Nico Piatkowski

Nico Piatkowski, Thore Gerlach, Romain Hugues et al.

Given is a set of images, where all images show views of the same area at different points in time and from different viewpoints. The task is the alignment of all images such that relevant information, e.g., poses, changes, and terrain, can be extracted from the fused image. In this work, we focus on quantum methods for keypoint extraction and feature matching, due to the demanding computational complexity of these sub-tasks. To this end, k-medoids clustering, kernel density clustering, nearest neighbor search, and kernel methods are investigated and it is explained how these methods can be re-formulated for quantum annealers and gate-based quantum computers. Experimental results obtained on digital quantum emulation hardware, quantum annealers, and quantum gate computers show that classical systems still deliver superior results. However, the proposed methods are ready for the current and upcoming generations of quantum computing devices which have the potential to outperform classical systems in the near future.

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.

Laura von Rueden, Sebastian Houben, Kostadin Cvejoski et al.

When training data is scarce, the incorporation of additional prior knowledge can assist the learning process. While it is common to initialize neural networks with weights that have been pre-trained on other large data sets, pre-training on more concise forms of knowledge has rather been overlooked. In this paper, we propose a novel informed machine learning approach and suggest to pre-train on prior knowledge. Formal knowledge representations, e.g. graphs or equations, are first transformed into a small and condensed data set of knowledge prototypes. We show that informed pre-training on such knowledge prototypes (i) speeds up the learning processes, (ii) improves generalization capabilities in the regime where not enough training data is available, and (iii) increases model robustness. Analyzing which parts of the model are affected most by the prototypes reveals that improvements come from deeper layers that typically represent high-level features. This confirms that informed pre-training can indeed transfer semantic knowledge. This is a novel effect, which shows that knowledge-based pre-training has additional and complementary strengths to existing approaches.

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.

Maurice Günder, Nico Piatkowski, Christian Bauckhage

The concept of Label Distribution Learning (LDL) is a technique to stabilize classification and regression problems with ambiguous and/or imbalanced labels. A prototypical use-case of LDL is human age estimation based on profile images. Regarding this regression problem, a so called Deep Label Distribution Learning (DLDL) method has been developed. The main idea is the joint regression of the label distribution and its expectation value. However, the original DLDL method uses loss components with different mathematical motivation and, thus, different scales, which is why the use of a hyperparameter becomes necessary. In this work, we introduce a loss function for DLDL whose components are completely defined by Kullback-Leibler (KL) divergences and, thus, are directly comparable to each other without the need of additional hyperparameters. It generalizes the concept of DLDL with regard to further use-cases, in particular for multi-dimensional or multi-scale distribution learning tasks.

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.

Christian Bauckhage, Thore Gerlach, Nico Piatkowski

We show that the fundamental tasks of sorting lists and building search trees or heaps can be modeled as quadratic unconstrained binary optimization problems (QUBOs). The idea is to understand these tasks as permutation problems and to devise QUBOs whose solutions represent appropriate permutation matrices. We discuss how to construct such QUBOs and how to solve them using Hopfield nets or adiabatic) quantum computing. In short, we show that neurocomputing methods or quantum computers can solve problems usually associated with abstract data structures.

Loong Kuan Lee, Geoffrey I. Webb, Daniel F. Schmidt et al.

The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications but doing so naively is intractable. Computing the alpha-beta divergence -- a family of divergences that includes the Kullback-Leibler divergence and Hellinger distance -- between the joint distribution of two decomposable models, i.e chordal Markov networks, can be done in time exponential in the treewidth of these models. However, reducing the dissimilarity between two high-dimensional objects to a single scalar value can be uninformative. Furthermore, in applications such as supervised learning, the divergence over a conditional distribution might be of more interest. Therefore, we propose an approach to compute the exact alpha-beta divergence between any marginal or conditional distribution of two decomposable models. Doing so tractably is non-trivial as we need to decompose the divergence between these distributions and therefore, require a decomposition over the marginal and conditional distributions of these models. Consequently, we provide such a decomposition and also extend existing work to compute the marginal and conditional alpha-beta divergence between these decompositions. We then show how our method can be used to analyze distributional changes by first applying it to a benchmark image dataset. Finally, based on our framework, we propose a novel way to quantify the error in contemporary superconducting quantum computers. Code for all experiments is available at: https://lklee.dev/pub/2023-icdm/code

