The Modern Mathematics of Deep Learning

Initialization variances

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: 2.1 A view through similarity

The source uses zero-mean normal initial weights and biases. Their variances are σw²/Nℓ and σb² respectively.

Variance specifies the spread of an initialization distribution.

Source formula example

\sigma_{w}^{2}/N_{\ell}

illustration · This computes variance parameters; it does not sample a normal distribution or show an infinite-width limit.

Symbols

$σw, σb$: Positive scale parameters.
$Nℓ$: Positive layer width.

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

sigmaW = 2
sigmaB = 1
width = 4

Calculated here

Result expression: { weightVariance: sigmaW ** 2 / width, biasVariance: sigmaB ** 2 }

Returns

Example result

weightVariance: 1
biasVariance: 1

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 variance parameters; it does not sample a normal distribution or show an infinite-width limit.

Source: Inline notation