Raoul Heese

Sascha Mücke, Raoul Heese, Sabine Müller et al.

In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a quadratic unconstrained binary optimization (QUBO) problem, which allows to select a specified number of features based on their importance and redundancy. In contrast to iterative or greedy methods, our direct approach yields higherquality solutions. QUBO problems are particularly interesting because they can be solved on quantum hardware. To evaluate our proposed algorithm, we conduct a series of numerical experiments using a classical computer, a quantum gate computer and a quantum annealer. Our evaluation compares our method to a range of standard methods on various benchmark datasets. We observe competitive performance.

Raoul Heese, Thore Gerlach, Sascha Mücke et al.

Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people's lives. This leads to explainable AI (XAI) manifesting itself as an important research field that helps humans to better comprehend ML systems. In parallel, quantum machine learning (QML) is emerging with the ongoing improvement of quantum computing hardware combined with its increasing availability via cloud services. QML enables quantum-enhanced ML in which quantum mechanics is exploited to facilitate ML tasks, typically in the form of quantum-classical hybrid algorithms that combine quantum and classical resources. Quantum gates constitute the building blocks of gate-based quantum hardware and form circuits that can be used for quantum computations. For QML applications, quantum circuits are typically parameterized and their parameters are optimized classically such that a suitably defined objective function is minimized. Inspired by XAI, we raise the question of the explainability of such circuits by quantifying the importance of (groups of) gates for specific goals. To this end, we apply the well-established concept of Shapley values. The resulting attributions can be interpreted as explanations for why a specific circuit works well for a given task, improving the understanding of how to construct parameterized (or variational) quantum circuits, and fostering their human interpretability in general. An experimental evaluation on simulators and two superconducting quantum hardware devices demonstrates the benefits of the proposed framework for classification, generative modeling, transpilation, and optimization. Furthermore, our results shed some light on the role of specific gates in popular QML approaches.

Raoul Heese, Sascha Mücke, Matthias Jakobs et al.

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of non-deterministic algorithms. We show that random effects can in fact be absorbed into a Shapley value with a noiseless but shifted value function. Hence, Shapley values with uncertain value functions can be used in analogy to regular Shapley values. However, their reliable evaluation typically requires more computational effort.

Dominik Leib, Tobias Seidel, Sven Jäger et al.

We present a comprehensive case study comparing the performance of D-Waves' quantum-classical hybrid framework, Fujitsu's quantum-inspired digital annealer, and Gurobi's state-of-the-art classical solver in solving a transport robot scheduling problem. This problem originates from an industrially relevant real-world scenario. We provide three different models for our problem following different design philosophies. In our benchmark, we focus on the solution quality and end-to-end runtime of different model and solver combinations. We find promising results for the digital annealer and some opportunities for the hybrid quantum annealer in direct comparison with Gurobi. Our study provides insights into the workflow for solving an application-oriented optimization problem with different strategies, and can be useful for evaluating the strengths and weaknesses of different approaches.

Sascha Mücke, Raoul Heese, Thore Gerlach et al.

Generative Artificial Intelligence (GenAI) for Natural Language Processing (NLP) is the predominant AI technology to date. An important perspective for Quantum Computing (QC) is the question whether QC has the potential to reduce the vast resource requirements for training and operating GenAI models. While large-scale generative NLP tasks are currently out of reach for practical quantum computers, the generation of short semantic structures such as passwords is not. Generating passwords that mimic real user behavior has many applications, for example to test an authentication system against realistic threat models. Classical password generation via deep learning have recently been investigated with significant progress in their ability to generate novel, realistic password candidates. In the present work we investigate the utility of adiabatic quantum computers for this task. More precisely, we study different encodings of token strings and propose novel approaches based on the Quadratic Unconstrained Binary Optimization (QUBO) and the Unit-Disk Maximum Independent Set (UD-MIS) problems. Our approach allows us to estimate the token distribution from data and adiabatically prepare a quantum state from which we eventually sample the generated passwords via measurements. Our results show that relatively small samples of 128 passwords, generated on the QuEra Aquila 256-qubit neutral atom quantum computer, contain human-like passwords such as "Tunas200992" or "teedem28iglove".

Raoul Heese, Moritz Wolter, Sascha Mücke et al.

Recent advances in practical quantum computing have led to a variety of cloud-based quantum computing platforms that allow researchers to evaluate their algorithms on noisy intermediate-scale quantum (NISQ) devices. A common property of quantum computers is that they can exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. The quantum random numbers for our experiments are obtained from real quantum hardware.

Raoul Heese, Patricia Bickert, Astrid Elisa Niederle

We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision tree can be realized via measurements of a quantum circuit. We describe how tree inductions and the prediction of class labels of query data can be integrated into this framework. An on-demand sampling method enables predictions with a constant number of classical memory slots, independent of the tree depth. We experimentally study our approach using both a quantum computing simulator and actual IBM quantum hardware. To our knowledge, this is the first realization of a decision tree classifier on a quantum device.

Moritz Wolter, Felix Blanke, Raoul Heese et al.

