The Modern Mathematics of Deep Learning

Network architecture

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.

Model classes and structure · Describe families of rules, their size and structural properties.

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: 1.2 Learning from examples · 1.2.2 Can the network express the answer? · 1.2.3 Does it work on new examples? · More source sections

N lists the number of neurons in each layer, including the input layer. L counts the layers after the input. The activation and widths together specify an architecture.

Layer sizes determine the shapes of inputs and weights.

Source formula example

{{a}}=(N,\varrho)

illustration · The example describes one architecture; actual network values also depend on its parameters.

Symbols

$a$: Architecture (N, ϱ).
$N$: Positive integer widths N₀ through Nᴸ.
$L$: Number of layers after the input.
$Nℓ$: Width of layer ℓ.
$x$: Input vector of length N₀.
$ϱ$: Activation function.

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 = [2, 3, 1]
x = [1, 2]

Calculated here

Result expression: { N, L, inputSize: N[0], outputSize: N[L], inputFits: x.length === N[0] }

L = N.length - 1 Uses: N

Returns

Example result

N: array (3 items): [2, 3, 1]
L: 2
inputSize: 2
outputSize: 1
inputFits: 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. The example describes one architecture; actual network values also depend on its parameters.

Source: Inline notation