Map of Artificial Intelligence

Summary

This video script delves into the expansive field of artificial intelligence, outlining its foundational mathematics including linear algebra, vector calculus, and probability theory. It then explores methods such as optimization, machine learning, and deep learning, highlighting their applications in areas like computer vision, natural language processing, robotics, computational biology, and recommender systems. The script emphasizes AI's versatility and its reliance on fundamental mathematical principles to solve a myriad of real-world problems.

Takeaways

• 🧠 Artificial Intelligence (AI) is a broad field with various subfields, each with its own experts, problems, and methods.
• 📚 The foundations of AI are based on three major types of mathematics: linear algebra, vector calculus, and probability theory.
• 📈 Linear algebra deals with linear equations and systems, and is essential for modeling real-world phenomena and understanding geometric interpretations.
• 🔍 Vector calculus, an extension of calculus to multiple dimensions, is crucial for AI as it helps in understanding how variables controlling a model change relative to each other.
• 🎲 Probability theory is important for dealing with uncertainty in the real world and is fundamental in building AI models that can reason about uncertain outcomes.
• 🔧 Optimization is a key method in AI, focusing on finding the best solution within given constraints, which is vital for tasks like pathfinding and machine learning.
• 🤖 Machine learning is the science of learning from data, involving the adjustment of model parameters to minimize error, often categorized into supervised, unsupervised, self-supervised, and semi-supervised learning.
• 👾 Reinforcement learning is about learning from action, where an AI system learns to perform tasks by taking actions and receiving rewards or penalties.
• 🧠 Deep learning involves the use of neural networks, which are versatile models capable of learning complex relationships and behaviors from data.
• 👀 Computer vision is an application of AI focused on understanding and interpreting visual information from photos, videos, and other digital images.
• 💬 Natural language processing (NLP) is AI's application to understanding and generating human language, including speech recognition and chatbots.
• 🤖 Robotics is where AI interacts with the physical world, with AI playing a key role in perception and control, often integrating computer vision and reinforcement learning.
• 🧬 Computational biology applies AI to life sciences, including drug discovery, protein structure prediction, and genomics for disease prediction.
• 🔑 Recommender systems use AI to predict user preferences and interests, influencing what content is recommended on various social media platforms.

Q & A

What are the three fundamental types of mathematics that all AI is based on?

The three fundamental types of mathematics that all AI is based on are linear algebra, vector calculus, and probability theory.

Why is linear algebra considered important in AI?

Linear algebra is important in AI because it deals with systems of linear equations and can model a wide range of real-world phenomena. Its versatility, combined with the efficiency of computers in handling linear algebra, makes it a powerful tool in AI.

What does vector calculus extend in the context of AI?

Vector calculus extends the concept of calculus to multiple dimensions, allowing for the study of changes in variables relative to each other in a multi-dimensional space, which is crucial for understanding the behavior of computer models.

How does probability theory contribute to AI?

Probability theory contributes to AI by providing a mathematical framework for dealing with uncertainty, which is inherent in real-world scenarios and helps AI systems make predictions and decisions under uncertain conditions.

What is optimization in the context of AI?

In the context of AI, optimization is the process of finding the best solution or setting within a set of constraints, often used to minimize error in machine learning models by adjusting parameters.

What is the main goal of machine learning?

The main goal of machine learning is to enable computers to learn from data and make predictions or decisions without being explicitly programmed to perform a specific task.

What is the difference between supervised and unsupervised learning?

Supervised learning involves learning from labeled data, where the correct answers are provided for each example. Unsupervised learning, on the other hand, involves learning from data without labels, discovering patterns and relationships within the data itself.

What is reinforcement learning and how does it differ from other types of learning?

Reinforcement learning is about learning from action, where an agent learns to make decisions by performing actions in an environment to achieve a goal. It differs from other types of learning in that it involves sequential decision-making and the environment changes based on the agent's actions.

What is deep learning and how does it relate to neural networks?

Deep learning is a subfield of machine learning that focuses on learning with neural networks, which are powerful models capable of learning complex patterns and relationships in data. Neural networks are the foundation of deep learning, allowing it to be versatile and applicable to various problems.

What are some of the major applications of AI mentioned in the script?

Some of the major applications of AI mentioned in the script include computer vision, natural language processing, robotics, computational biology, and recommender systems.

How is AI used in computer vision?

AI is used in computer vision for tasks such as object detection, facial recognition, image processing for self-driving cars, and automatic analysis of medical images, enabling machines to understand and interpret visual data.

What role does natural language processing (NLP) play in AI?

