The Modern Mathematics of Deep Learning

Electron coordinates

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.

Quantum models · Describe wavefunctions, particle coordinates and energy relations.

PDE and quantum models are not operations on these penguin measurements.

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

Each electron position rᵢ is a three-dimensional vector. Indices identify the electrons; n₊ counts those in the first spin group.

Position and spin-group indices define the wavefunction inputs.

Source formula example

r

illustration · The positions and spin counts are invented; they do not describe a specified physical system.

Symbols

$r, rᵢ$: Electron positions; each rᵢ has three coordinates.
$i, j, k$: Electron indices.
$n$: Number of electrons.
$n₊$: Number in the first spin group.

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

positions = [ [0, 0, 0], [1, 0, 0], [0, 1, 0], ]
nPlus = 2

Calculated here

Result expression: { positions, n, nPlus, remaining: n - nPlus }

n = positions.length Uses: positions

Returns

Example result

positions: array (3 items): [array (3 items): [0, 0, 0], array (3 items): [1, 0, 0], array (3 items): [0, 1, 0]]
n: 3
nPlus: 2
remaining: 1

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 positions and spin counts are invented; they do not describe a specified physical system.

Source: Inline notation