The Modern Mathematics of Deep Learning

Linear classifier prediction

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.

Individual losses · Give one observed example a loss score.

Project predictions and known answers produce losses. Classification uses cross-entropy and α/2 times squared non-bias weights; Ridge uses normalized-mass MSE and α times all squared coefficients, including the intercept.

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: 2.2 Weight size and room to decide

The source margin surrogate loss ranges from 0 to 1. It equals 1 for nonpositive margins and 0 at or above a positive threshold.

The endpoints describe the scale of the surrogate loss.

Source formula example

0

illustration · This computes two values of the margin loss; intermediate margins have intermediate losses.

Symbols

$0,1$: Endpoints of the loss range.
$γ$: A positive margin threshold.

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

gamma = 1

Calculated here

Result expression: { gamma, atNegative: loss(-1), atThreshold: loss(1) }

Returns

Example result

gamma: 1
atNegative: 1
atThreshold: 0

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 computes two values of the margin loss; intermediate margins have intermediate losses.

Source: Inline notation