The Modern Mathematics of Deep Learning

Pruning width and retained count

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.

Pruning · Describe removal of network weights and related error bounds.

The project uses a linear rule with two features. The fitted weights produce scores or normalized mass.

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: 6.5 Removing connections

The pruning statement assumes n ≥ 100 and retains at most n/100 indices, corresponding to at least 99% removed.

The conditions quantify the size of the resulting subnetwork.

Source formula example

n\geq 100

illustration · The example checks the stated counts; it does not prove an approximation bound.

Symbols

$n$: The hidden width.
$I$: The retained index set.
$|I|$: The number of retained indices.

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

n = 100
retained = 1

Calculated here

Result expression: { n, retained, retainedBound: n / 100, removedPercent: (100 * (n - retained)) / n, }

Returns

Example result

n: 100
retained: 1
retainedBound: 1
removedPercent: 99

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

The numerical values are invented. The example checks the stated counts; it does not prove an approximation bound.

Source: Inline notation