Welcome to understanding tensors - the building blocks of modern machine learning! You might think tensors sound intimidating, but you already work with them every day without realizing it.

A tensor is simply a multi-dimensional array. Think of it as a supercharged version of a list or table, perfect for organizing data in machine learning.

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How do you think a color image could be represented as numbers inside a tensor?

Let's start with scalars—0-dimensional tensors. A scalar is just a single number, like 5 or 3.14.
It's the simplest kind of tensor: one value, no axes, just a point.

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Can you think of a machine learning scenario where you'd use just one number?

Vectors are 1-dimensional tensors—a list of numbers, like [1, 2, 3, 4].
In machine learning, vectors often represent features of a single data point, such as a person's height, weight, age, and income.

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What other real-world data could you represent as a vector?

Matrices are 2-dimensional tensors—think of a table with rows and columns, like [[1, 2], [3, 4]].
In machine learning, matrices often store multiple data points, with each row representing one example and each column a feature.

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If you had 100 people with 5 features each, what would the matrix shape be?

3D tensors add another layer—imagine stacking matrices like sheets of paper.
A color image is often stored as a 3D tensor: (height, width, 3), where 3 stands for the red, green, and blue color channels.

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Why might time-series data also use 3D tensors?

4D tensors are common in deep learning, especially for batches of images.
For example, a batch of 32 color images sized 64x64 pixels would have shape (32, 64, 64, 3). Each number in the shape adds a new level of organization.

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What does each number in that shape represent?

Understanding shape and axes is crucial. Each dimension is an axis: axis 0, axis 1, axis 2, and so on.
For shape (10, 3, 224, 224), axis 0 has size 10, axis 1 has size 3, and so forth.

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Which axis would you use to access individual images in this batch?

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Let's test your tensor understanding!
What is each tensor called?

Suggested Answers

• Scalar
• Vector
• Matrix