Parameter robustness radius
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.
Optimization theory · Study convergence and loss geometry under assumptions.
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: 2.3 The path matters
δ denotes the radius of the parameter perturbations considered in the robustness condition.
The radius specifies how far a parameter can move in the test.
Source formula example
illustration · The example checks one perturbation; robustness requires the loss condition for all perturbations in the ball.
Symbols
- A positive perturbation radius.
- A parameter perturbation.
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
theta=2delta=0.5perturbation=0.25
Calculated here
Result expression: {
theta,
delta,
perturbation,
allowed: Math.abs(perturbation) < delta,
perturbed: theta + perturbation,
}
Returns
theta- 2
delta- 0.5
perturbation- 0.25
allowed- true
perturbed- 2.25
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values are invented. The example checks one perturbation; robustness requires the loss condition for all perturbations in the ball.
Source: Inline notation