# Briefing

## What is a neural 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
• Two-class classification (0 or 1)
• Regression $$y=f(x)\in \mathbb{R}$$
• Multiclass $$y=(y_1,y_2,\ldots,y_n)$$
• $$y_i=1$$ means membership in class 1
• Soft-decision: $$y$$ is a continuous variable
• higher values are more probably one
• Loss functiion
• Mean-squared error (common for regression) $L = (x-y)^2$
• Cross Entropy (common for classification) $L = \log \frac{ \exp x_{y} } { \sum \exp x_i }$
• There are others

## 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)

## Loss Functions and Evaluation

• Accuracy: ratio of correctly classified items
• What is the difference between a rate and a probability?
• Standard deviation?

## Some practical issues

• Neural Networks are Computationally Expensive
• GPU or CPU - what’s the difference?
• what resources do you have?
• Remedies
• Reduce image resolution
• Reduce number of images
• Reduce number of epochs
• In particular, it is necessary to sacrifice accuracy during development and testing.
• In the final stages you may need big datasets to achieve satisfactory results, and then you may need more computing power.