## Revision 69f06e631cf7d9116b7f9a6428bde6a49c4f74e1 (click the page title to view the current version)

# Neural Networks Lecture

# Briefing

## What is a newural network

- The single Neuron
- Weighted Input
- Activation

- The network model
- Input/Output
- Weights
- Activation Function

- The Tensor Model

## Output and Loss Function

- Classification versus Regression

**MSE**

\[L = (x-y)^2\]

**CrossEntropy**

\[L = \log \frac{ \exp x_{y} } { \sum \exp x_i }\]

## Training

- Optimisation problem
- tune the weights to minimise the loss function
- if the activation function is differentiable, the entire system is
- different optimisation algorithms; trust the API or do a more advanced module

## Activation Functions

- Threshold functions
- Approximations to the threshold function
- Logistic: \(f(x) = \frac1{1+e^{-\beta x}}\)
- ReLU: \(f(x)=\max(x,0)\)
- not differentiable

## Tools

Two main contenders.

- TensorFlow
- PyTorch
- A replacement for NumPy to use the power of GPUs and other accelerators.
- An automatic differentiation library that is useful to implement neural networks.

Note that PyTorch replaces NumPy; i.e. it is primarily a python tool, and operaes in the object oriented framework of python.

The reason for using PyTorch in these examples is primarily that I have lately been working off some code created by some final year students this Spring, and they happened to choose PyTorch. The choice of TensorFlow or PyTorch is otherwise arbitrary.

## Sample Program

### Training

```
model = Inception3(num_outputs=nparams)
criterion = nn.MSELoss()
optimizer = torch.optim.Adam(model.parameters(),
model.train()
for epoch in range(num_epochs):
tloss = 0.0
for i, (images, params) in enumerate(trainloader):
optimizer.zero_grad()
output = model(images)
loss = criterion(output, params)
loss.backward()
optimizer.step()
tloss += loss.item() * len(images)
print( f"Epoch {epoch+1}: Loss = {tloss}" )
```

### Testing

```
total_loss = 0
model.eval()
with torch.no_grad():
for images, params in testloader:
output = model(images)
loss = criterion(output, params)
total_loss += loss * len(images)
```