The Modern Mathematics of Deep Learning

Gradient directions across steps

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 sequence (D⁽ᵏ⁾) lists one update direction for each of K optimization steps.

The sequence records the directions used by an iterative method.

Source formula example

(D^{(k)})_{k=1}^{K}

illustration · The example lists two fixed directions; it does not define their random sampling law.

Symbols

$D⁽ᵏ⁾$: The update direction at step k.
$K$: The number of steps.

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

directions = [ [1, 0], [0, 1], ]

Calculated here

Result expression: { K: directions.length, directions }

Returns

Example result

K: 2
directions: array (2 items): [array (2 items): [1, 0], array (2 items): [0, 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. The example lists two fixed directions; it does not define their random sampling law.

Source: Inline notation