The Modern Mathematics of Deep Learning

A network at selected 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.

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.

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: 5.1 The shape of training loss

Φ(·,θmin) is the network function with a selected minimizing parameter vector. The dot leaves the input variable open.

A parameter vector determines a particular function.

Source formula example

\Phi(\cdot,\theta_{\min})

illustration · The chosen parameter vector illustrates evaluation only; this code does not establish that it minimizes any source objective.

Symbols

$Φ$: The network function.
$θmin$: A selected minimizing parameter vector.
$θ*$: Another parameter vector in the figure.
$·$: An input placeholder.

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

thetaMin = [2, 1]
x = 3

Calculated here

Result expression: { thetaMin, x, output }

output = thetaMin[0] * x + thetaMin[1] Uses: thetaMin, x

Returns

Example result

thetaMin: array (2 items): [2, 1]
x: 3
output: 7

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 chosen parameter vector illustrates evaluation only; this code does not establish that it minimizes any source objective.

Source: Inline notation