The Modern Mathematics of Deep Learning

Batch mean and standard deviation

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.

Batch normalization · Describe batch normalization and its derivatives.

The project uses a linear rule with two features. The fitted weights produce scores or normalized mass.

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: 6.4 Adjusting the scale

μ and σ are the mean and standard deviation of a random input in this batch-normalization discussion.

Mean and standard deviation describe the center and spread of the input law.

Source formula example

\mu

illustration · This computes exact moments under a finite law; it does not estimate them from a random batch.

Symbols

$μ$: The input mean.
$σ$: The input standard deviation.

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

values = [0, 2]
probabilities = [0.5, 0.5]

Calculated here

Result expression: { values, mu, sigma }

mu = values.reduce((s, v, i) => s + v * probabilities[i], 0) Uses: values, probabilities
sigma = Math.sqrt( values.reduce((s, v, i) => s + (v - mu) ** 2 * probabilities[i], 0), ) Uses: values, mu, probabilities

Returns

Example result

values: array (2 items): [0, 2]
mu: 1
sigma: 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 exact moments under a finite law; it does not estimate them from a random batch.

Source: Inline notation