As neural networks become able to generate realistic artificial images, they have the potential to improve movies, music, video games and make the internet an even more creative and inspiring place. Yet, the latest technology potentially enables new digital ways to lie. In response, the need for a diverse and reliable method toolbox arises to identify artificial images and other content. Previous work primarily relies on pixel-space CNNs or the Fourier transform. To the best of our knowledge, synthesized fake image analysis and detection methods based on a multi-scale wavelet representation, localized in both space and frequency, have been absent thus far. The wavelet transform conserves spatial information to a degree, which allows us to present a new analysis. Comparing the wavelet coefficients of real and fake images allows interpretation. Significant differences are identified. Additionally, this paper proposes to learn a model for the detection of synthetic images based on the wavelet-packet representation of natural and GAN-generated images. Our lightweight forensic classifiers exhibit competitive or improved performance at comparatively small network sizes, as we demonstrate on the FFHQ, CelebA and LSUN source identification problems. Furthermore, we study the binary FaceForensics++ fake-detection problem.

Raoul Heese, Jochen Schmid, Michał Walczak et al.

We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular $(n-1)$-dimensional simplex, $n$ being the number of classes. We design this representation in such a way that it well reflects the feature space distances of the datapoints to their own- and foreign-class neighbors. In a second step, the latent space representation of the training data is extended to the whole feature space by fitting a regression model to the transformed data. With this latent-space representation, our calibrated classifier is readily defined. We rigorously establish its core theoretical properties and benchmark its prediction and calibration properties by means of various synthetic and real-world data sets from different application domains.

Lukas Franken, Bogdan Georgiev, Sascha Mücke et al.

Variational quantum circuits build the foundation for various classes of quantum algorithms. In a nutshell, the weights of a parametrized quantum circuit are varied until the empirical sampling distribution of the circuit is sufficiently close to a desired outcome. Numerical first-order methods are applied frequently to fit the parameters of the circuit, but most of the time, the circuit itself, that is, the actual composition of gates, is fixed. Methods for optimizing the circuit design jointly with the weights have been proposed, but empirical results are rather scarce. Here, we consider a simple evolutionary strategy that addresses the trade-off between finding appropriate circuit architectures and parameter tuning. We evaluate our method both via simulation and on actual quantum hardware. Our benchmark problems include the transverse field Ising Hamiltonian and the Sherrington-Kirkpatrick spin model. Despite the shortcomings of current noisy intermediate-scale quantum hardware, we find only a minor slowdown on actual quantum machines compared to simulations. Moreover, we investigate which mutation operations most significantly contribute to the optimization. The results provide intuition on how randomized search heuristics behave on actual quantum hardware and lay out a path for further refinement of evolutionary quantum gate circuits.

Raoul Heese, Michael Bortz

We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a straightforward way for regression models with a normal probability density. We benchmark our approach with an evolutionary algorithm on multiple test problems.

Raoul Heese, Lukas Morand, Dirk Helm et al.

Using data from a simulated cup drawing process, we demonstrate how the inherent geometrical structure of cup meshes can be used to effectively prune an artificial neural network in a straightforward way.

Raoul Heese, Michał Walczak, Lukas Morand et al.

We address a non-unique parameter fitting problem in the context of material science. In particular, we propose to resolve ambiguities in parameter space by augmenting a black-box artificial neural network (ANN) model with two different levels of expert knowledge and benchmark them against a pure black-box model.

Laura von Rueden, Sebastian Mayer, Katharina Beckh et al.

Despite its great success, machine learning can have its limits when dealing with insufficient training data. A potential solution is the additional integration of prior knowledge into the training process which leads to the notion of informed machine learning. In this paper, we present a structured overview of various approaches in this field. We provide a definition and propose a concept for informed machine learning which illustrates its building blocks and distinguishes it from conventional machine learning. We introduce a taxonomy that serves as a classification framework for informed machine learning approaches. It considers the source of knowledge, its representation, and its integration into the machine learning pipeline. Based on this taxonomy, we survey related research and describe how different knowledge representations such as algebraic equations, logic rules, or simulation results can be used in learning systems. This evaluation of numerous papers on the basis of our taxonomy uncovers key methods in the field of informed machine learning.

Raoul Heese, Michal Walczak, Tobias Seidel et al.

In complex simulation environments, certain parameter space regions may result in non-convergent or unphysical outcomes. All parameters can therefore be labeled with a binary class describing whether or not they lead to valid results. In general, it can be very difficult to determine feasible parameter regions, especially without previous knowledge. We propose a novel algorithm to explore such an unknown parameter space and improve its feasibility classification in an iterative way. Moreover, we include an additional optimization target in the algorithm to guide the exploration towards regions of interest and to improve the classification therein. In our method we make use of well-established concepts from the field of machine learning like kernel support vector machines and kernel ridge regression. From a comparison with a Kriging-based exploration approach based on recently published results we can show the advantages of our algorithm in a binary feasibility classification scenario with a discrete feasibility constraint violation. In this context, we also propose an improvement of the Kriging-based exploration approach. We apply our novel method to a fully realistic, industrially relevant chemical process simulation to demonstrate its practical usability and find a comparably good approximation of the data space topology from relatively few data points.