Feedforward neural networks (FNN) Deep Learning

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# Feedforward neural networks (FNN) 
 Deep Learning - Part 1

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		Authors: 
<a href="/training-material/hall-of-fame/kxk302/" class="contributor-badge contributor-kxk302"><img src="https://avatars.githubusercontent.com/kxk302?s=27" alt="Avatar">Kaivan Kamali</a>

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<div class="footnote" style="bottom: 8em;"><i class="far fa-calendar" aria-hidden="true"></i><span class="visually-hidden">last_modification</span> Updated: Jul 9, 2021</div>

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## Requirements

Before diving into this slide deck, we recommend you to have a look at:

- [Introduction to Galaxy Analyses](/training-material/topics/introduction)

- [Statistics and machine learning](/training-material/topics/statistics)
    - Introduction to deep learning: [<i class="fas fa-laptop" aria-hidden="true"></i><span class="visually-hidden">tutorial</span> hands-on](/training-material/topics/statistics/tutorials/intro_deep_learning/tutorial.html)

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### <i class="far fa-question-circle" aria-hidden="true"></i><span class="visually-hidden">question</span> Questions

- What is a feedforward neural network (FNN)?

- What are some applications of FNN?

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### <i class="fas fa-bullseye" aria-hidden="true"></i><span class="visually-hidden">objectives</span> Objectives

- Understand the inspiration for neural networks

- Learn activation functions & various problems solved by neural networks

- Discuss various loss/cost functions and backpropagation algorithm

- Learn how to create a neural network using Galaxy’s deep learning tools

- Solve a sample regression problem via FNN in Galaxy

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# What is an artificial neural network?

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What is an artificial neural network?

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# Artificial Neural Networks

- ML discipline roughly inspired by how neurons in a human brain work
- Huge resurgence due to availability of data and computing capacity
- Various types of neural networks (Feedforward, Recurrent, Convolutional)
- FNN applied to classification, clustering, regression, and association

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# Inspiration for neural networks

- Neuron a special biological cell with information processing ability
	- Receives signals from other neurons through its *dendrites*
	- If the signals received exceeds a threshold, the neuron fires
	- Transmits signals to other neurons via its *axon*
- *Synapse*: contact between axon of a neuron and denderite of another
	- Synapse either enhances/inhibits the signal that passes through it
	- Learning occurs by changing the effectiveness of synapse

![Sketch of a biological neuron and its components](/training-material/topics/statistics/images/FNN_bio_neuron.png)

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# Celebral cortex

- Outter most layer of brain, 2 to 3 mm thick, surface area of 2,200 sq. cm
- Has about 10^11 neurons
	- Each neuron connected to 10^3 to 10^4 neurons
	- Human brain has 10^14 to 10^15 connections

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# Celebral cortex

- Neurons communicate by signals ms in duration
	- Signal transmission frequency up to several hundred Hertz
	- Millions of times slower than an electronic circuit
	- Complex tasks like face recognition done within a few hundred ms
	- Computation involved cannot take more than 100 serial steps
- The information sent from one neuron to another is very small
	- Critical information not transmitted
	- But captured by the interconnections
- Distributed computation/representation of the brain
	- Allows slow computing elements to perform complex tasks quickly

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# Perceptron

![Neurons forming the input and output layers of a single layer feedforward neural network](/training-material/topics/statistics/images/FFNN_no_hidden.png)

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# Learning in Perceptron

- Given a set of input-output pairs (called *training set*)
- Learning algorithm iteratively adjusts model parameters
	- Weights and biases
- So the model can accurately map inputs to outputs
- Perceptron learning algorithm

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# Limitations of Perceptron

- Single layer FNN cannot solve problems in which data is not linearly separable
	- E.g., the XOR problem
- Adding one (or more) hidden layers enables FNN to represent any function
	- *Universal Approximation Theorem*
- Perceptron learning algorithm could not extend to  multi-layer FNN
	- AI winter
- *Backpropagation* algorithm in 80's enabled learning in multi-layer FNN

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# Multi-layer FNN

![Neurons forming the input, output, and hidden layers of a multi-layer feedforward neural network](/training-material/topics/statistics/images/FFNN.png)

- More hidden layers (and more neurons in each hidden layer)
	- Can estimate more complex functions
	- More parameters increases training time
	- More likelihood of *overfitting*

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# Activation functions

![Table showing the formula, graph, derivative, and range of common activation functions](/training-material/topics/statistics/images/FNN_activation_functions.png)

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# Supervised learning

- Training set of size *m*: { (x^1,y^1),(x^2,y^2),...,(x^m,y^m) }
	- Each pair (x^i,y^i) is called a *training example*
	- x^i is called *feature vector*
	- Each element of feature vector is called a *feature*
	- Each x^i corresponds to a *label* y^i
- We assume an unknown function y=f(x) maps feature vectors to labels
- The goal is to use the training set to learn or estimate f
	- We want the estimate to be close to f(x) not only for training set
	- But for training examples not in training set

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# Classification problems

![Three images illustrating binary, multiclass, and multilabel classifications and their label representation](/training-material/topics/statistics/images/FNN_output_encoding.png)

