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---
title: Neural Networks Lecture
categories: 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
## Sample Problem
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