Thore Gerlach, Nico Piatkowski

The demand for high-performance computing in machine learning and artificial intelligence has led to the development of specialized hardware accelerators like Tensor Processing Units (TPUs), Graphics Processing Units (GPUs), and Field-Programmable Gate Arrays (FPGAs). A key strategy to enhance these accelerators is the reduction of precision in arithmetic operations, which increases processing speed and lowers latency - crucial for real-time AI applications. Precision reduction minimizes memory bandwidth requirements and energy consumption, essential for large-scale and mobile deployments, and increases throughput by enabling more parallel operations per cycle, maximizing hardware resource utilization. This strategy is equally vital for solving NP-hard quadratic unconstrained binary optimization (QUBO) problems common in machine learning, which often require high precision for accurate representation. Special hardware solvers, such as quantum annealers, benefit significantly from precision reduction. This paper introduces a fully principled Branch-and-Bound algorithm for reducing precision needs in QUBO problems by utilizing dynamic range as a measure of complexity. Experiments validate our algorithm's effectiveness on an actual quantum annealer.

Benjamin Sliwa, Nico Piatkowski, Christian Wietfeld

Exploiting big data knowledge on small devices will pave the way for building truly cognitive Internet of Things (IoT) systems. Although machine learning has led to great advancements for IoT-based data analytics, there remains a huge methodological gap for the deployment phase of trained machine learning models. For given resource-constrained platforms such as Microcontroller Units (MCUs), model choice and parametrization are typically performed based on heuristics or analytical models. However, these approaches are only able to provide rough estimates of the required system resources as they do not consider the interplay of hardware, compiler specific optimizations, and code dependencies. In this paper, we present the novel open source framework LIghtweight Machine learning for IoT Systems (LIMITS), which applies a platform-in-the-loop approach explicitly considering the actual compilation toolchain of the target IoT platform. LIMITS focuses on high level tasks such as experiment automation, platform-specific code generation, and sweet spot determination. The solid foundations of validated low-level model implementations are provided by the coupled well-established data analysis framework Waikato Environment for Knowledge Analysis (WEKA). We apply and validate LIMITS in two case studies focusing on cellular data rate prediction and radio-based vehicle classification, where we compare different learning models and real world IoT platforms with memory constraints from 16 kB to 4 MB and demonstrate its potential to catalyze the development of machine learning enabled IoT systems.

Maria Demidik, Cenk Tüysüz, Nico Piatkowski et al.

Quantum computers offer the potential for efficiently sampling from complex probability distributions, attracting increasing interest in generative modeling within quantum machine learning. This surge in interest has driven the development of numerous generative quantum models, yet their trainability and scalability remain significant challenges. A notable example is a quantum restricted Boltzmann machine (QRBM), which is based on the Gibbs state of a parameterized non-commuting Hamiltonian. While QRBMs are expressive, their non-commuting Hamiltonians make gradient evaluation computationally demanding, even on fault-tolerant quantum computers. In this work, we propose a semi-quantum restricted Boltzmann machine (sqRBM), a model designed for classical data that mitigates the challenges associated with previous QRBM proposals. The sqRBM Hamiltonian is commuting in the visible subspace while remaining non-commuting in the hidden subspace. This structure allows us to derive closed-form expressions for both output probabilities and gradients. Leveraging these analytical results, we demonstrate that sqRBMs share a close relationship with classical restricted Boltzmann machines (RBM). Our theoretical analysis predicts that, to learn a given probability distribution, an RBM requires three times as many hidden units as an sqRBM, while both models have the same total number of parameters. We validate these findings through numerical simulations involving up to 100 units. Our results suggest that sqRBMs could enable practical quantum machine learning applications in the near future by significantly reducing quantum resource requirements.

