Uniform approximation on a compact set
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.
Approximation and depth · Study approximation error and network size under stated conditions.
The project supplies finite observations and fitted parameters. A held-out sample does not establish population bounds or prove a theorem.
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 Learning from examples
The inequality asks that the largest absolute difference on K is smaller than 1/m.
For K = [0,1], g(x) = 0, and Φ(x) = x/2, the exact largest error is 1/2, reached at x = 1.
A uniform error bound controls all points in the set at once.
Source formula example
illustration · The supremum is known analytically for this particular pair of functions. Sampling points would not generally compute a supremum.
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.
You choose
input.m= 1
Initial values in code
exactSupremum=0.5
Calculated here
Result expression: { exactSupremum, limit, condition: exactSupremum < limit }
limit=1 / input.mUses:input.m
Returns
exactSupremum- 0.5
limit- 1
condition- true
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The source uses universal approximation to choose a network that satisfies this inequality on a compact set K containing the m distinct training points. Its general theorem requires an activation meeting the source hypotheses; this example only checks a specific known error.
Source: Source expression