The Modern Mathematics of Deep Learning

Pruned network construction

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 source construction zeros both the output weight and the incoming parameters for each removed unit.

These operations define structured network layers and their analysis.

Source formula example

\widetilde{w}_{i}^{(2)}=0,\quad\text{if }i\notin I,\qquad\text{and}\qquad(\widetilde{w}_{i}^{(1)},\tilde{b}_{i}^{(1)})=\begin{cases}(w_{i}^{(1)},b_{i}^{(1)}),&\text{if }i\in I,\\ (0,0),&\text{if }i\notin I.\end{cases}

illustration · The invented finite inputs illustrate this expression. They do not prove a general identity, bound, or existence claim.

Symbols

$I$: Set of kept hidden-unit indices.
$w⁽¹⁾,b⁽¹⁾$: Incoming weights and biases.
$w⁽²⁾$: Output weights.
$tilde$: Pruned parameter values.

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.

First output weight

This example’s data flow

You choose

input.first = 1

Initial values in code

incoming = [ [1, 0], [2, 1], ]
keep = [true, false]

Calculated here

Result expression: { outputWeights: outputWeights.map((w, i) => (keep[i] ? w : 0)), incoming: incoming.map((w, i) => (keep[i] ? w : [0, 0])), }

outputWeights = [input.first, 2] Uses: input.first

Returns

Example result

outputWeights: array (2 items): [1, 0]
incoming: array (2 items): [array (2 items): [1, 0], array (2 items): [0, 0]]

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

The numbers in this example are invented.

Source: Source expression