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# Output layer

- Binary classification
	- Single neuron in output layer
	- Sigmoid activation function
	- Activation > 0.5, output 1
	- Activation <= 0.5, output 0
- Multilabel classification
	- As many neurons in output layer as number of classes
	- Sigmoid activation function
	- Activation > 0.5, output 1
	- Activation <= 0.5, output 0
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# Output layer (Continued)

- Multiclass classification
	- As many neurons in output layer as number of classes
	- *Softmax* activation function
	- Takes input to neurons in output layer
	- Creates a probability distribution, sum of outputs adds up to 1
	- The neuron with the highest proability is the predicted label
- Regression problem
	- Single neuron in output layer
	- Linear activation function

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# Loss/Cost functions

- During training, for each training example (x^i,y^i), we present x^i to neural network
	- Compare predicted output with label y^1
	- Need loss function to measure difference between predicted & expected output
- Use *Cross entropy* loss function for classification problems
- And *Quadratic* loss function for regression problems
	- Quadratic cost function is also called *Mean Squared Error (MSE)*

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# Cross Entropy Loss/Cost functions

![Cross Entropy loss function](/training-material/topics/statistics/images/FNN_Cross_Entropy_Loss.png)

![Cross Entropy cost function](/training-material/topics/statistics/images/FNN_Cross_Entropy_Cost.png)

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# Quadratic Loss/Cost functions

![Quadratic loss function](/training-material/topics/statistics/images/FNN_Quadratic_Loss.png)

![Quadratic cost function](/training-material/topics/statistics/images/FNN_Quadratic_Cost.png)

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# Backpropagation (BP) learning algorithm

- A *gradient descent* technique
	- Find local minimum of a function by iteratively moving in opposite direction of gradient of function at current point
- Goal of learning is to minimize cost function given training set
	- Cost function is a function of network weights & biases of all neurons in all layers
	- Backpropagation iteratively computes gradient of cost function relative to each weight and bias
	- Updates weights and biases in the opposite direction of gradient
	- Gradients (partial derivatives) are used to update weights and biases
	- To find a local minimum

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# Backpropagation error

![Backpropagation error](/training-material/topics/statistics/images/FNN_BP_Error.png)

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# Backpropagation formulas

![Backpropagation formulas](/training-material/topics/statistics/images/FNN_BP.png)

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# Types of Gradient Descent

- *Batch* gradient descent
	- Calculate gradient for each weight/bias for *all* samples
	- Average gradients and update weights/biases
	- Slow, if we have too many samples

- *Stochastic* gradient descent
	- Update weights/biases based on gradient of *each* sample
	- Fast. Not accurate if sample gradient not representiative

- *Mini-batch* gradient descent
	- Middle ground solution
	- Calculate gradient for each weight/bias for all samples in *batch*
		- batch size is much smaller than training set size
	- Average batch gradients and update weights/biases

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# Vanishing gradient problem

- Second BP equation is recursive
	- We have derivative of activation function
	- Calc. error in layer prior to output: 1 mult. by derivative value
	- Calc. error in two layers prior output: 2 mult. by derivative values

- If derivative values are small (e.g. for Sigmoid), product of multiple small values will be a very small value
	- Since error values decide updates for biases/weights
	- Update to biases/weights in first layers will be very small
		- Slowing the learning algorithm to a halt
	- The reason Sigmoid not used in deep networks
		- Why ReLU is popular in deep networks

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# Car purchase price prediction

- Given 5 features of an individual (age, gender, miles driven per day, personal debt, and monthly income)
	- And, money they spent buying a car
	- Learn a FNN to predict how much someone will spend buying a car
- We evaluate FNN on test dataset and plot graphs to assess the model’s performance
	- Training dataset has 723 training examples
	- Test dataset has 242 test examples
	- Input features scaled to be in 0 to 1 range

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# For references, please see tutorial's References section

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- Galaxy Training Materials ([training.galaxyproject.org](https://training.galaxyproject.org))

![Screenshot of the gtn stats page with 21 topics, 170 tutorials, 159 contributors, 16 scientific topics, and a growing community](/training-material/topics/introduction/images/gtn_stats.png)

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- If you would like to learn more about Galaxy, there are a large number of tutorials available.
- These tutorials cover a wide range of scientific domains.

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# Getting Help

- **Help Forum** ([help.galaxyproject.org](https://help.galaxyproject.org))

![Galaxy Help](/training-material/topics/introduction/images/galaxy_help.png)

- **Gitter Chat**
    - [Main Chat](https://gitter.im/galaxyproject/Lobby)
    - [Galaxy Training Chat](https://gitter.im/Galaxy-Training-Network/Lobby)
    - Many more channels (scientific domains, developers, admins)

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- If you get stuck, there are ways to get help.
- You can ask your questions on the help forum.
- Or you can chat with the community on Gitter.

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# Join an event

- Many Galaxy events across the globe
- Event Horizon: [galaxyproject.org/events](https://galaxyproject.org/events)

![Event schedule](/training-material/topics/introduction/images/event_horizon.png)

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- There are frequent Galaxy events all around the world.
- You can find upcoming events on the Galaxy Event Horizon.

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## Thank You!

This material is the result of a collaborative work. Thanks to the [Galaxy Training Network](https://training.galaxyproject.org) and all the contributors!

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This material is licensed under the Creative Commons Attribution 4.0 International License</a>.