Swapping particles
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.
Quantum models · Describe wavefunctions, particle coordinates and energy relations.
PDE and quantum models are not operations on these penguin measurements.
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: 8.2 Equations as guides
An antisymmetric function changes sign when two particle coordinates are exchanged.
These expressions specify the inverse or quantum model.
Source formula example
illustration · The invented finite inputs illustrate this expression. They do not prove a general identity, bound, or existence claim.
Symbols
- Operator exchanging particle coordinates i and j.
- Many-particle wavefunction.
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.a= 1
Calculated here
Result expression: { original: psi(input.a, 3), swapped: psi(3, input.a) }
Returns
original- -2
swapped- 2
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The invented function ψ(a,b) = a − b illustrates one swap. The source requires antisymmetry under each relevant particle exchange.
Source: Source expression