The Modern Mathematics of Deep Learningexplained for non-mathematicians

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Union of index ranges

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.

Sets and notation · Describe domains, indices and membership.

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: 2.4 A second descent

The union contains indices 10 through 20 and 30 through 50, inclusive.

It selects two groups of coordinates.

Source formula example

i∈{10,…,20}∪{30,…,50}i\in\{10,\dots,20\}\cup\{30,\dots,50\}

illustration · This constructs the stated finite index set; it does not generate the associated random variables.

Symbols

ii
An index in either listed range.

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

Calculated here

Result expression: { first, second, count: first.length + second.length }

  • first = Array.from({ length: 11 }, (_, i) => i + 10)
  • second = Array.from({ length: 21 }, (_, i) => i + 30)

Returns

Example result
first
array (11 items): [10, 11, 12, 13, …]
second
array (21 items): [30, 31, 32, 33, …]
count
32

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

Result

Enable JavaScript to run this example.

Technical statement

The numerical values are invented unless the source values are stated. This constructs the stated finite index set; it does not generate the associated random variables.

Source: Inline notation