The Modern Mathematics of Deep Learning

Noisy observations

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.

Observations and sampling · Describe examples, targets and samples.

The selected rows supply measurements and known answers to training; held-out IDs remain separate.

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: 7.2 A few building blocks at a time

The noisy observation x̃ is the original vector x plus noise ν, coordinate by coordinate.

Denoising tries to recover the original from the noisy observation.

Source formula example

\tilde{x}\coloneqq x+\nu

illustration · The example adds specified noise; it does not assume or sample a noise distribution.

Symbols

$x$: The original signal.
$ν$: A noise vector of matching shape.
$x̃$: The observed noisy signal.

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

x = [1, 2]
noise = [0.5, -0.5]

Calculated here

Result expression: { x, noise, noisy: x.map((v, i) => v + noise[i]) }

Returns

Example result

x: array (2 items): [1, 2]
noise: array (2 items): [0.5, -0.5]
noisy: array (2 items): [1.5, 1.5]

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 example adds specified noise; it does not assume or sample a noise distribution.

Source: Inline notation