The Modern Mathematics of Deep Learning

Learned inverse reconstruction

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.

Inverse problems · Describe reconstruction from observations using a forward operator.

This application has its own inputs and assumptions; the penguin measurements are not its experimental data.

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: 8.1 Working back from measurements

Insert the selected parameter into the network to obtain a candidate reconstruction.

The reconstruction is the output after selecting model parameters.

Source formula example

y=\Phi(\xi,\hat{\theta})

illustration · The example does not solve an inverse problem on its own.

Symbols

$Φ$: Parameter-dependent model.
$ξ$: Fixed model input.
$θ̂$: Selected parameter.
$y$: Reconstructed candidate.

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.

Selected parameter

This example’s data flow

You choose

input.parameter = 1.5

Initial values in code

xi = 1

Calculated here

Result expression: { xi, theta, reconstruction: xi * theta }

theta = input.parameter Uses: input.parameter

Returns

Example result

xi: 1
theta: 1.5
reconstruction: 1.5

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

The invented model is Φ(ξ,θ) = ξθ with ξ = 1. This evaluates the chosen parameter without claiming it was optimized.

Source: Source expression