Practical Deep Learning

background-image: url('../figs/title.png')

---
class: center, middle

# Tensors

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# Numbers...

\$  5 \$

---

# Vectors...

\$  5 \$

\$  [1, 1, 2, 3, 5] \$

---

# Matrices...

\$  5 \$

\$  [1, 1, 2, 3, 5] \$

\$\begin{bmatrix}
9 & 8 & 1 \\\
0 & 7 & 7
\end{bmatrix}\$

---

# These are all tensors!

\$  5 \$

\$  [1, 1, 2, 3, 5] \$

\$\begin{bmatrix}
9 & 8 & 1 \\\
0 & 7 & 7
\end{bmatrix}\$

---

# A matrix is a 2-dimensional tensor

.col50[
\$\begin{bmatrix}
9 & 8 & 1 \\\
0 & 7 & 7
\end{bmatrix}\$
]
.col50[
Dimensionality = \$2\$, Size = \$(2,3)\$
]

---

# A vector is a 1-dimensional tensor

.col50[
\$  [1, 1, 2, 3, 5] \$
]
.col50[
Dimensionality = \$1\$, Size = \$(5)\$
]

---

# A number is a 0-dimensional tensor

.col50[
\$  5 \$
]
.col50[
Dimensionality = \$0\$, Size = \$1\$
]

---

# These are familiar tensors

.col50[
\$  5 \$

\$  [1, 1, 2, 3, 5] \$

\$\begin{bmatrix}
9 & 8 & 1 \\\
0 & 7 & 7
\end{bmatrix}\$
]
.col50[
Dimensionality = \$0\$, Size = \$1\$

Dimensionality = \$1\$, Size = \$(5)\$

Dimensionality = \$2\$, Size = \$(2,3)\$
]

---

# But tensors can have more dimensions too...

.col50[
\$
\left[ \begin{align}
\begin{bmatrix}
255 & 255 & 255 \\\
255 & 0 & 0
\end{bmatrix} \\\
\begin{bmatrix}
0 & 128 & 255 \\\
0 & 0 & 255
\end{bmatrix} \\\
\begin{bmatrix}
0 & 0 & 0 \\\
255 & 255 & 0
\end{bmatrix}
\end{align}
\right]
\$
]
.col50[
Dimensionality = \$4\$, Size = \$3,2,3\$
]

---

# We can interpret this tensor as an image

![A 3x2 image of with pixels the color of red, orange, yellow, magenta, blue, and green](../figs/6rainbow.png)

]
.col50[
Dimensionality = \$4\$, Size = \$3,2,3\$

The first dimension is channels (red, green, and blue)

The second dimension is height

The third dimension is width

This is referred to as CHW format

]

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# Tensors are handy for deep learning

In machine learning sometimes we process one example but usually we process multiple data points at a time. If we want to process a *batch* of images, each image is a tensor, say:

$$3 \times 128 \times 256 $$

If this image is in CHW format this would be a 256 width, 128 height, RGB image.

But in our batch say we have 64 images, then our whole batch is itself a tensor of size:

$$ 64 \times 3 \times 128 \times 256 $$

This is referred to as NCHW format (the most common for storing images in tensors for deep learning)

This is a 4 dimensional tensor used for batches of images. If you were processing video you might want a 5 dimensional tensor! Yay tensors

---

# How do we use tensors?

Tensors are common data structures in the big neural network frameworks.

Right now there are 2 main frameworks out there, PyTorch and Tensorflow.

PyTorch is developed at Facebook (mostly) and used for a lot of research code and fun projects you'll find online.

Tensorflow is developed at Google (mostly) and is kind of a mess but it can run on TPUs (Google's special purpose deep learning hardware) so it's useful for that.

We'll be playing around with PyTorch in class, but on Google hardware, ha!

[https://colab.research.google.com/](https://colab.research.google.com/)