The Modern Mathematics of Deep Learning

Positive-spin wavefunctions

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

Ψ⁺ is the collection of functions associated with the positive-spin electron group.

The construction treats positive and negative spin groups separately.

Source formula example

\Psi^{+}

illustration · The arrays only illustrate a collection of two function values; they do not calculate the source wavefunction.

Symbols

$Ψ⁺$: The positive-spin group of functions.

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

positiveFunctions = [ [1, 0], [0, 1], ]

Calculated here

Result expression: { positiveFunctions, count: positiveFunctions.length }

Returns

Example result

positiveFunctions: array (2 items): [array (2 items): [1, 0], array (2 items): [0, 1]]
count: 2

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 arrays only illustrate a collection of two function values; they do not calculate the source wavefunction.

Source: Inline notation