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.
By Denis Gueyffier (ONERA -- Institut Polytechnique de Paris)
arXiv:2606. 25151v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) embed governing equations in their loss function, enabling mesh-free solutions to partial differential equations.
By David McShannon, Nicholas Dietrich
arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
By Jose Marie Antonio Mi\~noza, Erika Fille T. Legara, Christopher P. Monterola
arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.
By Shijun Zhang, Zuowei Shen, Yuesheng Xu
arXiv:2605.06240v2 Announce Type: replace-cross
Abstract: Forward-Forward (FF) training lets each layer learn from a local goodness criterion. In cumulative-goodness variants, later layers can inheri...
By Amirhossein Yousefiramandi
The paper introduces a method for adversarial training that avoids computing input gradients by using a low‑rank Householder expansion (LRHE) to directly generate small‑norm adversarial examples from a network’s parameters. This approach requires only forward passes and standard back‑propagation, eliminating the inner maximization loop and reducing computational cost to roughly 2.8 PGD steps per epoch. The resulting models achieve comparable robustness to multi‑step PGD training for small relative ε budgets, demonstrating the feasibility of gradient‑free adversarial training.
By Tiana C. Johnson, Donsub Rim