Fairness holds a pivotal role in the realm of machine learning, particularly when it comes to addressing groups categorised by protected attributes, e.g., gender, race. Prevailing algorithms in fair learning predominantly hinge on accessibility or estimations of these protected attributes, at least in the training process. We design a single group-blind projection map that aligns the feature distributions of both groups in the source data, achieving (demographic) group parity, without requiring values of the protected attribute for individual samples in the computation of the map, as well as its use. Instead, our approach utilises the feature distributions of the privileged and unprivileged groups in a boarder population and the essential assumption that the source data are unbiased representation of the population. We present numerical results on synthetic data and real data.
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Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and unitary, but are rather augmented with probabilistic byproducts. Yet, the main algorithmic use of MBQC so far has been to completely counteract this probabilistic nature in order to simulate unitary computations expressed in the circuit model. In this work, we propose designing MBQC algorithms that embrace this inherent randomness and treat the random byproducts in MBQC as a resource for computation. As a natural application where randomness can be beneficial, we consider generative modeling, a task in machine learning centered around generating complex probability distributions. To address this task, we propose a variational MBQC algorithm equipped with control parameters that allow one to directly adjust the degree of randomness to be admitted in the computation. Our algebraic and numerical findings indicate that this additional randomness can lead to significant gains in expressivity and learning performance for certain generative modeling tasks, respectively. These results highlight the potential advantages in exploiting the inherent randomness of MBQC and motivate further research into MBQC-based algorithms.
We present a quantitative model for tracking dangerous AI capabilities over time. Our goal is to help the policy and research community visualise how dangerous capability testing can give us an early warning about approaching AI risks. We first use the model to provide a novel introduction to dangerous capability testing and how this testing can directly inform policy. Decision makers in AI labs and government often set policy that is sensitive to the estimated danger of AI systems, and may wish to set policies that condition on the crossing of a set threshold for danger. The model helps us to reason about these policy choices. We then run simulations to illustrate how we might fail to test for dangerous capabilities. To summarise, failures in dangerous capability testing may manifest in two ways: higher bias in our estimates of AI danger, or larger lags in threshold monitoring. We highlight two drivers of these failure modes: uncertainty around dynamics in AI capabilities and competition between frontier AI labs. Effective AI policy demands that we address these failure modes and their drivers. Even if the optimal targeting of resources is challenging, we show how delays in testing can harm AI policy. We offer preliminary recommendations for building an effective testing ecosystem for dangerous capabilities and advise on a research agenda.
Machine learning interatomic potentials (MLIPs) often neglect long-range interactions, such as electrostatic and dispersion forces. In this work, we introduce a straightforward and efficient method to account for long-range interactions by learning a latent variable from local atomic descriptors and applying an Ewald summation to this variable. We demonstrate that in systems including charged and polar molecular dimers, bulk water, and water-vapor interface, standard short-ranged MLIPs can lead to unphysical predictions even when employing message passing. The long-range models effectively eliminate these artifacts, with only about twice the computational cost of short-range MLIPs.
A common trait of many machine learning models is that it is often difficult to understand and explain what caused the model to produce the given output. While the explainability of neural networks has been an active field of research in the last years, comparably little is known for quantum machine learning models. Despite a few recent works analyzing some specific aspects of explainability, as of now there is no clear big picture perspective as to what can be expected from quantum learning models in terms of explainability. In this work, we address this issue by identifying promising research avenues in this direction and lining out the expected future results. We additionally propose two explanation methods designed specifically for quantum machine learning models, as first of their kind to the best of our knowledge. Next to our pre-view of the field, we compare both existing and novel methods to explain the predictions of quantum learning models. By studying explainability in quantum machine learning, we can contribute to the sustainable development of the field, preventing trust issues in the future.
We propose a method utilizing physics-informed neural networks (PINNs) to solve Poisson equations that serve as control variates in the computation of transport coefficients via fluctuation formulas, such as the Green--Kubo and generalized Einstein-like formulas. By leveraging approximate solutions to the Poisson equation constructed through neural networks, our approach significantly reduces the variance of the estimator at hand. We provide an extensive numerical analysis of the estimators and detail a methodology for training neural networks to solve these Poisson equations. The approximate solutions are then incorporated into Monte Carlo simulations as effective control variates, demonstrating the suitability of the method for moderately high-dimensional problems where fully deterministic solutions are computationally infeasible.
