The Modern Mathematics of Deep Learning

Optimization iterates

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 Learning from examples · 1.2.1 Finding better settings

Θ⁽⁰⁾ is an initial parameter, and Θ⁽ᵏ⁾ is the parameter after step k. K counts the steps.

The sequence records the values produced by optimization.

Source formula example

\Theta^{(0)}

illustration · This deterministic quadratic example shows two steps; the source also considers stochastic updates.

Symbols

$Θ⁽ᵏ⁾$: Parameter vector at step k; one scalar here.
$K$: Positive integer number of steps.
$k$: Step index.

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

theta = 2
K = 2

Calculated here

Result expression: { K, iterates, final: theta }

iterates = [theta] Uses: theta
for (let k = 1; k <= K; k++) { theta -= 0.25 * 2 * theta; iterates.push(theta); } Uses: K, theta, iterates

Returns

Example result

K: 2
iterates: array (3 items): [2, 1, 0.5]
final: 0.5

Some runtime paths or values are not resolved here.

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 deterministic quadratic example shows two steps; the source also considers stochastic updates.

Source: Inline notation