Testing and debugging quantum software pose significant challenges due to the inherent complexities of quantum mechanics, such as superposition and entanglement. One challenge is indeterminacy, a fundamental characteristic of quantum systems, which increases the likelihood of flaky tests in quantum programs. To the best of our knowledge, there is a lack of comprehensive studies on quantum flakiness in the existing literature. In this paper, we present a novel machine learning platform that leverages multiple machine learning models to automatically detect flaky tests in quantum programs. Our evaluation shows that the extreme gradient boosting and decision tree-based models outperform other models (i.e., random forest, k-nearest neighbors, and support vector machine), achieving the highest F1 score and Matthews Correlation Coefficient in a balanced dataset and an imbalanced dataset, respectively. Furthermore, we expand the currently limited dataset for researchers interested in quantum flaky tests. In the future, we plan to explore the development of unsupervised learning techniques to detect and classify quantum flaky tests more effectively. These advancements aim to improve the reliability and robustness of quantum software testing.

Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using discrete gridded representations of the physical variables and dynamics. Uncertainties are assessed by running the simulations multiple times, yielding ensembles of simulated fields as a high-dimensional stochastic representation of the forecast distribution. The high-dimensionality and large volume of ensemble datasets poses major computing challenges for subsequent forecasting stages. Data-driven dimensionality reduction techniques could help to reduce the data volume before further processing by learning meaningful and compact representations. However, existing dimensionality reduction methods are typically designed for deterministic and single-valued inputs, and thus cannot handle ensemble data from multiple randomized simulations. In this study, we propose novel dimensionality reduction approaches specifically tailored to the format of ensemble forecast fields. We present two alternative frameworks, which yield low-dimensional representations of ensemble forecasts while respecting their probabilistic character. The first approach derives a distribution-based representation of an input ensemble by applying standard dimensionality reduction techniques in a member-by-member fashion and merging the member representations into a joint parametric distribution model. The second approach achieves a similar representation by encoding all members jointly using a tailored variational autoencoder. We evaluate and compare both approaches in a case study using 10 years of temperature and wind speed forecasts over Europe. The approaches preserve key spatial and statistical characteristics of the ensemble and enable probabilistic reconstructions of the forecast fields.

Unsupervised machine learning methods are well suited to searching for anomalies at scale but can struggle with the high-dimensional representation of many modern datasets, hence dimensionality reduction (DR) is often performed first. In this paper we analyse unsupervised anomaly detection (AD) from the perspective of the manifold created in DR. We present an idealised illustration, "Finding Pegasus", and a novel formal framework with which we categorise AD methods and their results into "on manifold" and "off manifold". We define these terms and show how they differ. We then use this insight to develop an approach of combining AD methods which significantly boosts AD recall without sacrificing precision in situations employing high DR. When tested on MNIST data, our approach of combining AD methods improves recall by as much as 16 percent compared with simply combining with the best standalone AD method (Isolation Forest), a result which shows great promise for its application to real-world data.

Randomized experiments are the preferred approach for evaluating the effects of interventions, but they are costly and often yield estimates with substantial uncertainty. On the other hand, in silico experiments leveraging foundation models offer a cost-effective alternative that can potentially attain higher statistical precision. However, the benefits of in silico experiments come with a significant risk: statistical inferences are not valid if the models fail to accurately predict experimental responses to interventions. In this paper, we propose a novel approach that integrates the predictions from multiple foundation models with experimental data while preserving valid statistical inference. Our estimator is consistent and asymptotically normal, with asymptotic variance no larger than the standard estimator based on experimental data alone. Importantly, these statistical properties hold even when model predictions are arbitrarily biased. Empirical results across several randomized experiments show that our estimator offers substantial precision gains, equivalent to a reduction of up to 20% in the sample size needed to match the same precision as the standard estimator based on experimental data alone.

In the $k$-committee election problem, we wish to aggregate the preferences of $n$ agents over a set of alternatives and select a committee of $k$ alternatives that minimizes the cost incurred by the agents. While we typically assume that agent preferences are captured by a cardinal utility function, in many contexts we only have access to ordinal information, namely the agents' rankings over the outcomes. As preference rankings are not as expressive as cardinal utilities, a loss of efficiency is inevitable, and is quantified by the notion of \emph{distortion}. We study the problem of electing a $k$-committee that minimizes the sum of the $\ell$-largest costs incurred by the agents, when agents and candidates are embedded in a metric space. This problem is called the $\ell$-centrum problem and captures both the utilitarian and egalitarian objectives. When $k \geq 2$, it is not possible to compute a bounded-distortion committee using purely ordinal information. We develop the first algorithms (that we call mechanisms) for the $\ell$-centrum problem (when $k \geq 2$), which achieve $O(1)$-distortion while eliciting only a very limited amount of cardinal information via value queries. We obtain two types of query-complexity guarantees: $O(\log k \log n)$ queries \emph{per agent}, and $O(k^2 \log^2 n)$ queries \emph{in total} (while achieving $O(1)$-distortion in both cases). En route, we give a simple adaptive-sampling algorithm for the $\ell$-centrum $k$-clustering problem.

