Theory ideas

Provable properties, identifiability and convergence arguments, each attached to a toy numerical demonstration.

2 ideas found

Status: Unverified Category: Theory Math: Stochastic processes Clear all

Unverified 2026

Nullspace Inverse-Loss Identification

Use a window of observed neural-network update trajectories to identify the set of local quadratic objectives and preconditioners that are consistent with the observed optimizer behavior. Rather than selecting one arbitrary curvature model, retain the nullspace of compatible parameters and use its dimension or smallest singular value as an identifiability and stability diagnostic.

Useful6/10

Difficulty6/10

Novelty8/10

Theory Stability Generalization Optimizer

Paper: Infinite-Horizon Inverse Linear-Quadratic Differential Games with State- and Control-Dependent Noise arXiv:2608.17939

Unverified 2026

Factor-Two Neural Model-Criticism Test

Use a frozen neural discrepancy score and conditional Monte Carlo replicas to test whether a generative model or learned sampler is compatible with a null data distribution, without requiring mixed chains or joint exchangeability. The resulting empirical p-value has a finite-sample false-alarm bound of at most two times the nominal level, making it safer than an ordinary Monte Carlo rank test for validation and deployment monitoring.

Useful5/10

Difficulty4/10

Novelty7/10

Theory Accuracy Stability Sample efficiency

Paper: Monte Carlo testing: non-asymptotic guarantees without joint exchangeability arXiv:2607.23010