Unified derivation of Bohmian methods and the incorporation of interference effects

We present a unified derivation of Bohmian methods that serves as a common starting point for the derivative propagation method (DPM), Bohmian mechanics with complex action (BOMCA) and the zero-velocity complex action method (ZEVCA). The unified derivation begins with the ansatz $\psi=e^{\frac{iS}{\hbar}}$ where the action, $S$, is taken to be complex and the quantum force is obtained by writing a hierarchy of equations of motion for the phase partial derivatives. We demonstrate how different choices of the trajectory velocity field yield different formulations such as DPM, BOMCA and ZEVCA. The new derivation is used for two purposes. First, it serves as a common basis for comparing the role of the quantum force in the DPM and BOMCA formulations. Second, we use the new derivation to show that superposing the contributions of real, crossing trajectories yields a nodal pattern essentially identical to that of the exact quantum wavefunction. The latter result suggests a promising new approach to deal with the challenging problem of nodes in Bohmian mechanics

Complex trajectory method in time-dependent WKB

We present a significant improvement to a time-dependent WKB (TDWKB) formulation developed by Boiron and Lombardi [JCP {\bf108}, 3431 (1998)] in which the TDWKB equations are solved along classical trajectories that propagate in the complex plane. Boiron and Lombardi showed that the method gives very good agreement with the exact quantum mechanical result as long as the wavefunction does not exhibit interference effects such as oscillations and nodes. In this paper we show that this limitation can be overcome by superposing the contributions of crossing trajectories. We also demonstrate that the approximation improves when incorporating higher order terms in the expansion. These improvements could make the TDWKB formulation a competitive alternative to current time-dependent semiclassical methods

Auditing and Generating Synthetic Data with Controllable Trust Trade-offs

Data collected from the real world tends to be biased, unbalanced, and at risk of exposing sensitive and private information. This reality has given rise to the idea of creating synthetic datasets to alleviate risk, bias, harm, and privacy concerns inherent in the real data. This concept relies on Generative AI models to produce unbiased, privacy-preserving synthetic data while being true to the real data. In this new paradigm, how can we tell if this approach delivers on its promises? We present an auditing framework that offers a holistic assessment of synthetic datasets and AI models trained on them, centered around bias and discrimination prevention, fidelity to the real data, utility, robustness, and privacy preservation. We showcase our framework by auditing multiple generative models on diverse use cases, including education, healthcare, banking, human resources, and across different modalities, from tabular, to time-series, to natural language. Our use cases demonstrate the importance of a holistic assessment in order to ensure compliance with socio-technical safeguards that regulators and policymakers are increasingly enforcing. For this purpose, we introduce the trust index that ranks multiple synthetic datasets based on their prescribed safeguards and their desired trade-offs. Moreover, we devise a trust-index-driven model selection and cross-validation procedure via auditing in the training loop that we showcase on a class of transformer models that we dub TrustFormers, across different modalities. This trust-driven model selection allows for controllable trust trade-offs in the resulting synthetic data. We instrument our auditing framework with workflows that connect different stakeholders from model development to audit and certification via a synthetic data auditing report.Comment: 49 pages; submitte