Natural language processing (NLP) plays a crucial role in AI by enabling machines to understand, interpret, and generate human language, which is used in applications like speech recognition, chatbots, and language translation.

How does AI contribute to robotics?

AI contributes to robotics by providing perception, which helps robots understand the world through their sensors, and control, which involves making decisions based on the perceived information, often using techniques like computer vision and reinforcement learning.

What is computational biology and how does AI play a role in it?

Computational biology is an interdisciplinary field that applies AI and computational methods to the life sciences. AI plays a role in areas such as automatic drug discovery, predicting protein structures from DNA sequences, and analyzing genomic data to predict diseases.

What are recommender systems in AI and how do they work?

Recommender systems in AI are algorithms designed to predict user preferences and suggest items, such as products, movies, or content, that a user may like. They work by analyzing user behavior, preferences, and other data to provide personalized recommendations.

Outlines

00:00

🧠 Foundations of AI: The Mathematics Behind

This paragraph introduces the three fundamental mathematical disciplines that underpin all of artificial intelligence (AI). It emphasizes linear algebra, which is the study of linear equations and systems, allowing computers to solve complex systems efficiently. The paragraph explains how linear algebra can model real-world phenomena due to its versatility and the efficiency of computational methods. It also touches on vector spaces, which are essential for understanding dimensions beyond the three-dimensional world we are familiar with. The importance of linear algebra in AI is highlighted by its ability to frame problems in a way that unlocks powerful mathematical solutions.

05:01

📈 Vector Calculus and Probability: The Dynamics of AI

This section delves into vector calculus, the mathematics of change in multiple dimensions, which is crucial for understanding how variables interact within computer models. It explains how vector calculus helps in adjusting model parameters to minimize error, a fundamental process in AI known as learning. The paragraph also introduces probability theory as the mathematics of uncertainty, essential for building AI models that can reason about the unpredictable aspects of the real world. The importance of these mathematical fields is underscored by their role in creating AI systems that can adapt and learn from data.

10:03

🔧 Methods in AI: Optimization and Learning Paradigms

The paragraph discusses various methods used in AI, starting with optimization, which is about finding the best solution in a given setting, often subject to constraints. It uses the analogy of pathfinding to explain optimization and then transitions to machine learning, the science of learning from data. The paragraph distinguishes between supervised learning, where data includes labels, and unsupervised learning, where it does not. It also mentions reinforcement learning, which involves learning from actions in an environment that changes due to the system's decisions, and deep learning, which uses neural networks to learn complex relationships from data. The paragraph positions these methods as applications of the fundamental mathematics to solve specific problems.

🌐 Applications of AI: From Vision to Recommendation

The final paragraph outlines the various applications of AI, building upon the foundational mathematics and methods previously discussed. It covers computer vision, which involves AI's understanding of visual data, natural language processing, which enables AI to comprehend and generate language, and robotics, where AI is used for perception and control. The paragraph also touches on computational biology, which applies AI to life sciences, and recommender systems, which predict user preferences across various platforms. The summary highlights how these applications utilize the comprehensive framework of AI to solve real-world problems effectively.

Keywords

💡Artificial Intelligence (AI)

Artificial Intelligence, or AI, is the simulation of human intelligence in machines that are programmed to think like humans and mimic their actions. In the video, AI is the central theme, encompassing various subfields and applications that demonstrate how it is applied to solve complex problems and model real-world phenomena.

💡Linear Algebra

Linear Algebra is the study of linear equations and linear transformations in multiple dimensions. It is foundational to AI as it deals with systems of equations that can model real-world phenomena. The script mentions it as one of the 'dark magic' components of AI, highlighting its importance in framing problems and unlocking powerful mathematical solutions.

💡Vector Calculus

Vector Calculus extends the concepts of calculus to multiple dimensions, allowing for the study of rates of change in vector spaces. It is crucial in AI for understanding how changes in multiple variables affect a system, such as adjusting parameters in a computer model to minimize error, which is central to the learning process in AI.

💡Probability Theory

Probability Theory is the mathematics of uncertainty and is used in AI to reason about uncertain outcomes. The video emphasizes its importance in building models of the real world, where absolute certainty is unattainable, and predictions are made in terms of probabilities, such as weather forecasting.

💡Optimization

Optimization in AI refers to the process of finding the best solution or set of parameters for a given problem, often within certain constraints. The script uses the analogy of pathfinding, where the goal is to find the best route from a set of possible paths, illustrating how optimization is applied in AI to achieve the most efficient or effective outcome.

