# How to Build Your Own PyTorch Neural Network Layer from Scratch Well, for one, you’ll gain a deeper understanding of how all the pieces are put together. By comparing your code with the PyTorch code, you will gain knowledge of why and how these libraries are developed.

Also, once you’re done, you’ll have more confidence in implementing and using all these libraries, knowing how things work. There will be no myth to you.

And last but not least, you’ll be able to modify/tweak these modules should the situation require. And this is the difference between a noob and a pro.

OK, enough of the motivation, let’s get to it.

## Simple MNIST one layer NN as the backdrop

First of all, we need some ‘backdrop’ codes to test whether and how well our module performs. Let’s build a very simple one-layer neural network to solve the good-old MNIST dataset. The code (running in Jupyter Notebook) snippet below:

``````# We'll use fast.ai to showcase how to build your own 'nn.Linear' module
%matplotlib inline
from fastai.basics import *
import sys

path = Config().data_path()/'mnist'
path.mkdir(parents=True)
!wget http://deeplearning.net/data/mnist/mnist.pkl.gz -P {path}

with gzip.open(path/'mnist.pkl.gz', 'rb') as f:
((x_train, y_train), (x_valid, y_valid), _) = pickle.load(f, encoding='latin-1')

# Have a look at the images and shape
plt.imshow(x_train.reshape((28,28)), cmap="gray")
x_train.shape

# convert numpy into PyTorch tensor
x_train,y_train,x_valid,y_valid = map(torch.tensor, (x_train,y_train,x_valid,y_valid))
n,c = x_train.shape
x_train.shape, y_train.min(), y_train.max()

# prepare dataset and create fast.ai DataBunch for training
bs=64
train_ds = TensorDataset(x_train, y_train)
valid_ds = TensorDataset(x_valid, y_valid)
data = DataBunch.create(train_ds, valid_ds, bs=bs)

# create a simple MNIST logistic model with only one Linear layer
class Mnist_Logistic(nn.Module):
def __init__(self):
super().__init__()
self.lin = nn.Linear(784, 10, bias=True)

def forward(self, xb): return self.lin(xb)

model =Mnist_Logistic()

lr=2e-2
loss_func = nn.CrossEntropyLoss()

# define update function with weight decay
def update(x,y,lr):
wd = 1e-5
y_hat = model(x)
# weight decay
w2 = 0.
for p in model.parameters(): w2 += (p**2).sum()
loss = loss_func(y_hat, y) + w2*wd

loss.backward()
for p in model.parameters():
return loss.item()

# iterate through one epoch and plot losses
losses = [update(x,y,lr) for x,y in data.train_dl]
plt.plot(losses);`````` These codes are quite self-explanatory. We used the fast.ai library for this project. Download the MNIST pickle file and unzip it, transfer it into a PyTorch tensor, then stuff it into a fast.ai DataBunch object for further training. Then we created a simple neural network with only one

``Linear ``

layer. We also write our own

``update ``

``torch.optim``

optimizers since we could be writing our own optimizers from scratch as the next step of our PyTorch learning journey. Finally, we iterate through the dataset and plot the losses to see whether and how well it works.

## First Iteration: Just make it work

All PyTorch modules/layers are extended from the

``torch.nn.Module``

.

``````class myLinear(nn.Module):
``````
Within the class, we’ll need an

``__init__ ``

dunder function to initialize our linear layer and a

``forward ``

function to do the forward calculation. Let’s look at the

``__init__ ``

function first.

We’ll use the PyTorch official document as a guideline to build our module. From the document, an

``nn.Linear``

module has the following attributes: So we’ll get these three attributes in:

``````def __init__(self, in_features, out_features, bias=True):
super().__init__()
self.in_features = in_features
self.out_features = out_features
self.bias = bias``````

The class also needs to hold weight and bias parameters so it can be trained. We also initialize those. ``````self.weight = torch.nn.Parameter(torch.randn(out_features, in_features))
self.bias = torch.nn.Parameter(torch.randn(out_features))``````
Here we used

``torch.nn.Parameter``

to set our

``weight ``

and

``bias``

, otherwise, it won’t train.

Also, note that we used

``torch.randn``

instead of what’s described in the document to initialize the parameters. This is not the best way of doing weights initialization, but our purpose is to get it to work first, we’ll tweak it in our next iteration.

OK, now that the

``__init__ ``

part is done, let’s move on to

``forward ``

function. This is actually the easy part:

``````def forward(self, input):
_, y = input.shape
if y != self.in_features:
sys.exit(f'Wrong Input Features. Please use tensor with {self.in_features} Input Features')
output = input @ self.weight.t() + self.bias
return output``````

We first get the shape of the input, figure out how many columns are in the input, then check whether the input size match. Then we do the matrix multiplication (Note we did a transpose here to align the weights) and return the results. We can test whether it works by giving it some data:

``````my = myLinear(20,10)
a = torch.randn(5,20)
my(a)``````

We have a 5×20 input, it goes through our layer and gets a 5×10 output. You should get results like this: OK, now go back to our neural network codes and find the Mnist_Logistic class, change

