The paper investigates why transferring relational structure learned from abundant forward-simulation data fails for inverse problems, despite theoretical expectations. It demonstrates that dynamics‑learned graphs, such as those from Neural Relational Inference, can worsen performance by over 100% compared to a task‑optimised attention baseline, and that this failure persists across multiple evidence lines. The authors formalise the gap as an approximation‑error issue and propose a lightweight transferability test based on Jaccard similarity to predict successful transfer.
arXiv:2610.28555v1 Announce Type: cross Abstract: Statistical learning in high dimensions suffers from the curse of dimensionality. Fortunately, many functions of practical interest are compositional...
Posterior-First Neural PDE Simulation proposes a new paradigm where downstream tasks dictate the minimal problem state to infer, and a posterior over that state conditions future predictions. The approach replaces traditional field-to-future predictors, which collapse distinct latent states, with a task-to-target-to-interface framework that preserves necessary ambiguity. Experiments on synthetic and PDEBench tasks show that posterior recovery improves rollout accuracy, reducing error by 59.4% of the direct-to-oracle gap.
arXiv:2606.19101v2 Announce Type: replace-cross Abstract: We investigate a structure-first approach to dynamical learning in which the organization of stateful interactions is prescribed explicitly r...
arXiv:2608.20965v1 Announce Type: new Abstract: We define an atomic generation fact f=(u,tau,omega,z;rho), recording the origin, realized transformation, concrete occurrence, generated result and rel...
arXiv:2608. 15373v1 Announce Type: new Abstract: Inverse physics-informed neural networks (PINNs) can reconstruct a field accurately while returning an incorrect physical parameter.
arXiv:2603. 02462v2 Announce Type: replace-cross Abstract: A key challenge in developing unified neural solvers for combinatorial optimization (CO) is the efficient generalization of models from a given set of tasks to new tasks unseen during initial training.
arXiv:2607. 11116v1 Announce Type: cross Abstract: Deep equilibrium models promise input-adaptive implicit computation: harder problems should demand more solver iterations, and the solved equilibrium should encode the result of genuine iterative inference.
Deep equilibrium models promise input-adaptive implicit computation: harder problems should demand more solver iterations, and the solved equilibrium should encode the result of genuine iterative inference. We report a cautionary study of a port-Hamiltonian DEQ with a learned initialization on two reasoning tasks -- ProofWriter entailment over frozen DeBERTa embeddings and a BFS-verified graph-reachability benchmark -- in which the implicit computation is a silent no-op.
arXiv:2506. 20699v2 Announce Type: replace Abstract: Learning in non-stationary and multi-context environments requires more than ordinary within-task generalization.
The paper investigates how different attention mechanisms affect the performance of DeepONet neural operators. Five variants—varying in cross‑attention, self‑attention, tokenization, and attention depth—are trained in both data‑driven and physics‑informed settings on one‑ and two‑dimensional PDE benchmarks. Results show that per‑sensor tokenization with cross‑attention consistently reduces error, while branch self‑attention helps only in complex spatial problems, and deeper cross‑attention yields diminishing returns with higher cost.
arXiv:2607. 05271v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) encounter ill-posed optimization, loss competition, and parameter compensation in partial differential equation (PDE) inverse problems.
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.