Honest Physical-Support Inference after Latent Dictionary Learning: Collision Singularities and Minimax Resolution

What the math gives to ML

The paper provides a concrete way to prevent learned sparse representations from making overconfident, label-dependent predictions near nearly colliding dictionary atoms. Its key transferable asset is the separation of three information budgets: test-time support separation scales as Tβ_-²s²/σ_+², while dictionary orientation may require only Ns⁶ information, creating a regime where coordinate-level predictions look precise but physical-ray identification is statistically unjustified. This suggests neural sparse encoders and mixture-of-experts routers should emit permutation- and sign-invariant group-level support with an explicit child-level abstention criterion, rather than treating a learned dictionary as known. The same budgets can drive adaptive allocation of training data, test-time replication, or representation refinement.