💡Machine Learning

Machine Learning is a subset of AI that involves the development of algorithms that allow computers to learn from and make predictions or decisions based on data. The video describes it as a method derived from the fundamental maths, emphasizing its role in supervised learning, where the computer model is trained using labeled data.

💡Supervised Learning

Supervised Learning is a type of machine learning where the algorithm is trained on labeled data, learning to predict outcomes for new data. The script gives the example of a computer model distinguishing between images of dogs and cats, where the model adjusts its parameters to minimize error based on the provided labels.

💡Unsupervised Learning

Unsupervised Learning is another subfield of machine learning where the algorithm learns from data without any labeled outcomes. The script mentions clustering as an example, where the algorithm groups data points based on similarities without prior knowledge of what those groups should be.

💡Reinforcement Learning

Reinforcement Learning is a branch of AI that focuses on learning from action and its consequences, often used in situations where the correct decision depends on a sequence of actions. The video uses the example of a robot learning to open a door, where each action can change the environment and subsequent decisions.

💡Deep Learning

Deep Learning is a subset of machine learning that uses artificial neural networks with multiple layers to learn complex patterns in data. The script positions it as a method rather than a subfield, highlighting its versatility in various types of learning tasks and its ability to approximate any function given enough data.

💡Computer Vision

Computer Vision is an AI application that enables machines to interpret and understand visual information from the world, such as images and videos. The video describes it as AI for seeing, including tasks like object detection, facial recognition, and image processing for autonomous vehicles.

💡Natural Language Processing (NLP)

Natural Language Processing is an AI field focused on the interaction between computers and human language. It includes speech recognition, text analysis, and chatbots. The script mentions Siri and Alexa as examples of NLP applications, emphasizing its role in understanding and generating human language.

💡Robotics

Robotics is the branch of technology that deals with the design, construction, operation, and use of robots. In the context of AI, robotics is important for perception, which involves using sensors to understand the environment, and control, which involves making decisions based on that information, often using AI techniques like computer vision and reinforcement learning.

💡Computational Biology

Computational Biology is an interdisciplinary field that applies AI and computational methods to the life sciences. The video mentions its applications in drug discovery and predicting protein structures from DNA sequences, like the Alpha Fold project, which showcases AI's ability to analyze and predict complex biological data.

💡Recommender Systems

Recommender Systems are AI applications that predict user preferences and suggest items, such as products, movies, or content. The script refers to these as the 'algorithm' on social media platforms, which use AI to determine what content might engage users, based on their behavior and preferences.

Highlights

Artificial intelligence (AI) has seen a surge in popularity following the release of Chat GPT.

AI is a broad field with various subfields, each with its own experts, problems, and methods.

The video outlines the major subfields of AI and explains their significance.

AI is categorized into three main areas: fundamental maths, methods, and applications.

Linear algebra is the foundation of AI, dealing with linear equations and systems.

Linear algebra's versatility allows it to model a wide range of real-world phenomena.

Vector spaces, a concept from linear algebra, extend our understanding of dimensions beyond three.

Vector calculus, an extension of calculus, deals with change in multiple dimensions.

Parameters in AI models are analogous to knobs that control the model's behavior.

Learning in AI involves adjusting parameters to minimize error, guided by vector calculus.

Probability theory is essential for dealing with uncertainty in AI models.

Optimization is about finding the best solution within given constraints.

Machine learning is the science of learning from data, often involving supervised learning.

Unsupervised learning focuses on finding patterns in unlabeled data.

Reinforcement learning involves learning from actions and their consequences.

Deep learning uses neural networks to learn complex relationships from data.

Applications of AI include computer vision, natural language processing, robotics, computational biology, and recommender systems.

Computer vision enables AI to understand and process visual information.

Natural language processing allows AI to understand and generate human language.

Robotics combines AI with physical machines for tasks like perception and control.

Computational biology applies AI to life sciences, such as drug discovery and genomics.

Recommender systems use AI to predict user preferences and suggest content.