``self.lin = nn.Linear(784,10, bias=True)``

to

``self.lin = myLinear(784, 10, bias=True)``

. Run the code, you should see something like this plot: As you can see it doesn’t converge quite well (around 2.5 loss with one epoch). That’s probably because of our poor initialization. Also, we didn’t take care of the

``bias ``

part. Let’s fix that in the next iteration. The final code for iteration 1 looks like this:

``````class myLinear(nn.Module):
def __init__(self, in_features, out_features, bias=True):
super().__init__()
self.in_features = in_features
self.out_features = out_features
self.bias = bias
self.weight = torch.nn.Parameter(torch.randn(out_features, in_features))
self.bias = torch.nn.Parameter(torch.randn(out_features))

def forward(self, input):
x, y = input.shape
if y != self.in_features:
sys.exit(f'Wrong Input Features. Please use tensor with {self.in_features} Input Features')
output = input @ self.weight.t() + self.bias
return output``````

## Second iteration: Proper weight initialization and bias handling

We’ve handled

``__init__ ``

and

``forward``

, but remember we also have a

``bias ``

attribute that if

``False``

, will not learn additive bias. We have not implemented that yet. Also, we used

``torch.nn.randn``

to initialize the weight and bias, which is not optimum. Let’s fix this. The updated

``__init__ ``

function looks like this:

``````def __init__(self, in_features, out_features, bias=True):
super().__init__()
self.in_features = in_features
self.out_features = out_features
self.bias = bias
self.weight = torch.nn.Parameter(torch.Tensor(out_features, in_features))
if bias:
self.bias = torch.nn.Parameter(torch.Tensor(out_features))
else:
self.register_parameter('bias', None)
self.reset_parameters()``````
First of all, when we create the

``weight ``

and

``bias ``

parameters, we didn’t initialize them as the last iteration. We just allocate a regular Tensor object to it. The actual initialization is done in another function

``reset_parameters``

(will explain later).

For

``bias``

, we added a condition that if

``True``

, do what we did the last iteration, but if

``False``

, will use

``register_parameter``

(‘bias’, None) to give it

``None ``

value. Now for

``reset_parameter ``

function, it looks like this:

``````def reset_parameters(self):
torch.nn.init.kaiming_uniform_(self.weight, a=math.sqrt(5))
if self.bias is not None:
fan_in, _ torch.nn.init._calculate_fan_in_and_fan_out(self.weight)
bound = 1 / math.sqrt(fan_in)
torch.nn.init.uniform_(self.bias, -bound, bound)`````` What it actually does is by initializing weight with a normal distribution with mean 0 and variance

``bound``

, it avoids the issue of vanishing/exploding gradients issue(though we only have one layer here, when writing the Linear class, we should still keep MLN in mind).

Notice that for

``self.weight``

, we actually give the a

``a``

value of

``math.sqrt(5)``

``math.sqrt(fan_in)``

, this is explained in this GitHub issue of PyTorch repo for whom might be interested.

``extra_repr ``

string to the model:

``````def extra_repr(self):
return 'in_features={}, out_features={}, bias={}'.format(
self.in_features, self.out_features, self.bias is not None
)``````

The final model looks like this:

``````class myLinear(nn.Module):
def __init__(self, in_features, out_features, bias=True):
super().__init__()
self.in_features = in_features
self.out_features = out_features
self.bias = bias
self.weight = torch.nn.Parameter(torch.Tensor(out_features, in_features))
if bias:
self.bias = torch.nn.Parameter(torch.Tensor(out_features))
else:
self.register_parameter('bias', None)
self.reset_parameters()

def reset_parameters(self):
torch.nn.init.kaiming_uniform_(self.weight, a=math.sqrt(5))
if self.bias is not None:
fan_in, _ = torch.nn.init._calculate_fan_in_and_fan_out(self.weight)
bound = 1 / math.sqrt(fan_in)
torch.nn.init.uniform_(self.bias, -bound, bound)

def forward(self, input):
x, y = input.shape
if y != self.in_features:
print(f'Wrong Input Features. Please use tensor with {self.in_features} Input Features')
return 0
output = input.matmul(weight.t())
if bias is not None:
output += bias
ret = output
return ret

def extra_repr(self):
return 'in_features={}, out_features={}, bias={}'.format(
self.in_features, self.out_features, self.bias is not None
)``````

Rerun the code, you should be able to see this plot: We can see it converges much faster to a 0.5 loss in one epoch.

## Conclusion

I hope this helps you clear the cloud on these PyTorch

``nn.modules``

a bit. It might seem boring and redundant, but sometimes the fastest( and shortest) way is the ‘boring’ way. Once you get to the very bottom of this, the feeling of knowing that there’s nothing ‘more’ is priceless. You’ll come to the realization that:

Underneath PyTorch, there’s no trick, no myth, no catch, just rock-solid Python code.

Also by writing your own code, then compare it with official source code, you’ll be able to see where the difference is and learn from the best in the industry. How cool is that?

Previously published at https://towardsdatascience.com/how-to-build-your-own-pytorch-neural-network-layer-from-scratch-842144d623f6

Don't forget to share