The Modern Mathematics of Deep Learning

Matrix dimensions

Penguin learning project

The project uses 342 complete Palmer penguin records: 240 training-pool and 102 held-out rows. The selected training rows determine feature scaling and model parameters. Source CSV

This project trains weights with softmax, unlike the homepage lab, which uses nearest species averages. Same penguin measurements; different classification methods. Predictions can differ.

Vectors and matrices · Combine numbers using vector and matrix operations.

Project vectors have two features; the training matrix has n rows and two columns. Mathematical tools may operate on these values when their assumptions apply.

Consider this concept alongside the project; its source assumptions may differ. These observations do not prove a theorem.

Input: 12 × 2; Held-out evaluation: 102 · #58 · 40.6 mm, 193 mm. Known answer: Adélie; Prediction: Adélie · [≈0.7383, ≈0.2444, ≈0.01737].

Used in these source sections: 6.1 Looking locally

A 2 × 2 matrix has two rows and two columns.

Dimensions determine which matrix operations are valid.

Source formula example

2\times 2

illustration · This invented finite example illustrates the notation; it does not establish a general theorem.

Symbols

$2 × 2$: Two rows and two columns.

Source formula example

This source example uses its own inputs and assumptions. Editing it does not change the project.

Edit a value or the code, then run the example. This is a finite demonstration, not a proof of the paper’s theorem.

This example’s data flow

Initial values in code

matrix = [ [1, 2], [3, 4], ]

Calculated here

Result expression: { matrix, rows: matrix.length, columns: matrix[0].length }

Returns

Example result

matrix: array (2 items): [array (2 items): [1, 2], array (2 items): [3, 4]]
rows: 2
columns: 2

JavaScript

Read numbers from input and return the result. JavaScript basics.

Result

Enable JavaScript to run this example.

Technical statement

The numerical values in this example are invented. This invented finite example illustrates the notation; it does not establish a general theorem.

Source: Inline notation