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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
## Sample Problem