With our data in-place, it’s time to coach our first Neural Network. We’ll use an identical architecture to what we’ve done within the last blog post of the series, using a Linear version of our Neural Network with the flexibility to handle linear patterns:

`from torch import nn`class LinearModel(nn.Module):

def __init__(self):

super().__init__()

self.layer_1 = nn.Linear(in_features=12, out_features=5)

self.layer_2 = nn.Linear(in_features=5, out_features=1)

def forward(self, x):

return self.layer_2(self.layer_1(x))

This neural network uses the `nn.Linear`

module from `pytorch`

to create a Neural Network with 1 deep layer (one input layer, a deep layer and an output layers).

Although we will create our own class inheriting from `nn.Module`

, we can even use (more elegantly) the `nn.Sequential`

constructor to do the identical:

`model_0 = nn.Sequential(`

nn.Linear(in_features=12, out_features=5),

nn.Linear(in_features=5, out_features=1)

)

Cool! So our Neural Network incorporates a single inner layer with 5 neurons (this may be seen by the `out_features=5`

on the primary layer).

This inner layer receives the identical variety of connections from each input neuron. The 12 in `in_features`

in the primary layer reflects the variety of features and the 1 in `out_features`

of the second layer reflects the output (a single value raging from 0 to 1).

To coach our Neural Network, we’ll define a loss function and an optimizer. We’ll define `BCEWithLogitsLoss`

(PyTorch 2.1 documentation) as this loss function (torch implementation of Binary Cross-Entropy, appropriate for classification problems) and Stochastic Gradient Descent because the optimizer (using `torch.optim.SGD`

).

`# Binary Cross entropy`

loss_fn = nn.BCEWithLogitsLoss()# Stochastic Gradient Descent for Optimizer

optimizer = torch.optim.SGD(params=model_0.parameters(),

lr=0.01)

Finally, as I’ll also need to calculate the accuracy for each epoch of coaching process, we’ll design a function to calculate that:

`def compute_accuracy(y_true, y_pred):`

tp_tn = torch.eq(y_true, y_pred).sum().item()

acc = (tp_tn / len(y_pred)) * 100

return acc

Time to coach our model! Let’s train our model for 1000 epochs and see how an easy linear network is in a position to cope with this data:

`torch.manual_seed(42)`epochs = 1000

train_acc_ev = []

test_acc_ev = []

# Construct training and evaluation loop

for epoch in range(epochs):

model_0.train()

y_logits = model_0(X_train).squeeze()

loss = loss_fn(y_logits,

y_train)

# Calculating accuracy using predicted logists

acc = compute_accuracy(y_true=y_train,

y_pred=torch.round(torch.sigmoid(y_logits)))

train_acc_ev.append(acc)

# Training steps

optimizer.zero_grad()

loss.backward()

optimizer.step()

model_0.eval()

# Inference mode for prediction on the test data

with torch.inference_mode():

test_logits = model_0(X_test).squeeze()

test_loss = loss_fn(test_logits,

y_test)

test_acc = compute_accuracy(y_true=y_test,

y_pred=torch.round(torch.sigmoid(test_logits)))

test_acc_ev.append(test_acc)

# Print out accuracy and loss every 100 epochs

if epoch % 100 == 0:

print(f"Epoch: {epoch}, Loss: {loss:.5f}, Accuracy: {acc:.2f}% | Test loss: {test_loss:.5f}, Test acc: {test_acc:.2f}%")

Unfortunately the neural network we’ve just built isn’t ok to resolve this problem. Let’s see the evolution of coaching and test accuracy:

*(I’m plotting accuracy as an alternative of loss because it is simpler to interpret on this problem)*

Interestingly, our Neural Network isn’t able improve much of the test set accuracy.

With the knowledge have from previous blog posts, we will try so as to add more layers and neurons to our neural network. Let’s attempt to do each and see the consequence:

`deeper_model = nn.Sequential(`

nn.Linear(in_features=12, out_features=20),

nn.Linear(in_features=20, out_features=20),

nn.Linear(in_features=20, out_features=1)

)

Although our deeper model is a little more complex with an additional layer and more neurons, that doesn’t translate into more performance within the network:

Though our model is more complex, that doesn’t really bring more accuracy to our classification problem.

To have the opportunity to attain more performance, we want to unlock a recent feature of Neural Networks — activation functions!

If making our model wider and bigger didn’t bring much improvement, there have to be something else that we will do with Neural Networks that may have the opportunity to enhance its performance, right?

That’s where activation functions may be used! In our example, we’ll return to our simpler model, but this time with a twist:

`model_non_linear = nn.Sequential(`

nn.Linear(in_features=12, out_features=5),

nn.ReLU(),

nn.Linear(in_features=5, out_features=1)

)

What’s the difference between this model and the primary one? The difference is that we added a recent block to our neural network — `nn.ReLU`

. The rectified linear unit is an activation function that may change the calculation in each of the weights of the Neural Network:

Every value that goes through our weights within the Neural Network will likely be computed against this function. If the worth of the feature times the load is negative, the worth is about to 0, otherwise the calculated value is assumed. Just this small change adds loads of power to a Neural Network architecture — in `torch`

we have now different activation functions we will use reminiscent of `nn.ReLU`

, `nn.Tanh`

or `nn.ELU`

. For an outline of all activation functions, check this link.

Our neural network architecture incorporates a small twist, in the intervening time:

With this small twist within the Neural Network, every value coming from the primary layer (represented by `nn.Linear(in_features=12, out_features=5)`

) can have to undergo the “ReLU” test.

Let’s see the impact of fitting this architecture on our data:

Cool! Although we see among the performance degrading after 800 epochs, this model doesn’t exhibit overfitting because the previous ones. Take note that our dataset could be very small, so there’s a likelihood that our results are higher just by randomness. Nevertheless, adding activation functions to your `torch`

models definitely has a big impact by way of performance, training and generalization, particularly when you will have loads of data to coach on.

Now that you recognize the ability of non-linear activation functions, it’s also relevant to know:

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