The Modern Mathematics of Deep Learning

Atomic numbers

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

Zᵢ is the atomic number of nucleus i. The vector contains one positive integer per nucleus.

The nuclear charges enter the Hamiltonian.

Source formula example

(Z_{i})_{i=1}^{p}\in{\mathbb{N}}^{p}

illustration · This lists example atomic numbers; it does not compute an energy.

Symbols

$Zᵢ$: The positive integer atomic number of nucleus i.
$p$: The number of nuclei.

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

Z = [1, 2]

Calculated here

Result expression: { Z, p: Z.length, valid: Z.every((z) => Number.isInteger(z) && z > 0) }

Returns

Example result

Z: array (2 items): [1, 2]
p: 2
valid: true

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. This lists example atomic numbers; it does not compute an energy.

Source: Inline notation