Thore Gerlach, Loong Kuan Lee, Frédéric Barbaresco et al.

Multi-Agent Path Finding (MAPF) focuses on determining conflict-free paths for multiple agents navigating through a shared space to reach specified goal locations. This problem becomes computationally challenging, particularly when handling large numbers of agents, as frequently encountered in practical applications like coordinating autonomous vehicles. Quantum Computing (QC) is a promising candidate in overcoming such limits. However, current quantum hardware is still in its infancy and thus limited in terms of computing power and error robustness. In this work, we present the first optimal hybrid quantum-classical MAPF algorithms which are based on branch-andcut-and-price. QC is integrated by iteratively solving QUBO problems, based on conflict graphs. Experiments on actual quantum hardware and results on benchmark data suggest that our approach dominates previous QUBO formulationsand state-of-the-art MAPF solvers.

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".

Loong Kuan Lee, Thore Thassilo Gerlach, Nico Piatkowski

Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially operating on very different scales. This imbalance introduces complications such as the selection of appropriate weights when scalarizing multiple objectives into a single objective function. In this paper, we propose a novel technique for scaling QUBO objectives that uses an exact computation of the variance of each individual QUBO objective. By scaling each objective to have unit variance, we align all objectives onto a common scale, thereby allowing for more balanced solutions to be found when scalarizing the objectives with equal weights, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multi-objective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome, and reliable, efficient solutions are scarce.

Loong Kuan Lee, Nico Piatkowski, François Petitjean et al.

There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within these distributions, computing the divergence between them is an intractable problem in high dimensions. We show that we are able to compute a wide family of functionals and divergences, such as the alpha-beta divergence, between two decomposable models, i.e. chordal Markov networks, in time exponential to the treewidth of these models. The alpha-beta divergence is a family of divergences that include popular divergences such as the Kullback-Leibler divergence, the Hellinger distance, and the chi-squared divergence. Thus, we can accurately compute the exact values of any of this broad class of divergences to the extent to which we can accurately model the two distributions using decomposable models.

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.

Katharina Morik, Helena Kotthaus, Lukas Heppe et al.

Machine learning applications have become ubiquitous. This has led to an increased effort of making machine learning trustworthy. Explainable and fair AI have already matured. They address knowledgeable users and application engineers. For those who do not want to invest time into understanding the method or the learned model, we offer care labels: easy to understand at a glance, allowing for method or model comparisons, and, at the same time, scientifically well-based. On one hand, this transforms descriptions as given by, e.g., Fact Sheets or Model Cards, into a form that is well-suited for end-users. On the other hand, care labels are the result of a certification suite that tests whether stated guarantees hold. In this paper, we present two experiments with our certification suite. One shows the care labels for configurations of Markov random fields (MRFs). Based on the underlying theory of MRFs, each choice leads to its specific rating of static properties like, e.g., expressivity and reliability. In addition, the implementation is tested and resource consumption is measured yielding dynamic properties. This two-level procedure is followed by another experiment certifying deep neural network (DNN) models. There, we draw the static properties from the literature on a particular model and data set. At the second level, experiments are generated that deliver measurements of robustness against certain attacks. We illustrate this by ResNet-18 and MobileNetV3 applied to ImageNet.

Katharina Morik, Helena Kotthaus, Raphael Fischer et al.

Machine learning applications have become ubiquitous. Their applications range from embedded control in production machines over process optimization in diverse areas (e.g., traffic, finance, sciences) to direct user interactions like advertising and recommendations. This has led to an increased effort of making machine learning trustworthy. Explainable and fair AI have already matured. They address the knowledgeable user and the application engineer. However, there are users that want to deploy a learned model in a similar way as their washing machine. These stakeholders do not want to spend time in understanding the model, but want to rely on guaranteed properties. What are the relevant properties? How can they be expressed to the stakeholder without presupposing machine learning knowledge? How can they be guaranteed for a certain implementation of a machine learning model? These questions move far beyond the current state of the art and we want to address them here. We propose a unified framework that certifies learning methods via care labels. They are easy to understand and draw inspiration from well-known certificates like textile labels or property cards of electronic devices. Our framework considers both, the machine learning theory and a given implementation. We test the implementation's compliance with theoretical properties and bounds.

