The Modern Mathematics of Deep Learning

An undefined source symbol

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 paper uses Ψ⁺ here without defining it. I don't know what it denotes. The surrounding sentence describes the input size of Γₖ.

The input-size calculation requires a supplied output dimension.

Source formula example

\Psi^{+}

illustration · This computes only the stated input-size addition using a reader-supplied output dimension. It does not define Ψ⁺.

Symbols

$\Psi^{+}$: Undefined in the source at this occurrence.
$\Gamma_k$: A fully connected network whose input combines an embedding and negative-spin particle coordinates.
$n_-$: Number of negative-spin particles; each has three position coordinates.

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.

Supplied output dimensionNegative-spin particles

This example’s data flow

You choose

input.outputDimension = 2
input.negativeElectrons = 1

Calculated here

Result expression: { suppliedOutputDimension, negativeElectronCoordinates, gammaInputDimension: suppliedOutputDimension + negativeElectronCoordinates, sourceDefinesPsiPlus: false, }

suppliedOutputDimension = input.outputDimension Uses: input.outputDimension
negativeElectronCoordinates = 3 * input.negativeElectrons Uses: input.negativeElectrons

Returns

Example result

suppliedOutputDimension: 2
negativeElectronCoordinates: 3
gammaInputDimension: 5
sourceDefinesPsiPlus: false

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

The source describes Γₖ receiving an embedding output concatenated with positions of n₋ negative-spin particles, each with three coordinates. The example dimensions are reader-supplied assumptions, not a definition of Ψ⁺ or a claim about its output.

Source: Undefined source notation