The Modern Mathematics of Deep Learningexplained for non-mathematicians

Two-point source sample

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.

Observations and sampling · Describe examples, targets and samples.

The selected rows supply measurements and known answers to training; held-out IDs remain separate.

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: 1.3 The questions ahead

The source example uses the sample ((−1,0),(1,1)), with each pair containing an input and target.

The stated sample determines the empirical risk in that example.

Source formula example

s=((−1,0),(1,1)){s}=((-1,0),(1,1))

illustration · This reproduces the two source pairs; it does not evaluate the network risk.

Symbols

ss
The ordered sample of input-target pairs.

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

  • sample = [ [-1, 0], [1, 1], ]

Calculated here

Result expression: { sample, m: sample.length }

Returns

Example result
sample
array (2 items): [array (2 items): [-1, 0], array (2 items): [1, 1]]
m
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 reproduces the two source pairs; it does not evaluate the network risk.

Source: Inline notation