The Modern Mathematics of Deep Learning

Index set difference

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.

Source assumptions and notation · Interpret symbols and assumptions in a source statement.

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: 8.2 Equations as guides

The indices in [n] ∖ [n₊] start after n₊ and end at n.

This selects the indices outside the first group.

Source formula example

i,j,k\in[n]\setminus[n_{+}]

illustration · The example uses one valid pair of counts.

Symbols

$n$: Total number of indices.
$n₊$: Size of the first group, at most n.
$i, j, k$: Indices in the set difference.

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

n = 5
nPlus = 2

Calculated here

Result expression: { n, nPlus, indices: Array.from({ length: n }, (_, i) => i + 1).filter((i) => i > nPlus), }

Returns

Example result

n: 5
nPlus: 2
indices: array (3 items): [3, 4, 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. The example uses one valid pair of counts.

Source: Inline notation