The Modern Mathematics of Deep Learning

Eigenvalue equation

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

An eigenfunction is transformed into a scaled copy of itself. The scale is its eigenvalue.

This equation appears in the source discussion of quantum models.

Source formula example

\mathcal{H}_{R}\psi=\lambda_{\psi}\psi,\hskip 28.45274pt

illustration · This finite-dimensional toy uses three times the identity matrix. It is not the molecular Hamiltonian or a PDE solver.

Symbols

$ψ$: An eigenfunction in the source equation.
$λ_ψ$: Its eigenvalue.
$ℋ_R$: The source Hamiltonian operator.

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.

First entry

This example’s data flow

You choose

input.first = 1

Calculated here

Result expression: { psi, transformed, scaled: psi.map((value) => 3 * value) }

psi = [input.first, 2] Uses: input.first
transformed = psi.map((value) => 3 * value) Uses: psi

Returns

Example result

psi: array (2 items): [1, 2]
transformed: array (2 items): [3, 6]
scaled: array (2 items): [3, 6]

JavaScript

Read numbers from input and return the result. JavaScript basics.

Result

Enable JavaScript to run this example.

Technical statement

Change the input and run the same code again. The displayed result uses the values shown above.

Source: Source expression