From Numbers to Neural Networks: The Unspoken Connection Between Math and Successful AI

Week 4 Blog 8 — Unlocking the Pathway to AI Brilliance Through the Language of Mathematics

Hey!!! 👋 My fellow readers,

I hope you guys had a wonderful week. 🌟 So, it’s Sunday again and I’m back with some exciting news. 📰 Well, as you read from the title… Yes! We are making a breakthrough from all the long reads of the past… the present… the future of AI… AI… and AI… I’m definitely tired of that word, Sheesh!!! 😅

Firstly, Congratulations on completing the exhilarating journey through Phase One of our AI/ML series! 🎉 You’ve laid a robust foundation by mastering the theory concepts that underpin this fascinating field. 💡 But hold onto your seats, because now we’re ready to embark on an even more exhilarating adventure. 🚀

From this blog onward, we are going to delve into some of the best parts of AI and ML. 🤖 We’re about to venture into the heart of AI/ML, diving deep into the core concepts that drive innovation and reshape our world. 🌎 Whether you’re a seasoned tech enthusiast or a curious newcomer, this blog is your compass to navigate the captivating world of AI/ML with confidence. 🧭

So, buckle up and prepare to dive deeper than ever before. The voyage into the heart of AI/ML starts now, and we can’t wait to uncover the secrets that await us. 🔍 Let’s transform curiosity into understanding and theory into real-world prowess. Are you ready? 🌊 Let’s set sail! ⛵

Not hate… Just PUN intended!!!

**It’s so freakin’ hard to find the perfect emojis for every sentence. Ufff How do you guys even do it?**

Now, we get to our actual ‘Hero of the Day’ — MATH. Before we go further into this, I know more than 70% of the readers would just avoid this just because it had the word M-A-T-H. There would be around 20% who actually didn’t know math and AI/ML is a thing. So, they just came here to pop in and give it a cool skip. There’s the 5% who just want to give it a try (TBH they would be Engg students, they faced far worse).

The next is the 4% who just know the reality that AI is nothing… ML is everything… DL is just Black Magic. But, the actual boss is MATH. Math in this field is like the final boss who has been secretly controlling all the other mini-bosses. You only know he exists only when you really devote yourself to encountering him. And for the 1% to whom this blog is solely concerned is the Math-manics who just love math. They want math in everything. For you guys, there is no better place than this.

I belong to the 4%. I know the risks yet, I’m ready to beckon with it. In the past 2 minutes, I would have used the word MATH a million times. Because further on the risks on you because all you get to hear further is just MATH. This is your last call — Either run or sit with me into a dreamy world of Math or your Nightmare.

I won’t lie: It’s a lot of Math.

Algebra You Need to Know for AI

Mathematics serves as the foundation for a multitude of fields, with algebra being a pivotal component. Beyond basic arithmetic operations, such as addition, subtraction, multiplication, and division, a comprehensive grasp of the following algebraic concepts is essential for delving into Artificial Intelligence (AI).

Exponents

Exponents are a crucial aspect of algebra, denoting the power to which a number is raised. They play a pivotal role in AI algorithms, aiding in the representation and manipulation of large numerical values efficiently.

What is an Exponent?

Radicals

Radicals, often involving square roots, are vital in AI to handle complex calculations and determine magnitudes, distances, and relationships between data points.

Algebra - Radicals

Factorials

Factorials play a significant role in combinatorial mathematics and are utilized in probability calculations that form the backbone of AI models and predictions.

Summations

Summations, the result of adding a sequence of numbers together, find applications in various AI algorithms, including those related to pattern recognition and data analysis.

Scientific Notations

Scientific notation, expressing numbers in the form of a base multiplied by 10 raised to a certain power, is pivotal for dealing with extremely large or small values encountered in AI computations.

Roots, exponents, & scientific notation | Pre-algebra | Math | Khan Academy

Linear Algebra You Need to Know for AI

In the realm of Artificial Intelligence, Linear Algebra takes center stage as a fundamental computational tool. It underpins numerous AI concepts and applications across various scientific and engineering domains. Key concepts in Linear Algebra include:

Scalars

Scalars are single numeric values, which can be either real or natural. They find applications in representing constants and coefficients in AI equations.

Scalar and Vector Algebra

Vectors

Vectors, ordered lists of numbers representing coordinates in space, play a central role in AI data representation and manipulation.

Scalar and Vector Algebra

Matrices

Matrices, two-dimensional arrays of numbers, offer a robust framework for data storage and transformation in AI, applicable to tasks like image processing and transformation.

Matrices

Tensors

Tensors, multi-dimensional arrays with N axes, are integral to machine learning, deep learning, and computer vision. They enable the efficient handling of complex data structures.

Tensor -- from Wolfram MathWorld

Eigenvectors & Eigenvalues

Eigenvectors and eigenvalues hold significance in AI algorithms, aiding in tasks like dimensionality reduction and feature extraction.

Eigenvector and Eigenvalue

Singular Value Decomposition

Singular Value Decomposition is a matrix factorization technique that finds applications in data compression, noise reduction, and latent semantic analysis.

Singular Value Decomposition (SVD) tutorial

Principal Component Analysis (PCA)

PCA, a dimensionality reduction technique, is employed in AI for data visualization, noise reduction, and feature selection.

Calculus You Need to Know for AI

Calculus forms the backbone of AI algorithms that involve continuous changes, optimization, and approximation. Proficiency in multi-dimensional calculus is essential for tackling intricate AI challenges. Key concepts include:

Derivatives

Derivatives, encompassing rules like the chain rule and partial derivatives, are instrumental in understanding how quantities change in AI algorithms.

