The Modern Mathematics of Deep Learning

Network parameters

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.

Classification predicts three species; Ridge predicts body mass in grams using the same observations. These are separate models. Training predictions feed the objective; 102 separate test predictions never update the weights.

Prediction rules and layers · Describe or apply prediction rules, layers and parameters.

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

TaskTraining rowsTraining stepsPenalty αHeld-out row ID

Project operation

Output: Count: 9 · Shape: [3, 3]

Project operation

The project calculation uses these records; the source formula and example follow below. Code edits run locally; project settings travel between pages.

Prediction → Project operation → Project operation

Project input

Showing first three entries; the operation receives the complete array. Rounded preview; the operation uses full precision.

input.weights · Model: [≈-0.2895, ≈-2.052, ≈-1.016] … (9 entries)
input.width · Project settings or constant: 3

JavaScript

Result

Count: 9 · Shape: [3, 3]

Used in these source sections: 1.2 Learning from examples · 1.2.1 Finding better settings · 1.2.3 Does it work on new examples? · More source sections

θ is a vector of trainable real numbers. P(N) counts its entries for an architecture N.

Parameters determine a particular network in the architecture.

Source formula example

\theta\in{\mathbb{R}}^{P(N)}

illustration · This invented finite example illustrates the notation; it does not establish a general theorem.

Symbols

$θ$: Real parameter vector.
$N$: The network architecture.
$P(N)$: Number of parameters.

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.

Value

This example’s data flow

You choose

input.x = 2

Calculated here

Result expression: { theta, parameterCount: theta.length }

theta = [input.x, -1, 3] Uses: input.x

Returns

Example result

theta: array (3 items): [2, -1, 3]
parameterCount: 3

JavaScript

Read numbers from input and return the result. JavaScript basics.

Result

Enable JavaScript to run this example.

Technical statement

The numerical values in this example are invented. This invented finite example illustrates the notation; it does not establish a general theorem.

Source: Inline notation