Introduction To Deep Learning

What Is Deep Learning And How Can I Study It?

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Jun 13, 2018

I took a Deep Learning course through The Bradfield School of Computer Science in June. This series is a journal about what I learned in class, and what I've learned since.

This is the first article in this series, and is is about the recommended preparation for the Deep Learning course and what we learned in the first class. Read the second article here , and the third here .

Although normally the "prework" comes before the introduction, I'm going to give the 30,000 foot view of the fields of artificial intelligence, machine learning, and deep learning at the top. I have found that this context can really help us understand why the prerequisites seem so broad, and help us study just the essentials. Besides, the history and landscape of artificial intelligence is interesting, so lets dive in!

Artificial Intelligence, Machine Learning, and Deep Learning

Deep learning is a subset of machine learning. Machine learning is a subset of artificial intelligence. Said another way --- all deep learning algorithms are machine learning algorithms, but many machine learning algorithms do not use deep learning. As a Venn Diagram, it looks like this:

Deep learning refers specifically to a class of algorithm called a neural network, and technically only to "deep" neural networks (more on that in a second). This first neural network was invented in 1949, but back then they weren't very useful. In fact, from the 1970's to the 2010's traditional forms of AI would consistently outperform neural network based models.

These non-learning types of AI include rule based algorithms (imagine an extremely complex series of if/else blocks); heuristic based AIs such as A* search; constraint satisfaction algorithms like Arc Consistency; tree search algorithms such as minimax (used by the famous Deep Blue chess AI); and more.

There were two things preventing machine learning, and especially deep learning, from being successful. Lack of availability of large datasets and lack of availability of computational power. In 2018 we have exabytes of data, and anyone with an AWS account and a credit card has access to a distributed supercomputer. Because of the new availability of data and computing power, Machine learning --- and especially deep learning --- has taken the AI world by storm.

You should know that there are other categories of machine learning such as unsupervised learning and reinforcement learning but for the rest of this article, I will be talking about a subset of machine learning called supervised learning.

Supervised learning algorithms work by forcing the machine to repeatedly make predictions. Specifically, we ask it to make predictions about data that we (the humans) already know the correct answer for. This is called "labeled data" --- the label is whatever we want the machine to predict.

Here's an example: let's say we wanted to build an algorithm to predict if someone will default on their mortgage. We would need a bunch of examples of people who did and did not default on their mortgages. We will take the relevant data about these people; feed them into the machine learning algorithm; ask it to make a prediction about each person; and after it guesses we tell the machine what the right answer actually was. Based on how right or wrong it was the machine learning algorithm changes how it makes predictions .

We repeat this process many many times, and through the miracle of mathematics, our machine's predictions get better. The predictions get better relatively slowly though, which is why we need so much data to train these algorithms.

Machine learning algorithms such as linear regression, support vector machines, and decision trees all "learn" in different ways, but fundamentally they all apply this same process: make a prediction, receive a correction, and adjust the prediction mechanism based on the correction. At a high level, it's quite similar to how a human learns.

Recall that deep learning is a subset of machine learning which focuses on a specific category of machine learning algorithms called neural networks. Neural networks were originally inspired by the way human brains work --- individual "neurons" receive "signals" from other neurons and in turn send "signals" to other "neurons". Each neuron transforms the incoming "signals" in some way, and eventually an output signal is produced. If everything went well that signal represents a correct prediction!

This is a helpful mental model, but computers are not biological brains. They do not have neurons, or synapses, or any of the other biological mechanisms that make brains work. Because the biological model breaks down, researchers and scientists instead use graph theory to model neural networks --- instead of describing neural networks as "artificial brains", they describe them as complex graphs with powerful properties.

Viewed through the lens of graph theory a neural network is a series of layers of connected nodes; each node represents a "neuron" and each connection represents a "synapse".

Different kinds of nets have different kinds of connections. The simplest form of deep learning is a deep neural network. A deep neural network is a graph with a series of fully connected layers. Every node in a particular layer has an edge to every node in the next layer; each of these edges is given a different weight. The whole series of layers is the "brain". It turns out, if the weights on all these edges are set just right these graphs can do some incredible "thinking".

Ultimately, the Deep Learning Course will be about how to construct different versions of these graphs; tune the connection weights until the system works; and try to make sure our machine does what we think it's doing. The mechanics that make Deep Learning work, such as gradient descent and backpropagation, combine a lot of ideas from different mathematical disciplines. In order to really understand neural networks we need some math background.

Background Knowledge --- A Little Bit Of Everything

Given how easy to use libraries like PyTorch and TensorFlow are, it's really tempting to say, "you don't need the math that much. " But after doing the required reading for the two classes, I'm glad I have some previous math experience. A subset of topics from linear algebra, calculus, probability, statistics, and graph theory have already come up.

Getting this knowledge at university would entail taking roughly 5 courses. Calculus 1, 2 and 3; linear algebra; and computer science 101. Luckily, you don't need each of those fields in their entirety. Based on what I've seen so far, this is what I would recommend studying if you want to get into neural networks yourself:

From linear algebra, you need to know the dot product, matrix multiplication (especially the rules for multiplying matrices with different sizes), and transposes. You don't have to be able to do these things quickly by hand, but you should be comfortable enough to do small examples on a whiteboard or paper. You should also feel comfortable working with "multidimensional spaces" --- deep learning uses a lot of many dimensional vectors.

I love 3Blue1Brown's Essence of Linear Algebra for a refresher or an introduction into linear algebra. Additionally, compute a few dot products and matrix multiplications by hand (with small vector/matrix sizes). Although we use graph theory to model neural networks these graphs are represented in the computer by matrices and vectors for efficiency reasons. You should be comfortable both thinking about and programming with vectors and matrices.

From calculus you need to know the derivative, and you ideally should know it pretty well. Neural networks involve simple derivatives, the chain rule, partial derivatives, and the gradient . The derivative is used by neural nets to solve optimization problems , so you should understand how the derivative can be used to find the "direction of greatest increase". A good intuition is probably enough, but if you solve a couple simple optimization problems using the derivative, you'll be happy you did. 3Blue1Brown also has an Essence of Calculus series, which is lovely as a more holistic review of calculus.

Gradient descent and backpropagation both make heavy use of derivatives to fine tune the networks during training. You don't have to know how to solve big complex derivatives with compounding chain and product rules, but having a feel for partial derivatives with simple equations helps a lot.

From probability and statistics, you should know about common distributions, the idea of metrics, accuracy vs precision, and hypothesis testing. By far the most common applications of neural networks are to make predictions or judgements of some kind. Is this a picture of a dog? Will it rain tomorrow? Should I show Tyler this advertisement, or that one? Statistics and probability will help us assess the accuracy and usefulness of these systems.

It's worth noting that the statistics appear more on the applied side; the graph theory, calculus, and linear algebra all appear on the implementation side. I think it's best to understand both, but if you're only going to be using a library like TensorFlow and are not interested in implementing these algorithms yourself --- it might be wise to focus on the statistics more than the calculus & linear algebra.

Finally, the graph theory. Honestly, if you can define the terms "vertex", "edge" and "edge weight" you've probably got enough graph theory under your belt. Even this "Gentle Introduction" has more information than you need.

In the next article in this series I'll be examining Deep Neural Networks and how they are constructed. See you then!

Part 2: Deep Neural Networks as Computational Graphs

Part 3: Classifying MNIST Digits With Different Neural Network Architectures