Transcripts

artificial intelligence has exploded in

popularity since the release of chat GPT

and for a lot of people chat GPT and

mid-journey are pretty much the only AI

systems they know but AI as a field is

so much broader than that and like any

scientific field it's broken into a

bunch of different subfields with their

own experts problems and methods in this

video I'll lay out the major subfields

of AI and explain what each of them

means

I'm going to split it into three

different categories fundamental maths

methods and applications let's start

with the foundations the math there are

three major types of math on which all

of AI is based all of AI boils down in

one way or another to these three kinds

of math these are like the Deep lore or

the dark magic of AI first among these

is linear algebra which is the study of

linear equations equations in any number

of variables where the highest power of

any variable is one you can add subtract

multiply and divide and Shuffle around

these terms however you want but you

can't include powers of variables so y

equals MX plus b which you might

recognize from middle school that's

linear 4X plus 3y equals 10 that's

linear 4X plus 3y plus 5z equals one

that's linear but x squared plus 4X plus

3y plus four Z equals one that's not

linear because of the x squared y cubed

plus x equals one not linear y plus x

equals one linear when you stack a bunch

of these equations together you get a

system of equations and you can use

computers to really quickly solve these

systems of equations to figure out what

X Y and Z make all of these equations

true at the same time now why do linear

equations matter well Gilbert Strang one

of the Godfathers of linear algebra put

it really well when he said that linear

algebra is the study of flat things and

flat things surprisingly can be used to

model all sorts of real world phenomenon

even things that aren't flat get flat if

you zoom in enough so you pair that

level of Versatility with how

efficiently computers can deal with

linear algebra and you get a very

powerful combination linear algebra also

studies all of the geometric

interpretations of the math where we get

ideas like vector spaces which lie at

the heart of all of AI without getting

too into the weeds Vector spaces are

basically the mathematic radical

extension of what lies Beyond three

dimensions we can all visualize 1D and

2D and 3D pretty well but when we get

beyond that things start to get tricky

Vector spaces allow us to extend these

things we do understand from the math of

three dimensions or less to any number

of Dimensions thousands hundreds of

thousands or millions in a nutshell if

you can find a way to frame a problem in

terms of linear algebra you unlock an

entire library of super powerful math

that probably already contains the

solution somewhere inside of it thank

you

[Music]

next we have Vector calculus calculus is

the mathematics of change Vector

calculus is the extension of calculus to

multiple Dimensions to the kind of

vector spaces that we get from linear

algebra so if regular calculus is the

study of how Y is changing relative to X

Vector calculus extends that to 3D 4D

and Way Beyond if we stick to three

dimensions the X the Y and the Z then

Vector calculus answers the questions

how are z and y changing relative to X

but also how is y changing relative to Z

and Z relative to Y and X relative to Y

and Z how are all these variables

changing relative to each other and how

does changing X Y and Z change some

arbitrary function of x y and z

foreign

[Music]

now the reason why Vector calculus is so

important to AI is because generally x y

and z are not just random numbers

they're numbers that control the

behavior of a computer model you can

think of these like knobs that were

turning to tune a radio we call numbers

that control the behavior of a computer

model parameters we also generally have

a function that measures how good each

setting of The Knobs is and we call that

the loss if we're trying to get as close

as we possibly can to matching some data

points that we collected out in the

field the loss might be the difference

between our estimate and the actual data

points in other words we have this

function that measures our error Vector

calculus lets us calculate how changing

each knob will change our error if we

know how changing each knob will change

the error we can keep turning the knob

in the direction that reduces the error

and if we do that over and over and over

again we can get to the best possible

setting of these knobs and we call that

process learning

[Music]

welcome

all right here we are the last of the

fundamental three maths is probability

Theory probability is the math of

uncertainty and the real world is full

of uncertainty if we're predicting the

weather for example we can only really

tell you what the probability of rain is

we can't ever be sure so whenever we're

building a model of the real world

whenever we're building AI probability

helps us reason about uncertainty

[Applause]

