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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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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❤3👍1
🚨 Cambridge has just released a real bombshell this time.
📚 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
#AI #MachineLearning #FreeBooks #DataScience #DeepLearning #Tech
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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
#AI #MachineLearning #FreeBooks #DataScience #DeepLearning #Tech
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📖 "A Little Book on the Fundamentals of Generative AI" - an intuitive introduction to the mathematics:
arxiv.org/pdf/2605.29713
#GenerativeAI #Mathematics #DeepLearning #AIResearch #MachineLearning #arXiv
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arxiv.org/pdf/2605.29713
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Forwarded from Data Analytics
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:
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
#Transformers #DeepLearning #AI #MachineLearning #NeuralNetworks #Tech
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"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
#Transformers #DeepLearning #AI #MachineLearning #NeuralNetworks #Tech
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Forwarded from Machine Learning
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The platform offers:
🫡 1200+ machine learning tasks;
🫡 Mathematics, from linear algebra to PCA;
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🫡 Labs with real datasets;
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🫡 Projects using GPT, RL, and CUDA.
Almost everything can be accessed directly in your browser, and basic tasks are available for free.
⛓️ Link to the platform
https://enghusseinsheikho.substack.com/p/a-comprehensive-resource-for-machine?r=3hwnr8&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true
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Learn Deep Learning Cheat Sheet
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We found a practical course on applying modern AI methods in astronomy and astrophysics.
It covers neural network architectures, generative models, training on scientific data, simulation-based inference, and research AI agents.
⛓ Link to the course
https://deeplearning4astro.com/
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