The Modern Mathematics of Deep Learningexplained for non-mathematicians

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Frame vectors

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 sequences list local vectors vⱼ and global vectors uᵢ used as frames.

Each frame contains multiple vectors indexed by its count.

Source formula example

(vj)j=1q(v_{j})_{j=1}^{q}

illustration · This uses two standard bases; general frames need not be bases or have the same dimension.

Symbols

uiuᵢ
A global frame vector.
vjvⱼ
A local frame vector.
p,qp,q
Their respective counts.

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

  • u = [ [1, 0], [0, 1], ]
  • v = [ [1, 0], [0, 1], ]

Calculated here

Result expression: { u, v, p: u.length, q: v.length }

Returns

Example result
u
array (2 items): [array (2 items): [1, 0], array (2 items): [0, 1]]
v
array (2 items): [array (2 items): [1, 0], array (2 items): [0, 1]]
p
2
q
2

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 uses two standard bases; general frames need not be bases or have the same dimension.

Source: Inline notation