The Modern Mathematics of Deep Learning

Trajectory figure architectures

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.

Model classes and structure · Describe families of rules, their size and structural properties.

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: 3.3 Other ways to measure possibility

The figure compares networks with 0, 3 and 10 hidden layers. Each hidden layer has n = 20 neurons.

These values describe the networks in the source figure.

Source formula example

0,3,10

illustration · This counts hidden neurons; it does not reproduce the plotted trajectories.

Symbols

$n$: Number of neurons per hidden layer.
$0, 3, 10$: The hidden-layer counts in the figure.

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

hiddenCounts = [0, 3, 10]
n = 20

Calculated here

Result expression: { n, hiddenCounts, neuronCounts: hiddenCounts.map((count) => n * count) }

Returns

Example result

n: 20
hiddenCounts: array (3 items): [0, 3, 10]
neuronCounts: array (3 items): [0, 60, 200]

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. This counts hidden neurons; it does not reproduce the plotted trajectories.

Source: Inline notation