The Modern Mathematics of Deep Learningexplained for non-mathematicians

Concepts / Start here

Frame sizes

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: 6.3 Taking apart and rebuilding

The source compares frame counts p and q with dimensions d and n, and uses r for a shared count in a special case.

These inequalities and equalities constrain frame sizes.

Source formula example

p≥dp\geq d

illustration · This checks one set of compatible counts; it does not construct the source frames.

Symbols

d,nd,n
Signal and window dimensions.
p,qp,q
Frame sizes.
rr
A common frame count in the special case.

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

  • d = 2
  • n = 2
  • p = 2
  • q = 2
  • r = 2

Calculated here

Result expression: { d, n, p, q, r, valid: p >= d && q >= n && p === d && q === n && p === q && q === r && r <= n, }

Returns

Example result
d
2
n
2
p
2
q
2
r
2
valid
true

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

Result

Enable JavaScript to run this example.

Technical statement

The numerical values are invented. This checks one set of compatible counts; it does not construct the source frames.

Source: Inline notation