The Modern Mathematics of Deep Learning

A multichannel signal window

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.

Frames and sparse signals · Encode or reconstruct signals with frames and dictionaries.

The project scales bill and flipper measurements using training-row means and scales; its feature vector has two entries.

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

At each channel, collect the values in the window starting at position g, wrapping around the signal.

Local windows describe which values interact with a local convolutional dictionary.

Source formula example

((x_{i})_{g+h})_{i\in[c],h\in H}

illustration · This displays one input patch and does not prove a sparse recovery result.

Symbols

$xᵢ$: Signal in channel i.
$g$: Starting position on the cyclic group.
$h$: Window index.
$H$: Window index set.
$c$: Number of output channels.

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.

Starting position

This example’s data flow

You choose

input.position = 2

Initial values in code

channels = [ [1, 2, 3], [4, 5, 6], ]

Calculated here

Result expression: { channels, window }

position = input.position Uses: input.position
window = channels.map((channel) => [ channel[position], channel[(position + 1) % 3], ]) Uses: channels, position

Returns

Example result

channels: array (2 items): [array (3 items): [1, 2, 3], array (3 items): [4, 5, 6]]
window: array (2 items): [array (2 items): [3, 1], array (2 items): [6, 4]]

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

The cyclic signal has d = 3 positions, the window has n = 2 positions, and c = 2 channels. Positions in this code start at zero.

Source: Source expression