Harness the Power of Math

Mix.install([
  {:nx, "~> 0.6.2"},
  {:exla, "~> 0.6.1"},
  {:kino, "~> 0.11.0"},
  {:stb_image, "~> 0.6.3"},
  {:vega_lite, "~> 0.1.8"},
  {:kino_vega_lite, "~> 0.1.10"}
])

Speaking the Language of Data

Linear algebra is the language of data

The power of Nx tensors and Nx operations build on existing theory and operations in Linear Algebra

Deep Learning especially leans on the power of Linear Algebra

Nx.default_backend(EXLA.Backend)

The Building Blocks of Linear Algebra

The fundamental object in Linear Algebra is the vector

Another object in Linear Algebra is the scalar, which are just numbers

vect = Nx.tensor([1.0, 2.0, 3.0], type: :f32)

scalar = Nx.tensor(3.0, type: :f32)

Important Operations in Linear Algebra

Vector Addition

sales_day1 = Nx.tensor([32, 10, 14])
sales_day2 = Nx.tensor([43, 23, 76])

total_sales = Nx.add(sales_day1, sales_day2)

Scalar Multiplication

keep_rate = 0.9
unreturned_sales = Nx.multiply(keep_rate, total_sales)

price_per_product = Nx.tensor([9.95, 10.95, 5.99])
revenue_per_product = Nx.multiply(unreturned_sales, price_per_product)

Transpose

The transpose of a matrix is a matrix that’s flipped along its diagonal, where the rows and columns of the matrix are swapped

Imagine some sales data is encoded into a matrix. Each row represents a day of sales while each column represents a sales data for a given product. To flip this relationship, such that each column represents a day of sales and each row represents a product:

sales_matrix =
  Nx.tensor([
    [32, 10, 14],
    [43, 23, 76]
  ])
  |> Nx.transpose()

Linear Transformations

A linear transformation, also known as a linear map, is a function that maps inputs to outputs

Linear transformations are special because they preserve linearity meaning they produce a different representation of an input, while still preserving it’s fundamental properties. This is useful when a different or more convenient representation of the input is required

Given an image, the colors can be invereted as follows

image = "/Users/charlie/github.com/charlieroth/machine-learning-in-elixir/files/IMG_0061.jpeg"

image
|> StbImage.read_file!()
|> StbImage.resize(512, 512)
|> StbImage.to_nx()
|> Nx.as_type({:u, 8})
|> Kino.Image.new()

invert_color_channels =
  Nx.tensor([
    [-1, 0, 0],
    [0, -1, 0],
    [0, 0, -1]
  ])

image
|> StbImage.read_file!()
|> StbImage.resize(512, 512)
|> StbImage.to_nx()
|> Nx.dot(invert_color_channels)
|> Nx.as_type({:u, 8})
|> Kino.Image.new()