The paper investigates the gap between trainability diagnostics and actual optimization performance in variational quantum algorithms. By introducing step‑level diagnostics that treat coefficient‑weighted Hamiltonian‑term gradients as task‑like components, the authors derive an exact relationship between signed termwise organization, directional activity, and first‑order descent. Experiments on transverse‑field Ising models with different ansatzes show that while certain projection techniques can improve diagnostic metrics, they do not consistently translate into better final energies or first‑order predictability once update norm and search budget are controlled.
By Pilsung Kang
arXiv:2608. 09396v1 Announce Type: new Abstract: Invariant learning seeks representations that remain predictive across environments, yet the behavior of its objectives along the regularization path is often opaque.
By Pinli Wang, Yue He, Peng Cui
arXiv:2608.23725v1 Announce Type: new
Abstract: Deep Equilibrium Models (DEQs) compute predictions from a hidden representation unchanged by the model update. Training through this equilibrium uses i...
By Jose Luis Lima de Jesus Silva
The paper investigates how stochastic reconfiguration (SR), the standard optimizer for neural quantum states (NQS), functions as a statistical filter in overparameterized regimes where parameters outnumber Monte Carlo samples. By interpreting SR as ridge regression on tangent features, the authors show that the diagonal shift balances useful update directions against variance from fitting finite-sample residuals, leading to a U-shaped validation risk curve. They introduce multi-shift SR (MS‑SR), which averages ridge solutions at data‑adaptive shifts, and demonstrate that it reduces validation risk and update variance compared to fixed‑shift SR in both small and large system experiments.
By Tak Hur
Invariant learning seeks representations that remain predictive across environments, yet the behavior of its objectives along the regularization path is often opaque. We address this objective-behavior gap by viewing representation learning as multimode magnetization and deriving, from concrete invariant-learning objectives, a Landau-type effective free energy whose low-order coefficients form objective signatures and induce distinct regularization phenotypes.
The paper presents a graph-theoretic framework for analyzing Heisenberg antiferromagnets, where the Hamiltonian in a fixed-magnetization sector is represented as a constant minus the weighted Laplacian of a Hilbert graph (HG). The ground-state energy is linked to the largest eigenvalue of this Laplacian, equivalent to a spectral relaxation of weighted Max‑Cut on the HG, while the phase-dependent part of the variational energy maps to an antiferromagnetic XY model on the same graph. Restricting to real variational states reduces the problem to an Ising model, and the optimal sign structure of the ground state can be recovered in polynomial time from the HG weights, with the bipartiteness of the HG determining whether a diagonal sign transformation can eliminate all positive off-diagonal elements.
By Mahmud Ashraf Shamim, Md Moshiur Rahman Raj, Mohamed Hibat-Allah, Ruy Fabila-Monroy, Nobuchika Okada, Paulo T. Araujo