The Modern Mathematics of Deep Learning

Interpolation parameter-count factors

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.

Approximation and depth · Study approximation error and network size under stated conditions.

The project supplies finite observations and fitted parameters. A held-out sample does not establish population bounds or prove a theorem.

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: 1.2.2 Can the network express the answer? · 1.3 The questions ahead

The source writes parameter counts using O(m(d+k)), O(d+mk), or O(d+m) in different interpolation settings.

Big-O expresses a growth bound up to constants.

Source formula example

{\mathcal{O}}(m(d+k))

illustration · These values evaluate the factors for one input; they do not prove a big-O bound or determine its hidden constant.

Symbols

$d$: Input dimension.
$m$: Number of examples.
$k$: Output dimension where stated.
$O$: A growth upper bound up to a constant.

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

d = 2
m = 3
k = 1

Calculated here

Result expression: { d, m, k, first: m * (d + k), second: d + m * k, third: d + m }

Returns

Example result

d: 2
m: 3
k: 1
first: 9
second: 5
third: 5

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. These values evaluate the factors for one input; they do not prove a big-O bound or determine its hidden constant.

Source: Inline notation