The Modern Mathematics of Deep Learningexplained for non-mathematicians

Finite range with a fixed bound

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.

Source assumptions and notation · Interpret symbols and assumptions in a source statement.

The project supplies finite observations and fitted parameters. A held-out sample does not establish population bounds or prove a theorem.

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: 1.3 The questions ahead · 2.4 A second descent

The notation [N] includes every integer from 1 to N. For example, [150] contains 150 integers.

This specifies the valid index or degree range.

Source formula example

d∈[40]d\in[40]

illustration · This describes the ranges, not the results of the experiments using them.

Symbols

d,id, i
Integer indices in the specified range.
[40],[150][40], [150]
The integers 1 through the specified endpoint.

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

  • bounds = [40, 150]

Calculated here

Result expression: { bounds, sizes: bounds.map((n) => Array.from({ length: n }, (_, i) => i + 1).length), first: 1, last: 150, }

Returns

Example result
bounds
array (2 items): [40, 150]
sizes
array (2 items): [40, 150]
first
1
last
150

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

Result

Enable JavaScript to run this example.

Technical statement

The numerical values are invented. This describes the ranges, not the results of the experiments using them.

Source: Inline notation