We make a full landscape analysis of the (generally non-convex) orthogonal Procrustes problem. This problem is equivalent with computing the polar factor of a square matrix. We reveal a convexity-like structure, which explains the already established tractability of the problem and show that gradient descent in the orthogonal group computes the polar factor of a square matrix with linear convergence rate if the matrix is invertible and with an algebraic one if the matrix is singular. These results are similar to the ones of Alimisis and Vandereycken (2024) for the symmetric eigenvalue problem. We present an instance of a distributed Procrustes problem, which is hard to deal by standard techniques from numerical linear algebra. Our theory though can provide a solution.
Not accounting for competing events in survival analysis can lead to biased estimates, as individuals who die from other causes do not have the opportunity to develop the event of interest. Formal definitions and considerations for causal effects in the presence of competing risks have been published, but not for the mediation analysis setting. We propose, for the first time, an approach based on the path-specific effects framework to account for competing risks in longitudinal mediation analysis with time-to-event outcomes. We do so by considering the pathway through the competing event as another mediator, which is nested within our longitudinal mediator of interest. We provide a theoretical formulation and related definitions of the effects of interest based on the mediational g-formula, as well as a detailed description of the algorithm. We also present an application of our algorithm to data from the Strong Heart Study, a prospective cohort of American Indian adults. In this application, we evaluated the mediating role of the blood pressure trajectory (measured during three visits) on the association between arsenic and cadmium, in separate models, with time to cardiovascular disease, accounting for competing risks by death. Identifying the effects through different paths enables us to evaluate the impact of metals on the outcome of interest, as well as through competing risks, more transparently.
'A trustworthy representation of uncertainty is desirable and should be considered as a key feature of any machine learning method' (Huellermeier and Waegeman, 2021). This conclusion of Huellermeier et al. underpins the importance of calibrated uncertainties. Since AI-based algorithms are heavily impacted by dataset shifts, the automotive industry needs to safeguard its system against all possible contingencies. One important but often neglected dataset shift is caused by optical aberrations induced by the windshield. For the verification of the perception system performance, requirements on the AI performance need to be translated into optical metrics by a bijective mapping (Braun, 2023). Given this bijective mapping it is evident that the optical system characteristics add additional information about the magnitude of the dataset shift. As a consequence, we propose to incorporate a physical inductive bias into the neural network calibration architecture to enhance the robustness and the trustworthiness of the AI target application, which we demonstrate by using a semantic segmentation task as an example. By utilizing the Zernike coefficient vector of the optical system as a physical prior we can significantly reduce the mean expected calibration error in case of optical aberrations. As a result, we pave the way for a trustworthy uncertainty representation and for a holistic verification strategy of the perception chain.
Statistical learning under distribution shift is challenging when neither prior knowledge nor fully accessible data from the target distribution is available. Distributionally robust learning (DRL) aims to control the worst-case statistical performance within an uncertainty set of candidate distributions, but how to properly specify the set remains challenging. To enable distributional robustness without being overly conservative, in this paper, we propose a shape-constrained approach to DRL, which incorporates prior information about the way in which the unknown target distribution differs from its estimate. More specifically, we assume the unknown density ratio between the target distribution and its estimate is isotonic with respect to some partial order. At the population level, we provide a solution to the shape-constrained optimization problem that does not involve the isotonic constraint. At the sample level, we provide consistency results for an empirical estimator of the target in a range of different settings. Empirical studies on both synthetic and real data examples demonstrate the improved accuracy of the proposed shape-constrained approach.
We prove, for stably computably enumerable formal systems, direct analogues of the first and second incompleteness theorems of G\"odel. A typical stably computably enumerable set is the set of Diophantine equations with no integer solutions, and in particular such sets are generally not computably enumerable. And so this gives the first extension of the second incompleteness theorem to non classically computable formal systems. Let's motivate this with a somewhat physical application. Let $\mathcal{H} $ be the suitable infinite time limit (stabilization in the sense of the paper) of the mathematical output of humanity, specializing to first order sentences in the language of arithmetic (for simplicity), and understood as a formal system. Suppose that all the relevant physical processes in the formation of $\mathcal{H} $ are Turing computable. Then as defined $\mathcal{H} $ may \emph{not} be computably enumerable, but it is stably computably enumerable. Thus, the classical G\"odel disjunction applied to $\mathcal{H} $ is meaningless, but applying our incompleteness theorems to $\mathcal{H} $ we then get a sharper version of G\"odel's disjunction: assume $\mathcal{H} \vdash PA$ then either $\mathcal{H} $ is not stably computably enumerable or $\mathcal{H} $ is not 1-consistent (in particular is not sound) or $\mathcal{H} $ cannot prove a certain true statement of arithmetic (and cannot disprove it if in addition $\mathcal{H} $ is 2-consistent).
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