My work studies the order structure of learning problems: the order among the answers a learner proposes, among the corruption states a generative model passes through, and among the noise levels a diffusion model is trained on.
2026
MWRL credits each proposal for the coverage the group’s union of certified sets would lose without it. The credit, derived from the problem definition, asks for minimality and for every alternative at once, and MWRL recovers most minimal witnesses where other methods return redundant supersets or a single witness.
2026
Diffusion, autoregression and the models between them are paths on one corruption lattice. The fewest steps of a zero-cost decoding schedule are set by the geometry of the data, and below that bound the ranking of schedules is predicted before decoding.
2026
One network shared across noise levels benefits from their adjacency in the noise-level embedding, not from their direction: reversing the embeddings leaves the fitting error unchanged, while shuffling them raises it.
2026
The information a projected filter discards bounds its cost only on average. Through the Mori–Zwanzig formalism, assumed-density filtering is the Markovian closure and every other projected filter adds a defect; its error is the propagated sum of its defects and of the returns of what it discards.