv1D filter
    4: lambda x: torch.nn.init.xavier_uniform_(x, gain=1.), # can be conv2D filter
    "default": lambda x: torch.nn.init.constant(x, 1.), # everything else
}

init_all(model, init_funcs)

You can try with torch.nn.init.constant_(x, len(x.shape)) to check that they are appropriately initialized:

init_funcs = {
    "default": lambda x: torch.nn.init.constant_(x, len(x.shape))
}

If you want some extra flexibility, you can also set the weights manually.

Say you have input of all ones:

import torch
import torch.nn as nn

input = torch.ones((8, 8))
print(input)

tensor([[1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.],
        [1., 1., 1., 1., 1., 1., 1., 1.]])

And you want to make a dense layer with no bias (so we can visualize):

d = nn.Linear(8, 8, bias=False)

Set all the weights to 0.5 (or anything else):

d.weight.data = torch.full((8, 8), 0.5)
print(d.weight.data)

The weights:

Out[14]: 
tensor([[0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
        [0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
        [0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
        [0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
        [0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
        [0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
        [0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
        [0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000, 0.5000]])

All your weights are now 0.5. Pass the data through:

d(input)

Out[13]: 
tensor([[4., 4., 4., 4., 4., 4., 4., 4.],
        [4., 4., 4., 4., 4., 4., 4., 4.],
        [4., 4., 4., 4., 4., 4., 4., 4.],
        [4., 4., 4., 4., 4., 4., 4., 4.],
        [4., 4., 4., 4., 4., 4., 4., 4.],
        [4., 4., 4., 4., 4., 4., 4., 4.],
        [4., 4., 4., 4., 4., 4., 4., 4.],
        [4., 4., 4., 4., 4., 4., 4., 4.]], grad_fn=<MmBackward>)

Remember that each neuron receives 8 inputs, all of which have weight 0.5 and value of 1 (and no bias), so it sums up to 4 for each.

We compare different mode of weight-initialization using the same neural-network(NN) architecture.

All Zeros or Ones

If you follow the principle of Occam's razor, you might think setting all the weights to 0 or 1 would be the best solution. This is not the case.

With every weight the same, all the neurons at each layer are producing the same output. This makes it hard to decide which weights to adjust.

    # initialize two NN's with 0 and 1 constant weights
    model_0 = Net(constant_weight=0)
    model_1 = Net(constant_weight=1)

• After 2 epochs:

Validation Accuracy
9.625% -- All Zeros
10.050% -- All Ones
Training Loss
2.304  -- All Zeros
1552.281  -- All Ones

Uniform Initialization

A uniform distribution has the equal probability of picking any number from a set of numbers.

Let's see how well the neural network trains using a uniform weight initialization, where low=0.0 and high=1.0.

Below, we'll see another way (besides in the Net class code) to initialize the weights of a network. To define weights outside of the model definition, we can:

1. Define a function that assigns weights by the type of network layer, then
2. Apply those weights to an initialized model using model.apply(fn), which applies a function to each model layer.

    # takes in a module and applies the specified weight initialization
    def weights_init_uniform(m):
        classname = m.__class__.__name__
        # for every Linear layer in a model..
        if classname.find('Linear') != -1:
            # apply a uniform distribution to the weights and a bias=0
            m.weight.data.uniform_(0.0, 1.0)
            m.bias.data.fill_(0)

    model_uniform = Net()
    model_uniform.apply(weights_init_uniform)

• After 2 epochs:

Validation Accuracy
36.667% -- Uniform Weights
Training Loss
3.208  -- Uniform Weights

General rule for setting weights

The general rule for setting the weights in a neural network is to set them to be close to zero without being too small.

Good practice is to start your weights in the range of [-y, y] where y=1/sqrt(n)
(n is the number of inputs to a given neuron).

    # takes in a module and applies the specified weight initialization
    def weights_init_uniform_rule(m):
        classname = m.__class__.__name__
        # for every Linear layer in a model..
        if classname.find('Linear') != -1:
            # get the number of the inputs
            n = m.in_features
            y = 1.0/np.sqrt(n)
            m.weight.data.uniform_(-y, y)
            m.bias.data.fill_(0)

    # create a new model with these weights
    model_rule = Net()
    model_rule.apply(weights_init_uniform_rule)

below we compare performance of NN, weights initialized with uniform distribution [-0.5,0.5) versus the one whose weight is initialized using general rule

• After 2 epochs:

Validation Accuracy
75.817% -- Centered Weights [-0.5, 0.5)
85.208% -- General Rule [-y, y)
Training Loss
0.705  -- Centered Weights [-0.5, 0.5)
0.469  -- General Rule [-y, y)

normal distribution to initialize the weights

The normal distribution should have a mean of 0 and a standard deviation of y=1/sqrt(n), where n is the number of inputs to NN

    ## takes in a module and applies the specified weight initialization
    def weights_init_normal(m):
        '''Takes in a module and initializes all linear layers with weight
           values taken from a normal distribution.'''

        classname = m.__class__.__name__
        # for every Linear layer in a model
        if classname.find('Linear') != -1:
            y = m.in_features
        # m.weight.data shoud be taken from a normal distribution
            m.weight.data.normal_(0.0,1/np.sqrt(y))
        # m.bias.data should be 0
            m.bias.data.fill_(0)

below we show the performance of two NN one initialized using uniform-distribution and the other using normal-distribution

• After 2 epochs:

Validation Accuracy
85.775% -- Uniform Rule [-y, y)
84.717% -- Normal Distribution
Training Loss
0.329  -- Uniform Rule [-y, y)
0.443  -- Normal Distribution

    import torch.nn as nn        

    # a simple network
    rand_net = nn.Sequential(nn.Linear(in_features, h_size),
                             nn.BatchNorm1d(h_size),
                             nn.ReLU(),
                             nn.Linear(h_size, h_size),
                             nn.BatchNorm1d(h_size),
                             nn.ReLU(),
                             nn.Linear(h_size, 1),
                             nn.ReLU())

    # initialization function, first checks the module type,
    # then applies the desired changes to the weights
    def init_normal(m):
        if type(m) == nn.Linear:
            nn.init.uniform_(m.weight)

    # use the modules apply function to recursively apply the initialization
    rand_net.apply(init_normal)

Sorry for being so late, I hope my answer will help.

To initialise weights with a normal distribution use:

torch.nn.init.normal_(tensor, mean=0, std=1)

Or to use a constant distribution write:

torch.nn.init.constant_(tensor, value)

Or to use an uniform distribution:

torch.nn.init.uniform_(tensor, a=0, b=1) # a: lower_bound, b: upper_bound

You can check other methods to initialise tensors here

If you see a deprecation warning (@Fábio Perez)...

def init_weights(m):
    if type(m) == nn.Linear:
        torch.nn.init.xavier_uniform_(m.weight)
        m.bias.data.fill_(0.01)

net = nn.Sequential(nn.Linear(2, 2), nn.Linear(2, 2))
net.apply(init_weights)

Here is the better way, just pass your whole model

import torch.nn as nn
def initialize_weights(model):
    # Initializes weights according to the DCGAN paper
    for m in model.modules():
        if isinstance(m, (nn.Conv2d, nn.ConvTranspose2d, nn.BatchNorm2d)):
            nn.init.normal_(m.weight.data, 0.0, 0.02)
        # if you also want for linear layers ,add one more elif condition