The Modern Mathematics of Deep Learning

Mini-batch epoch count

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.

Learning and parameter updates · Select a rule or update parameters using a learning rule.

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

The ceiling of m/m′ is the number of batches needed to cover m examples when each batch holds at most m′.

A final batch can contain fewer examples.

Source formula example

\lceil m/m^{\prime}\rceil

illustration · The count assumes every example is visited once and no examples are dropped.

Symbols

$m$: Sample size.
$m^{\prime}$: Positive batch size.
$⌈m/m^{\prime}⌉$: Number of batches when a final partial batch is kept.

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

m = 10
batchSize = 4

Calculated here

Result expression: { m, batchSize, batches: Math.ceil(m / batchSize) }

Returns

Example result

m: 10
batchSize: 4
batches: 3

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. The count assumes every example is visited once and no examples are dropped.

Source: Inline notation