Collective variables (CVs) play a crucial role in capturing rare events in high-dimensional systems, motivating the continual search for principled approaches to their design. In this work, we revisit the framework of quantitative coarse graining and identify the orthogonality condition from Legoll and Lelievre (2010) as a key criterion for constructing CVs that accurately preserve the statistical properties of the original process. We establish that satisfaction of the orthogonality condition enables error estimates for both relative entropy and pathwise distance to scale proportionally with the degree of scale separation. Building on this foundation, we introduce a general numerical method for designing neural network-based CVs that integrates tools from manifold learning with group-invariant featurization. To demonstrate the efficacy of our approach, we construct CVs for butane and achieve a CV that reproduces the anti-gauche transition rate with less than ten percent relative error. Additionally, we provide empirical evidence challenging the necessity of uniform positive definiteness in diffusion tensors for transition rate reproduction and highlight the critical role of light atoms in CV design for molecular dynamics.

The expressiveness of flow-based models combined with stochastic variational inference (SVI) has, in recent years, expanded the application of optimization-based Bayesian inference to include problems with complex data relationships. However, until now, SVI using flow-based models has been limited to problems of fixed dimension. We introduce CoSMIC, normalizing flows (COntextually-Specified Masking for Identity-mapped Components), an extension to neural autoregressive conditional normalizing flow architectures that enables using a single amortized variational density for inference over a transdimensional target distribution. We propose a combined stochastic variational transdimensional inference (VTI) approach to training CoSMIC flows using techniques from Bayesian optimization and Monte Carlo gradient estimation. Numerical experiments demonstrate the performance of VTI on challenging problems that scale to high-cardinality model spaces.

While deep learning methods have achieved strong performance in time series prediction, their black-box nature and inability to explicitly model underlying stochastic processes often limit their generalization to non-stationary data, especially in the presence of abrupt changes. In this work, we introduce Neural MJD, a neural network based non-stationary Merton jump diffusion (MJD) model. Our model explicitly formulates forecasting as a stochastic differential equation (SDE) simulation problem, combining a time-inhomogeneous Itô diffusion to capture non-stationary stochastic dynamics with a time-inhomogeneous compound Poisson process to model abrupt jumps. To enable tractable learning, we introduce a likelihood truncation mechanism that caps the number of jumps within small time intervals and provide a theoretical error bound for this approximation. Additionally, we propose an Euler-Maruyama with restart solver, which achieves a provably lower error bound in estimating expected states and reduced variance compared to the standard solver. Experiments on both synthetic and real-world datasets demonstrate that Neural MJD consistently outperforms state-of-the-art deep learning and statistical learning methods.

--Training with huge datasets and a large number of participating devices leads to bottlenecks in federated learning (FL). Furthermore, the challenges of heterogeneity between multiple FL clients affect the overall performance of the system. In a quantum federated learning (QFL) context, we address these three main challenges: i) training bottlenecks from massive datasets, ii) the involvement of a substantial number of devices, and iii) non-IID data distributions. We introduce a model-driven quantum federated learning algorithm (mdQFL) to tackle these challenges. Our proposed approach is efficient and adaptable to various factors, including different numbers of devices. T o the best of our knowledge, it is the first to explore training and update personalization, as well as test generalization within a QFL setting, which can be applied to other FL scenarios. We evaluated the efficiency of the proposed mdQFL framework through extensive experiments under diverse non-IID data heterogeneity conditions using various datasets within the Qiskit environment. Our results demonstrate a nearly 50% decrease in total communication costs while maintaining or, in some cases, exceeding the accuracy of the final model and consistently improving local model training compared to the standard QFL baseline. Moreover, our experimental evaluation thoroughly explores the QFL and mdQFL algorithms, along with several influencing factors. In addition, we present a theoretical analysis to clarify the complexities of the proposed algorithm. Federated Learning (FL) has emerged as a pivotal technique to address the challenges of privacy and security in distributed machine learning [1], [2].

--T o boost the encoder stealing attack under the perturbation-based defense that hinders the attack performance, we propose a boosting encoder stealing attack with perturbation recovery named BESA. It aims to overcome perturbation-based defenses. The core of BESA consists of two modules: perturbation detection and perturbation recovery, which can be combined with canonical encoder stealing attacks. The perturbation detection module utilizes the feature vectors obtained from the target encoder to infer the defense mechanism employed by the service provider . Once the defense mechanism is detected, the perturbation recovery module leverages the well-designed generative model to restore a clean feature vector from the perturbed one. Through extensive evaluations based on various datasets, we demonstrate that BESA significantly enhances the surrogate encoder accuracy of existing encoder stealing attacks by up to 24.63% when facing state-of-the-art defenses and combinations of multiple defenses. Pre-trained encoders are extensively utilized across various domains in real-world scenarios [1]. However, training well-performing pre-trained encoders is a time-consuming, resource-intensive, and costly process [2]. Hence, encoder owners are highly motivated to safeguard the privacy of their pre-trained encoders. Unfortunately, recent works have shown that pre-trained encoders are susceptible to encoder stealing attacks [3]. These attacks allow an attacker to create a surrogate encoder that closely mimics the functionality of a targeted encoder by simply querying it through the APIs. The consequences of such attacks can be quite severe.

