The Modern Mathematics of Deep Learning

Matching residual dimensions

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.

Residual networks · Describe residual layer updates and their continuous analogue.

Convolution, recurrent and residual architectures are not part of this linear penguin model.

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: 6.2 Shortcuts between layers

Nℓ = Nℓ₋₁ means the output and previous layer have the same width.

Equal widths permit direct residual addition.

Source formula example

N_{\ell}=N_{\ell-1}

illustration · This checks one pair of widths; it does not establish a network-wide training result.

Symbols

$Nℓ$: Current layer width.
$Nℓ₋₁$: Previous layer width.

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

N = [3, 3]

Calculated here

Result expression: { previous: N[0], current: N[1], match: N[0] === N[1] }

Returns

Example result

previous: 3
current: 3
match: true

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 unless the source values are stated. This checks one pair of widths; it does not establish a network-wide training result.

Source: Inline notation