Function infinity norm
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.
Norms and distances · Measure size or difference in a specified space.
Project vectors have two features; the training matrix has n rows and two columns. Mathematical tools may operate on these values when their assumptions apply.
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: 1.2.2 Can the network express the answer? · 4.2 Approximating with random pieces
The L∞ norm is the essential supremum of the absolute value of a function, ignoring sets of measure zero.
It bounds function size almost everywhere.
Source formula example
illustration · The example assumes every listed point has positive measure; general essential suprema need not be attained.
Symbols
- Functions essentially bounded under the relevant measure.
- The domain set where stated.
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
Code changed. Reset to restore this example’s data flow.
Initial values in code
values=[-2, 1, 3]
Calculated here
Result expression: { values, norm }
norm=Math.max(...values.map(Math.abs))Uses:values
Returns
values- array (3 items): [-2, 1, 3]
norm- 3
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values are invented. The example assumes every listed point has positive measure; general essential suprema need not be attained.
Source: Inline notation