A neural network is a set of neuron nodes that are interconnected with one another. The neurons are not just connected to their adjacent neurons but also to the ones that are farther away.
The main idea behind neural networks is that every neuron in a layer has one or more input values, and they produce output values by applying some mathematical functions to the input. The outputs of the neurons in one layer become the inputs for the next layer.
A single layer neural network is a type of artificial neural network where there is only one hidden layer between the input and output layers. This is the classic architecture before the deep learning became popular. In this tutorial, you will get a chance to build a neural network with only a single hidden layer. Particularly, you will learn:
 How to build a single layer neural network in PyTorch.
 How to train a single layer neural network with PyTorch.
 How to classify onedimensional data using a single layer neural network.
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Overview
This tutorial is in three parts; they are

 Preparing the Dataset
 Build the Model
 Train the Model
Preparing the Data
A neural network simply a function that approximates other functions with some parameters. Let’s build some data and see how our single layer neural network approximates the function to make the data linearly separable. Later in this tutorial, you will visualize the function during training to see how the approximated function overlaps over the given set of data points.
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import torch import matplotlib.pyplot as plt # generate synthetic the data X = torch.arange(30, 30, 1).view(1, 1).type(torch.FloatTensor) Y = torch.zeros(X.shape[0]) Y[(X[:, 0] <= 10)] = 1.0 Y[(X[:, 0] > 10) & (X[:, 0] < 10)] = 0.5 Y[(X[:, 0] > 10)] = 0 
The data, as plotted using matplotlib, looks like the following.
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... plt.plot(X, Y) plt.show() 
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Build the Model with nn.Module
Next, letâ€™s build our custom module for single layer neural network with nn.Module
. Please check previous tutorials of the series if you need more information on nn.Module
.
This neural network features an input layer, a hidden layer with two neurons, and an output layer. After each layer, a sigmoid activation function is applied. Other kind of activation functions are available in PyTorch but the classic design for this network is to use sigmoid function.
Here is how your single layer neural network looks like in code.
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... # Define the class for single layer NN class one_layer_net(torch.nn.Module): # Constructor def __init__(self, input_size, hidden_neurons, output_size): super(one_layer_net, self).__init__() # hidden layer self.linear_one = torch.nn.Linear(input_size, hidden_neurons) self.linear_two = torch.nn.Linear(hidden_neurons, output_size) # defining layers as attributes self.layer_in = None self.act = None self.layer_out = None # prediction function def forward(self, x): self.layer_in = self.linear_one(x) self.act = torch.sigmoid(self.layer_in) self.layer_out = self.linear_two(self.act) y_pred = torch.sigmoid(self.linear_two(self.act)) return y_pred 
Let’s also instantiate a model object.
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# create the model model = one_layer_net(1, 2, 1) # 2 represents two neurons in one hidden layer 
Train the Model
Before starting the training loop, let’s define loss function and optimizer for the model. You will write a loss function for the cross entropy loss and use stochastic gradient descent for parameter optimization.
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def criterion(y_pred, y): out = 1 * torch.mean(y * torch.log(y_pred) + (1  y) * torch.log(1  y_pred)) return out optimizer = torch.optim.SGD(model.parameters(), lr=0.01) 
Now you have all components to train the model. Letâ€™s train the model for 5000 epochs. You will see a plot of how the neural network approximates the function after every 1000 epochs.
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# Define the training loop epochs=5000 cost = [] total=0 for epoch in range(epochs): total=0 epoch = epoch + 1 for x, y in zip(X, Y): yhat = model(x) loss = criterion(yhat, y) loss.backward() optimizer.step() optimizer.zero_grad() # get total loss total+=loss.item() cost.append(total) if epoch % 1000 == 0: print(str(epoch)+ " " + "epochs done!") # visualze results after every 1000 epochs # plot the result of function approximator plt.plot(X.numpy(), model(X).detach().numpy()) plt.plot(X.numpy(), Y.numpy(), 'm') plt.xlabel('x') plt.show() 
After 1000 epochs, the model approximated the function like the following:
But after 5000 epochs, it improves to the following:
From which, you can see the approximation in blue is closer to the data in purple. As you can see, the neural network approximates the functions quite nicely. If the function is more complex, you may need more hidden layers or more neurons in the hidden layer, i.e., a more complex model.
Let’s also plot to see how the loss reduced during training.
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# plot the cost plt.plot(cost) plt.xlabel('epochs') plt.title('cross entropy loss') plt.show() 
You should see:
Putting everything together, the following is the complete code:
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import torch import matplotlib.pyplot as plt # generate synthetic the data X = torch.arange(30, 30, 1).view(1, 1).type(torch.FloatTensor) Y = torch.zeros(X.shape[0]) Y[(X[:, 0] <= 10)] = 1.0 Y[(X[:, 0] > 10) & (X[:, 0] < 10)] = 0.5 Y[(X[:, 0] > 10)] = 0 plt.plot(X, Y) plt.show() # Define the class for single layer NN class one_layer_net(torch.nn.Module): # Constructor def __init__(self, input_size, hidden_neurons, output_size): super(one_layer_net, self).__init__() # hidden layer self.linear_one = torch.nn.Linear(input_size, hidden_neurons) self.linear_two = torch.nn.Linear(hidden_neurons, output_size) # defining layers as attributes self.layer_in = None self.act = None self.layer_out = None # prediction function def forward(self, x): self.layer_in = self.linear_one(x) self.act = torch.sigmoid(self.layer_in) self.layer_out = self.linear_two(self.act) y_pred = torch.sigmoid(self.linear_two(self.act)) return y_pred # create the model model = one_layer_net(1, 2, 1) # 2 represents two neurons in one hidden layer def criterion(y_pred, y): out = 1 * torch.mean(y * torch.log(y_pred) + (1  y) * torch.log(1  y_pred)) return out optimizer = torch.optim.SGD(model.parameters(), lr=0.01) # Define the training loop epochs=5000 cost = [] total=0 for epoch in range(epochs): total=0 epoch = epoch + 1 for x, y in zip(X, Y): yhat = model(x) loss = criterion(yhat, y) loss.backward() optimizer.step() optimizer.zero_grad() # get total loss total+=loss.item() cost.append(total) if epoch % 1000 == 0: print(str(epoch)+ " " + "epochs done!") # visualze results after every 1000 epochs # plot the result of function approximator plt.plot(X.numpy(), model(X).detach().numpy()) plt.plot(X.numpy(), Y.numpy(), 'm') plt.xlabel('x') plt.show() # plot the cost plt.plot(cost) plt.xlabel('epochs') plt.title('cross entropy loss') plt.show() 
Summary
In this tutorial, you learned how you can build and train a neural network and estimate the function. Particularly, you learned:
 How to build a single layer neural network in PyTorch.
 How to train a single layer neural network with PyTorch.
 How to classify onedimensional data using a single layer neural network.
I have followed Mr Khan’s tutorials.
First, they are clearly written and secondly a byproduct of his tutorials are the application of instatiating classes and inheritance from superior classes and implementaion of inherited classes.
Thank you,
Anthony of Sydney
Hi, followed the code, using jupyter notebook, works well.
The epochs calculations takes time. How can I convert the code to run with CUDA, to accelarate the speed?
Hi Alex.A…The following resource is a great starting point:
https://www.vincentlunot.com/post/anintroductiontocudainpythonpart1/