Laura von Rueden, Tim Wirtz, Fabian Hueger et al.

Artificial intelligence for autonomous driving must meet strict requirements on safety and robustness, which motivates the thorough validation of learned models. However, current validation approaches mostly require ground truth data and are thus both cost-intensive and limited in their applicability. We propose to overcome these limitations by a model agnostic validation using a-priori knowledge from street maps. In particular, we show how to validate semantic segmentation masks and demonstrate the potential of our approach using OpenStreetMap. We introduce validation metrics that indicate false positive or negative road segments. Besides the validation approach, we present a method to correct the vehicle's GPS position so that a more accurate localization can be used for the street-map based validation. Lastly, we present quantitative results on the Cityscapes dataset indicating that our validation approach can indeed uncover errors in semantic segmentation masks.

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.

Lukas Heppe, Michael Kamp, Linara Adilova et al.

The communication between data-generating devices is partially responsible for a growing portion of the world's power consumption. Thus reducing communication is vital, both, from an economical and an ecological perspective. For machine learning, on-device learning avoids sending raw data, which can reduce communication substantially. Furthermore, not centralizing the data protects privacy-sensitive data. However, most learning algorithms require hardware with high computation power and thus high energy consumption. In contrast, ultra-low-power processors, like FPGAs or micro-controllers, allow for energy-efficient learning of local models. Combined with communication-efficient distributed learning strategies, this reduces the overall energy consumption and enables applications that were yet impossible due to limited energy on local devices. The major challenge is then, that the low-power processors typically only have integer processing capabilities. This paper investigates an approach to communication-efficient on-device learning of integer exponential families that can be executed on low-power processors, is privacy-preserving, and effectively minimizes communication. The empirical evaluation shows that the approach can reach a model quality comparable to a centrally learned regular model with an order of magnitude less communication. Comparing the overall energy consumption, this reduces the required energy for solving the machine learning task by a significant amount.

Sibylle Hess, Nico Piatkowski, Katharina Morik

Boolean matrix factorization (BMF) is a popular and powerful technique for inferring knowledge from data. The mining result is the Boolean product of two matrices, approximating the input dataset. The Boolean product is a disjunction of rank-1 binary matrices, each describing a feature-relation, called pattern, for a group of samples. Yet, there are no guarantees that any of the returned patterns do not actually arise from noise, i.e., are false discoveries. In this paper, we propose and discuss the usage of the false discovery rate in the unsupervised BMF setting. We prove two bounds on the probability that a found pattern is constituted of random Bernoulli-distributed noise. Each bound exploits a specific property of the factorization which minimizes the approximation error---yielding new insights on the minimizers of Boolean matrix factorization. This leads to improved BMF algorithms by replacing heuristic rank selection techniques with a theoretically well-based approach. Our empirical demonstration shows that both bounds deliver excellent results in various practical settings.

Sibylle Hess, Katharina Morik, Nico Piatkowski

Mining and exploring databases should provide users with knowledge and new insights. Tiles of data strive to unveil true underlying structure and distinguish valuable information from various kinds of noise. We propose a novel Boolean matrix factorization algorithm to solve the tiling problem, based on recent results from optimization theory. In contrast to existing work, the new algorithm minimizes the description length of the resulting factorization. This approach is well known for model selection and data compression, but not for finding suitable factorizations via numerical optimization. We demonstrate the superior robustness of the new approach in the presence of several kinds of noise and types of underlying structure. Moreover, our general framework can work with any cost measure having a suitable real-valued relaxation. Thereby, no convexity assumptions have to be met. The experimental results on synthetic data and image data show that the new method identifies interpretable patterns which explain the data almost always better than the competing algorithms.