The Modern Mathematics of Deep Learning

Zero initialization

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.

Initialization · Describe initial parameters and their distributions.

The current objective supplies a gradient; training updates the model parameters.

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: 1.2.1 Finding better settings

Θ⁽⁰⁾ = 0 means every parameter starts at zero.

The initialization specifies the first iterate.

Source formula example

\Theta^{(0)}=0

illustration · This example uses a two-entry vector.

Symbols

$Θ⁽⁰⁾$: The initial parameter vector.

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

theta0 = [0, 0]

Calculated here

Result expression: { theta0, isZero: theta0.every((v) => v === 0) }

Returns

Example result

theta0: array (2 items): [0, 0]
isZero: true

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 unless the source values are stated. This example uses a two-entry vector.

Source: Inline notation