While Fourier-based neural operators are best suited to learning mappings between functions on periodic domains, several works have introduced techniques for incorporating non trivial boundary conditions. However, all previously introduced methods have restrictions that limit their applicability. In this work, we introduce an alternative approach to imposing boundary conditions inspired by volume penalization from numerical methods and Mixture of Experts (MoE) from machine learning. By introducing competing experts, the approach additionally allows for model selection. To demonstrate the method, we combine a spatially conditioned MoE with the Fourier based, Modal Operator Regression for Physics (MOR-Physics) neural operator and recover a nonlinear operator on a disk and quarter disk. Next, we extract a large eddy simulation (LES) model from direct numerical simulation of channel flow and show the domain decomposition provided by our approach. Finally, we train our LES model with Bayesian variational inference and obtain posterior predictive samples of flow far past the DNS simulation time horizon.

Concerns about the use of data and algorithms for decision-making have risen in concert with the ascendancy of data-driven methods. Prior research has investigated problems ranging from privacy violations to explainability and accountability [10] [12]. Here, we focus on fairness, which addresses discrimination and disparate treatment in data and algorithms [1]. Recently, fairness research has focused significantly on algorithmic fairness, which aims to investigate algorithms for unfairness and intervene on algorithms to prevent unfair outcomes. Prior work has developed metrics for fairness, methods for fair variable selection, and mechanisms to correct unfair models [14] [11]. Algorithmic fairness evolved out of concerns about the use of algorithms in high-stakes contexts, particularly those that have a history of disparity and discrimination. When training an algorithm on data from a discriminatory process, it is common for the algorithm to learn to replicate that discrimination, or'garbage in, garbage out'. Much work in algorithmic fairness focuses on detecting, evaluating, and correcting unfair algorithms under a garbage-in-garbage-out regime. However, little work focuses on assessing the extent to which the data-generating process itself is'garbage',

Contrastive learning leverages data augmentation to develop feature representation without relying on large labeled datasets. However, despite its empirical success, the theoretical foundations of contrastive learning remain incomplete, with many essential guarantees left unaddressed, particularly the realizability assumption concerning neural approximability of an optimal spectral contrastive loss solution. In this work, we overcome these limitations by analyzing the pointwise and spectral consistency of the augmentation graph Laplacian. We establish that, under specific conditions for data generation and graph connectivity, as the augmented dataset size increases, the augmentation graph Laplacian converges to a weighted Laplace-Beltrami operator on the natural data manifold. These consistency results ensure that the graph Laplacian spectrum effectively captures the manifold geometry. Consequently, they give way to a robust framework for establishing neural approximability, directly resolving the realizability assumption in a current paradigm.

We propose an innovative algorithm for non-convex composite federated learning that decouples the proximal operator evaluation and the communication between server and clients. Moreover, each client uses local updates to communicate less frequently with the server, sends only a single d-dimensional vector per communication round, and overcomes issues with client drift. In the analysis, challenges arise from the use of decoupling strategies and local updates in the algorithm, as well as from the non-convex and non-smooth nature of the problem. We establish sublinear and linear convergence to a bounded residual error under general non-convexity and the proximal Polyak-Lojasiewicz inequality, respectively. In the numerical experiments, we demonstrate the superiority of our algorithm over state-of-the-art methods on both synthetic and real datasets.

Existing studies on preference optimization (PO) have centered on constructing pairwise preference data following simple heuristics, such as maximizing the margin between preferred and dispreferred completions based on human (or AI) ranked scores. However, none of these heuristics has a full theoretical justification. In this work, we develop a novel PO framework that provides theoretical guidance to effectively sample dispreferred completions. To achieve this, we formulate PO as minimizing the negative log-likelihood (NLL) of a probability model and propose to estimate its normalization constant via a sampling strategy. As we will demonstrate, these estimative samples can act as dispreferred completions in PO. We then select contrastive divergence (CD) as the sampling strategy, and propose a novel MC-PO algorithm that applies the Monte Carlo (MC) kernel from CD to sample hard negatives w.r.t. the parameterized reward model. Finally, we propose the OnMC-PO algorithm, an extension of MC-PO to the online setting. On popular alignment benchmarks, MC-PO outperforms existing SOTA baselines, and OnMC-PO leads to further improvement.