The paper establishes a theoretical bound on the cost of enforcing a physics prior in machine learning models, showing that the excess risk of a shape‑constrained hypothesis class is always bounded by the excess risk of an ablated model that ignores the prior. Empirical tests on an ordinal wildfire‑severity task confirm that a constrained model can never be outperformed by its own ablation, and that the cost of the prior is protocol‑dependent and can be quantified using a self‑calibrating floor. The authors also propose a two‑fit screening method to reject unidentifiable experiments before training a constrained model.
arXiv:2606. 17529v1 Announce Type: cross Abstract: Scientific machine-learning (SciML) surrogates approximate expensive simulations, but exact expected outputs for arbitrary inputs are unavailable (the oracle problem).
arXiv:2608. 11243v1 Announce Type: new Abstract: We argue that a single structural fact organizes a wide range of phenomena in contemporary AI safety: a semantic safety constraint (e.
arXiv:2606. 29054v1 Announce Type: new Abstract: Large language models (LLMs) deployed for structured generation (NER, JSON extraction, QA, and classification) lack formal reliability guarantees, and standard heuristic abstention policies miss user-specified risk targets by 7.
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:2607. 07379v1 Announce Type: new Abstract: In agentic scientific machine learning (SciML), large language model (LLM) agents can discover surrogate models and select one by an automated score, typically an error metric.
arXiv:2606. 13780v1 Announce Type: cross Abstract: Machine-learned anomaly detection is reshaping searches for new physics, but it has outrun the statistics used to interpret it.
arXiv:2607. 12735v1 Announce Type: new Abstract: Companion work showed the grokking delay is causally the time to form task-structured representations, injectable via a contrastive prior.
arXiv:2606. 11266v1 Announce Type: new Abstract: The cost signal that constrained-RL algorithms optimize against is almost always reactive: the simulator emits a non-zero cost only after a collision has begun, and the Lagrange multiplier of PPO-Lagrangian grows only after the episode budget has been exceeded.
arXiv:2607. 20171v1 Announce Type: cross Abstract: Learned solvers for compressible flow are usually compared to classical methods at equal mesh resolution rather than at equal computational cost, and they typically offer no guarantee that their solutions remain physically admissible.
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. We show that this widely adopted recipe samples the wrong distribution.
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.
arXiv:2609.26272v1 Announce Type: new Abstract: Neural samplers are trained against an unnormalised target $\tilde\pi=e^{-E}$ with no samples from $\pi$, which leaves the practitioner with no way to...