Introduction to Derivatives

Vector/Matrix Calculus

Vector and matrix calculus are indispensable in AI optimization, gradient-based algorithms, and deep learning backpropagation.

Gradient Algorithms

Gradient algorithms are pivotal for optimizing AI models, identifying optimal parameters, and refining model performance through techniques like stochastic gradient descent.

Gradient Descent Algorithm and Its Variants

Statistics & Probability Concepts You Need to Know for AI

Statistics and probability are the bedrock of AI, enabling us to make informed decisions and predictions based on data. In the AI landscape, the following concepts are paramount:

Basic Statistics

Understanding measures like mean, median, and variance is essential for interpreting data in AI applications.

Statistics For Dummies Cheat Sheet

Basic Probability Rules

Mastery of basic probability rules, including events and sample spaces, forms the basis for probabilistic AI models.

Probability Rules

Random Variables

Random variables are at the heart of AI models that deal with uncertainty and randomness, contributing to tasks such as prediction and decision-making.

Random variables | Statistics and probability | Math | Khan Academy

Bayes’ Theorem

Bayesian probability is a cornerstone of AI algorithms, providing a framework for updating beliefs based on new evidence.

Bayes' Rule - Explained For Beginners

Maximum Likelihood Estimation (MLE)

MLE aids in parameter estimation for AI models, relying on probability concepts such as joint probability and independence of events.

Probability concepts explained: Maximum likelihood estimation

Common Distributions

Familiarity with distributions like binomial, Poisson, and Gaussian is pivotal in understanding and modeling data in AI applications.

Information Theory Concepts You Need to Know for AI

Information theory, a blend of calculus, statistics, and probability, holds profound significance in AI, particularly in data compression and modeling. Key concepts include:

Entropy

Entropy quantifies uncertainty and randomness in data, making it crucial for developing AI models that handle incomplete or noisy information.

What is entropy, really?

Cross-Entropy

Cross-entropy measures the difference between probability distributions, often employed in training machine learning models.

Kullback Leibler Divergence

This divergence metric assesses the difference between two probability distributions and is utilized in various AI applications, including model comparison.

Kullback-Leibler Divergence Explained - Count Bayesie

Viterbi Algorithm

The Viterbi algorithm is indispensable in AI tasks involving sequence analysis, such as natural language processing and speech recognition.

Encoder-Decoder

The encoder-decoder architecture is a pivotal framework in AI, used extensively in machine translation and sequence-to-sequence tasks.

Information Theory of Neural Networks

TASK OF THE WEEK: Week 4 Blog 8

Answer to Week 4 Blog 7

Self-Attention Mechanism

The core component of a transformer responsible for capturing relationships between words is “attention.” This mechanism allows the transformer model to weigh the importance of each word in a sequence based on its relationship with other words in the same sequence. It enables the model to consider the context and dependencies between words, regardless of their distance from each other, thereby capturing long-range relationships and improving the model’s ability to understand and generate coherent text.

As for today’s task — Um another coding task but related to math… Yes, indeed it’s math. It feels like Math Independence… Retribution of Math in my life XD…

Task: Secret Number Game

You’ve stumbled upon a secret number game based on a mathematical trick! Here’s how it works:

Think of a number (your secret number).

Add 3 to it.

Double the result.

Subtract 4.

Divide by 2.

Subtract your original secret number.

The result is always 1!

Your task is to write a Python program that simulates this secret number trick.

Math is just Magic!!! Have fun creating this game…

Understanding the Need for Math

I’m pretty sure most of the people for the 5% would have already considered a different field. But, those who stayed till the very end. It’s worth the wait.

This is the big secret broken to you:

AI/ML Developer:

• Building Practical Solutions: AI/ML developers create useful applications using AI. They use math to make these applications smart and effective.
• Basic Math: They need to know math concepts like matrices, which are like grids of numbers used to organize data. They also use derivatives, which help adjust AI systems to work better.
• Optimizing Models: Developers adjust AI models to make them accurate and fast. They do this using math techniques that find the best settings for the AI.
• Coding Skills: They use programming languages and special software libraries to turn math into working AI programs.

AI/ML Researcher:

• Creating New Techniques: AI/ML researchers invent fresh ideas for AI. They make AI smarter by thinking up new ways for it to learn and solve problems.
• Advanced Math: Researchers go deeper into math. They use fancy math like abstract algebra (math about rules that work in different situations) and calculus (math about how things change).
• Dealing with Uncertainty: They use math to predict things when they’re not sure. This is like guessing based on what they know.
• Complex Problem Solving: Researchers tackle big challenges by using complicated math techniques. They use these techniques to figure out how to make AI learn even better.

So, both developers and researchers need math. Developers use it to make AI useful, while researchers use more complex math to make AI even smarter and solve harder problems.

If you are terrified at the mere mention of “math”, you’re probably not going to have much fun in Artificial Intelligence.

But if you’re willing to invest time to improve your familiarity with the principles underlying calculus, linear algebra, stats, and probability, nothing — not even math — should get in the way of you getting into

I don’t even know more than half of the concepts up there. You don’t need to know all the concepts above. I’d say you don’t need to study math exclusively. You will learn it in the due course of time when actually go deeper into the working of the algorithms.

My personal suggestion for the Math-Haters → Just Basic Linear Algebra, Statistics, and Crust of Calculus should do the deed.

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Catch you on the flip side!!! See ya Toddles👋

Resources for the Math-Extravaganza's

GitHub - dair-ai/Mathematics-for-ML: 🧮 A collection of resources to learn mathematics for machine…

Mathematics for Machine Learning

3Blue1Brown

Linear Algebra | Khan Academy

Statistics and Probability | Khan Academy

Multivariable Calculus | Khan Academy

Mathematics for Machine Learning and Data Science Specialization