The Modern Mathematics of Deep Learning

Curvature index and loss

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: 5.1 The shape of training loss

The source figure sketches critical-point index against loss and marks loss values 0, 0.25 and 0.5.

The labels describe the axes of a schematic figure.

Source formula example

0

illustration · The figure is schematic; these ticks alone do not provide a dataset or quantify the plotted distribution.

Symbols

$Index$: The critical-point index on the figure.
$Loss$: The figure loss axis.

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

lossTicks = [0, 0.25, 0.5]

Calculated here

Result expression: { lossTicks }

Returns

Example result

lossTicks: array (3 items): [0, 0.25, 0.5]

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 figure is schematic; these ticks alone do not provide a dataset or quantify the plotted distribution.

Source: Inline notation