Can training beat Lloyd?

2jw5U060C4 · three trained seeds · paired held-out and OOD controls

Training worked

3 / 3 seeds

Validation improved, parameters moved, and every checkpoint stayed within 2.6% of Lloyd-10.

Held-out superiority

Not detected

Normalized costs: trained 0.64676, Lloyd-10 0.64306; paired CI crosses zero.

OOD generalization

Significantly worse

Trained 1.03585 vs Lloyd-10 1.01574; 95% CI [0.01119, 0.03040].

Paper source

Question left open

The paper uses chosen parameters without training and expressly leaves learnability to future work.

Bounded conclusion

The challenge claim is falsified in this executed protocol: successful optimization does not produce superior clustering or OOD generalization. This does not prove impossibility for every conceivable learning environment.