The Modern Mathematics of Deep Learning

Growing parameter norms

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.

Optimization theory · Study convergence and loss geometry under assumptions.

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: 2.1 A view through similarity · 2.3 The path matters · 4.1 When data live on a smaller shape

The source considers time or a parameter norm growing without bound, or an approximation tolerance approaching zero.

Limit notation describes behavior along a sequence of values.

Source formula example

t\to\infty

illustration · Finite lists illustrate directions of change; they do not establish any infinite limit or convergence theorem.

Symbols

$t$: Time.
$\Vert θ\Vert ₂$: The Euclidean parameter norm.
$ε$: A positive tolerance.

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

parameters = [1, 2, 4]
tolerances = [0.5, 0.25, 0.125]

Calculated here

Result expression: { parameters, tolerances }

Returns

Example result

parameters: array (3 items): [1, 2, 4]
tolerances: array (3 items): [0.5, 0.25, 0.125]

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. Finite lists illustrate directions of change; they do not establish any infinite limit or convergence theorem.

Source: Inline notation