"Introduction to Machine Learning" is another free textbook on machine learning, approximately 600 pages long, which emphasizes a deep mathematical understanding of the subject. 📚🧮

The book begins with the mathematical foundations necessary for further study: linear algebra, mathematical analysis, probability theory, matrix analysis, and optimization methods. It then covers the main supervised learning algorithms: linear and logistic regression, the k-nearest neighbors method, decision trees, random forests, boosting, and neural networks. 🤖📈

A significant portion of the book is dedicated to probabilistic and generative models. It discusses Monte Carlo methods, graphical models, Bayesian networks, variational methods, normalizing flows, variational autoencoders (VAEs), and generative adversarial networks (GANs). 🎲🧠

The final chapters discuss clustering, principal component analysis (PCA), learning on manifolds, and theoretical estimates of a model's ability to generalize. 🔍📊

In my opinion, this is an excellent resource for those who want to gain a broad understanding of machine learning and understand the mathematics underlying the key methods, rather than treating them as "black boxes." 💡✨

https://arxiv.org/pdf/2409.02668

#MachineLearning #DeepLearning #AI #Mathematics #DataScience #NeuralNetworks

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Tensor Algebra: A Small Concept That Has a Big Impact in AI 🧠

One thing I realized while learning deep learning is that tensors are everywhere. Whether you're working with TensorFlow, PyTorch, or building transformer models, almost everything revolves around tensor operations.

Although we often think of tensors as multi-dimensional arrays in machine learning, they're the structures that allow neural networks to efficiently represent and process complex data.

Here's a quick summary:
- Scalar (Rank 0): A single value
- Vector (Rank 1): A one-dimensional collection of values
- Matrix (Rank 2): A two-dimensional arrangement of values
- Tensor (Rank 3 or higher): A higher-dimensional representation used to model complex data

A few places where tensors show up every day:
- Images are represented as 3D tensors (Height × Width × Channels).
- Mini-batches become 4D tensors during model training.
- Transformer models process embeddings, attention scores, and hidden states as tensors throughout the network.
- Operations like matrix multiplication, broadcasting, reshaping, tensor contraction, and automatic differentiation power modern deep learning.

I created the infographic below as a simple visual reference while revisiting tensor algebra. I hope it's helpful for anyone learning deep learning or refreshing the fundamentals.

I'm curious. How did you first learn about tensors?
- Through mathematics?
- While using TensorFlow or PyTorch?
- During your first deep learning project?
- Or was there another resource that made the concept finally click?

I'd love to hear your experience and any resources you'd recommend for beginners. Looking forward to learning from your experiences and recommendations.

#DeepLearning #TensorFlow #PyTorch #AI #MachineLearning #Tensors

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📚 A whole collection of classic textbooks on AI and machine learning is now available for free in PDF format.

If you want to really understand machine learning and don't want to waste money on overpriced courses, these ten books will be enough to build a very solid foundation.

From simple to complex.

1️⃣ Understanding Machine Learning

One of the best books for beginners. It covers the basic theoretical algorithms of machine learning.

🔗 https://cs.huji.ac.il/~shais/UnderstandingMachineLearning/understanding-machine-learning-theory-algorithms.pdf

2️⃣ Mathematical Foundations of Machine Learning

If you're not very confident in your math skills, I would start here.

🔗 https://mml-book.github.io/book/mml-book.pdf

3️⃣ Mathematical Analysis of Machine Learning Algorithms

A more in-depth look at the mathematical principles of machine learning algorithms.

🔗 https://tongzhang-ml.org/lt-book/lt-book.pdf

4️⃣ Theoretical Principles of Deep Learning

The theoretical foundations of deep learning and an understanding of why it all works.

🔗 https://arxiv.org/pdf/2106.10165

5️⃣ Neural Networks and Learning Machines

A systematic analysis of neural networks and the principles of their training.

🔗 https://arxiv.org/pdf/1901.05639

6️⃣ Graph Deep Learning

A good starting point for those who want to understand graph neural networks.

🔗 https://yaoma24.github.io/dlg_book/dlg_book.pdf

7️⃣ Machine Learning: A Probabilistic Perspective

It allows you to look at machine learning from a probabilistic and algorithmic perspective.

🔗 https://people.csail.mit.edu/moitra/docs/bookexv2.pdf

8️⃣ Probability Theory: Theory and Examples

Fundamental theory of probability. Very useful if you want to understand machine learning beyond the level of using ready-made libraries.

🔗 https://sites.math.duke.edu/~rtd/PTE/PTE5_011119.pdf

9️⃣ Fundamentals of Applied Probability

More focus on the practical application of probability theory.

🔗 https://sites.math.duke.edu/~rtd/EP4A/EP4A_April2021.pdf

🔟 Advanced Data Analysis

An advanced level for those who want to seriously improve their data analysis skills.

🔗 https://stat.cmu.edu/~cshalizi/ADAfaEPoV/ADAfaEPoV.pdf

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📚 This is probably one of the best technical books on how large language models are trained at scale:

> GPU memory and profiling
> Breaking down computations into blocks, kernel fusion, and FlashAttention
> Data parallelism, tensor parallelism, pipeline parallelism, and context parallelism

I've already read the free online version, but I still had to buy a physical copy for my library. 📖

You can also read it for free on Hugging Face:

https://huggingface.co/spaces/nanotron/ultrascale-playbook

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One of the key moments when I truly understood how transformers work: 🧠✨

"Stop thinking of a transformer as a conveyor belt, where each layer transforms the output of the previous one."

"Start thinking of it as a residual flow." 🌊

Each block in a transformer has a residual connection that adds the input of the block to its output:

x' = f(x) + x

Because of this addition, the attention mechanism or MLP within the layer – the function f in the formula above – actually does NOT transform the input. Instead, it calculates the information that needs to be ADDED to the input before passing it to the next block! ➕

Imagine the main part of the transformer as a shared whiteboard. 📝 Each block reads what it needs from it and adds its own notes. All changes are additions.

Furthermore, layers can exchange information over distances. A block in the first layer can write information, and a block in the fifth layer can read it, even though there is no direct connection between them. 🔗

I owe these ideas to an older article by Anthropic about the architecture of transformers:
transformer-circuits.pub/2021/framework

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