so those are the three fundamental kinds

of math behind AI all of AI boils down

to these three kinds of math so much so

that you'll sometimes hear people in the

field refer to AI as applied linear

algebra and they're only half joking

let's move on to methods these are ways

that we use the three fundamental maths

to build problem-solving approaches that

can be applied to a wide array of

specific problems the first one here

could also be considered a fundamental

math for AI but here I'm thinking of it

as the group of methods which we call

optimization optimization is the

mathematics of finding the best thing

and if that sounds incredibly vague and

Broad that's because it is optimization

is a super versatile field studying any

setting where we're trying to find the

best thing out of all things like it a

good example of this is pathfinding like

how Google Maps routes you to your

destination there the problem is to find

the best set of direct out of all

possible sets of directions most of the

time optimization is constrained meaning

there are some rules or limitations that

it has to obey in this case for example

you have to obey the rules of the road

you can't go the wrong way up a one-way

road we also have to Define what we mean

by best we have to Define some Criterion

for choosing between the things that

we're choosing between in this case that

would be the length of the path one

subfield of optimization is machine

learning which is the science of

learning from data in machine learning

our Criterion and our constraints come

from the data let's imagine that we're

trying to build a computer model that

tells us whether an image contains a dog

or a cat in this case the data would be

a collection of images each one with an

Associated label that says dog or cat

our computer model like before has these

knobs or parameters that control Its

Behavior and our optimization problem is

to find the best setting of these knobs

that minimizes our error on the data

data rather than painstakingly writing

out a solution that says you know for

example if this pixel is white and this

pixel is black then this is a cat and if

this pixel is green but this pixel is

gray then this is a dog we want instead

for the computer to optimize this

problem on its own minimizing its error

on the data and that's machine learning

that also happens to be supervised

learning a subfield of machine learning

that studies learning from data when the

data is labeled meaning when the data

includes the right answer for each

example within supervised learning you

have all sorts of methods like support

Vector machines and decision trees and

random forests

improvised learning is a subfield of

machine learning that studies learning

from data when the data doesn't include

labels for an idea of how this might

work you can look at clustering which

uses just similarities between the data

points to discover what should be

together and what should be a part and

where the separations lie there is also

self-supervised and semi-supervised

learning but those are out of scope for

this video

and next we have reinforcement learning

which is the science of learning from

action let's say you want a robot to

open a door this might sound simple but

it's actually hard for many reasons

first of all for our dog cat classifier

there is always a single right answer

cat if the image contains the cat and

dog if the image contains a dog but

there are many possible motor control

actions that the robot can take to open

a door and success is only determined

after many consecutive decisions this

means that we can't provide labels or

write answers that the system can learn

from like we can with the dog cat

example second of all every decision

that our system makes changes the

environment the dog cat classifier

doesn't have to worry that answering cat

to one image might change the next image

from a dog to a cat but if a robot moves

its arm forward it might bump the door

and close it which will change the

correct decision to make at the next

step in other words every decision it

makes has a ripple effect that changes

the correct decisions it should make in

the future and the science of solving

problems like this of learning from

action is called reinforcement learning

finally we have deep learning the

science of learning with neural networks

neural networks are just a kind of

computer model but they're really

powerful because their Universal

function approximators which means that

given the right data and the right

algorithm these models can learn to

mimic anything and to replicate any

Behavior they can learn all sorts of

different relationships no matter how

complicated and because of that they're

super versatile so you'll see them used

in supervised unsupervised

semi-supervised self-supervised and

reinforcement learning you'll often find

neural networks and deep learning listed

as subfields of their own and I think

that's wrong there's a science and a

theory underlying neural networks and a

kind of expertise in knowing how to use

them right but at their core they're

just application versions of the three

fundamental maths that can be applied to

all sorts of different problems so I'll

call them methods

and now finally we get to the

applications which you'll find on many

online lists ranked right alongside the

methods and the fundamental maths we

just described with no differentiation

you might be surprised at how short the

rest of this video is that's because I

hope I've spent the time and organized

this video so that you can see the

hierarchy here how each layer builds

upon the last so that by the time I get

to these applications I actually don't

have to spend that much time getting

into the weeds you can just know that

they use everything from the methods

which uses everything from the maths to

solve these specific classes of problems

so first is computer vision computer

vision is AI for understanding the

visual World basically AI that sees and

concretely this means any AI that has to

do with photos videos or any other kind

of digital image object detection facial

recognition image processing for

self-driving cars and automatic analysis

of medical images all of these are

computer vision

[Music]

the next one is natural language

processing which is AI for understanding

language this includes things like

speech to text like Siri or Alexa this

also includes chat Bots like Chachi BT

and other large language models

[Music]

thank you

then there's robotics which is AI for

interacting with the physical world

everyone knows what robots are you can

probably recognize Boston Dynamics spot

or the Roomba you might have in your

house but AI is important to robotics

mainly for perception which is basically

how does the robot use its sensors to

understand the world and is often highly

intertwined with computer vision and

control which is how does the robot use

that information to make decisions in

its frequently intertwined with

reinforcement learning

[Music]

there's also computational biology which

is AI for the life sciences and includes

things like automatic drug Discovery or

predicting protein structures from DNA

sequences like deepminds Alpha fold

which made headlines a couple years ago

this also includes things like a

molecular simulations and predictions of

diseases from genomics

[Music]

finally we have recommender systems

which is AI for predicting what you like

this is what people on YouTube Tick Tock

Twitter and all other sorts of social

media call the algorithm that's ai2

trying to figure out what will make you

click there are of course more subfields

and many more subfields of subfields

there's expert systems planning

reasoning symbolic Ai and many more but

we just don't have the time for that

today so let me know what you think in

the comments Please Subscribe if you

learned something today and as always

I'll see you next week