arXiv:2607. 21721v3 Announce Type: replace-cross Abstract: Where truths are scarce (e.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
arXiv:2607. 21721v1 Announce Type: cross Abstract: Learned generative priors are increasingly used for ill-posed Bayesian inverse problems, their posterior uncertainty treated as earned from data.
arXiv:2606. 02309v1 Announce Type: new Abstract: Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions.
arXiv:2606. 04804v1 Announce Type: new Abstract: Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty.
arXiv:2608. 15147v1 Announce Type: new Abstract: Machine intelligence has conquered the symbolic world but stalled at the physical one.
arXiv:2506. 20181v2 Announce Type: replace Abstract: We study operator relevance in data-driven partial differential equation (PDE) discovery.
The paper investigates why differentiable causal discovery methods that encode expert priors as forbidden-edge constraints via an Augmented Lagrangian (ALM) penalty—termed the "guide, not bind" approach—often fail. It identifies two key failures: (1) the sequential penalty‑ramping ALM suppresses a true edge before counterfactual checks can detect it, and the proposed adaptive relaxation rule DADU violates necessary conditions for safe relaxation, leading to a high failure rate across thousands of training runs; (2) the standard correlation‑matching objective inherently ties a true edge and its reverse to the same cost, whereas covariance matching can separate them by a provable margin. The authors provide theoretical propositions, corollaries, and empirical evidence to support these claims.