Semi-implicit variational inference (SIVI) is a powerful framework for approximating complex posterior distributions, but training with the Kullback-Leibler (KL) divergence can be challenging due to high variance and bias in high-dimensional settings. While current state-of-the-art semi-implicit variational inference methods, particularly Kernel Semi-Implicit Variational Inference (KSIVI), have been shown to work in high dimensions, training remains moderately expensive. In this work, we propose a kernelized KL divergence estimator that stabilizes training through nonparametric smoothing. To further reduce the bias, we introduce an importance sampling correction. We provide a theoretical connection to the amortized version of the Stein variational gradient descent, which estimates the score gradient via Stein's identity, showing that both methods minimize the same objective, but our semi-implicit approach achieves lower gradient variance. In addition, our method's bias in function space is benign, leading to more stable and efficient optimization. Empirical results demonstrate that our method outperforms or matches state-of-the-art SIVI methods in both performance and training efficiency.

Chronoamperometry (CA) is a fundamental electrochemical technique used for quantifying redox-active species. However, in room-temperature ionic liquids (RTILs), the high viscosity and slow mass transport often lead to extended measurement durations. This paper presents a novel mathematical regression approach that reduces CA measurement windows to under 1 second, significantly faster than previously reported methods, which typically require 1-4 seconds or longer. By applying an inference algorithm to the initial transient current response, this method accurately predicts steady-state electrochemical parameters without requiring additional hardware modifications. The approach is validated through comparison with standard chronoamperometric techniques and is demonstrated to maintain reasonable accuracy while dramatically reducing data acquisition time. The implications of this technique are explored in analytical chemistry, sensor technology, and battery science, where rapid electrochemical quantification is critical. Our technique is focused on enabling faster multiplexing of chronoamperometric measurements for rapid olfactory and electrochemical analysis.

Distributionally robust optimization offers a compelling framework for model fitting in machine learning, as it systematically accounts for data uncertainty. Focusing on Wasserstein distributionally robust optimization, we investigate the regularized problem where entropic smoothing yields a sampling-based approximation of the original objective. We establish the convergence of the approximate gradient over a compact set, leading to the concentration of the regularized problem critical points onto the original problem critical set as regularization diminishes and the number of approximation samples increases. Finally, we deduce convergence guarantees for a projected stochastic gradient method. Our analysis covers a general machine learning situation with an unbounded sample space and mixed continuous-discrete data.

Modern large language models are capable of in-context learning, the ability to perform new tasks at inference time using only a handful of input-output examples in the prompt, without any fine-tuning or parameter updates. We develop a universal approximation theory to better understand how transformers enable in-context learning. For any class of functions (each representing a distinct task), we demonstrate how to construct a transformer that, without any further weight updates, can perform reliable prediction given only a few in-context examples. In contrast to much of the recent literature that frames transformers as algorithm approximators -- i.e., constructing transformers to emulate the iterations of optimization algorithms as a means to approximate solutions of learning problems -- our work adopts a fundamentally different approach rooted in universal function approximation. This alternative approach offers approximation guarantees that are not constrained by the effectiveness of the optimization algorithms being approximated, thereby extending far beyond convex problems and linear function classes. Our construction sheds light on how transformers can simultaneously learn general-purpose representations and adapt dynamically to in-context examples.

Neural networks (NNs) have achieved tremendous success over the past decade, yet they are still extremely difficult to interpret. In contrast, linear models are less expressive but offer inherent interpretability. Linear coefficients are interpretable as the marginal effect of a feature on the prediction, assuming all other features are kept fixed. To combine the benefits of both approaches, we introduce NIMO (Nonlinear Interpretable MOdel). The key idea is to define a model where the NN is designed to learn nonlinear corrections to the linear model predictions, while also maintaining the original interpretability of the linear coefficients. Relevantly, we develop an optimization algorithm based on profile likelihood that elegantly allows for optimizing over the NN parameters while updating the linear coefficients analytically. By relying on adaptive ridge regression we can easily incorporate sparsity constraints as well. We show empirically that we can recover the underlying linear coefficients while significantly improving the predictive accuracy. Compared to other hybrid interpretable approaches, our model is the only one that actually maintains the same interpretability of linear coefficients as in linear models. We also achieve higher performance on various regression and classification settings.