Student-Abstracts-EN

Path-Connectedness of the Boundary between Features that Are Labeled Differently by a Single Layer Perceptron

Abstract:

Due to the remarkable advancements in high-performance computing, machines can process an increasingly high amount of data to adjust numerous parameters in a Machine Learning model (ML model). In this way, the machine recognizes and learns patterns and might come to good and fast decisions. Though, the success of an ML model does not just depend on the performance of the computer where it is deployed on that assures the capability of processing huge databases. Mostly, a high amount of data is helpful, but not the key to obtain a reliable model itself. Already models with just a few trainable parameters, where smaller data sets are sufficient for the training, can produce stunning outputs if the basic model is chosen adequately and fits to the data and to the task.

From an abstract point of view, ML models are parameterized functions, where the parameters are optimized during the learning process. To examine if a certain ML model qualitatively fits, we can set up requirements in a mathematical way. Here, we discuss specifications that do not consider a concrete assignment of the parameters but expect a certain behavior of the to a model corresponding function for arbitrary parameters. Subsequently, we can prove that a certain model fulfills them, or give a more specific counter-example, which yields that a certain mathematical property does not hold, in general, for the regarded model.

In this thesis, we consider a Single Layer Perceptron (SLP), the root of Deep Neural Networks, that categorizes features between two different labels. We show that under certain preconditions the boundary between the two categories within the feature space is path-connected. This indicates the SLP being a proper choice if we have pre-knowledge about the features: If we know that the boundary between the two categories is path-connected in reality, we can exclude such models that generate a boundary with gaps.

Author:

Advisors:

Maximilian Balthasar Mansky, Thomas Gabor, Claudia Linnhoff-Popien

Student Thesis | Published December 2023 | Copyright © QAR-Lab
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Using Quantum Machine Learning to Predict Asset Prices in Financial Markets

Abstract:

In the financial world, a lot of effort is spent on predicting future asset prices. Gaining even a modest increase in forecasting capability can generate enormous profits. Some statistical models identify patterns, trends, and correlations in past prices, and apply those patterns to forecast future values. A more novel approach is the use of artificial intelligence to learn underlying trends in the data and predict future prices. As quantum computing matures, its potential applications in this task have also become increasingly more interesting. In this thesis, several different models of these various types are implemented: ARIMA, RBM, LSTM, and QDBM (Quantum Deep Boltzmann Machine). These models are trained on historical asset prices and used to predict future asset prices. The model predictions are then also used as the input for a simulated trading algorithm, which investigates the effectiveness of these predictions in the active trading of assets. The predictions are performed for ten different assets listed on the NYSE, NASDAQ, and XETRA, for the five-year period from 2018 to 2022. The assets were chosen from varying industrial sectors and with diverse price histories. Trading based on the model predictions was able to either match or outperform the classic buy-and-hold approach in nine out of the ten assets tested.

Author:

Maximilian Adler

Advisors:

Claudia Linnhoff-Popien, Jonas Stein, Jonas Nüßlein, Nico Kraus (Aqarios GmbH)

Student Thesis | Published November 2023 | Copyright © QAR-Lab
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Quantum-Enhanced Denoising Diffusion Models

Abstract:

Machine learning models for generating images have gained much notoriety in the past year. DALL-E, Craiyon and Stable Diffusion can generate high-resolution images, by users simply typing a short description (prompt) of the desired image. Another growing field is quantum computing, particularly quantum-enhanced machine learning. Quantum computers solve problems using their unique quantum mechanical properties. In this paper we investigate how the use of Quantum-enhanced Machine Learning and Variational Quantum Circuits can improve image generation by diffusion-based models. The two major weaknesses of classical diffusion models are addressed, the low sampling speed
and the high number of required parameters. Implementations of a quantum-enhanced denoising diffusion model will be presented, and their performance is compared with that of classical models, by training the models on well-known datasets (MNIST digits and fashion, CIFAR10). We show, that our models deliver better performance (measured in FID, SSIM and PSNR) than the classical models with comparable number of parameters.

Author:

Gerhard Stenzel

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Jonas Stein, Andreas Sedlmeier

Student Thesis | Published October 2023 | Copyright © QAR-Lab
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Dimensionality Reduction with Autoencoders for Efficient Classification with Variational Quantum Circuits

Abstract:

Quantum computing promises performance advantages, especially for data-intensive and complex computations. However, we are currently in the Noisy Intermediate-Scale Quantum era with a limited number of qubits available, which makes it challenging to realize these potential quantum advantages in machine learning. Several solutions, like hybrid transfer learning have been proposed, whereby a pre-trained classical neural network acts as the feature extractor and a variational quantum circuit as the classifier. While these approaches often yield good performance, it is not possible to clearly determine the contribution of the classical and quantum part. The goal of this thesis is therefore to introduce a hybrid model that addresses these limitations and implements a clear distinction between the classical and quantum parts. An autoencoder is used to reduce the input dimension. We compare the performance of transfer learning models (Dressed Quantum Circuit and SEQUENT) and a variational quantum circuit with amplitude embedding against our model. Additionally, the performance of a purely classical neural network on the uncompressed input and an autoencoder in combination with a neural network will be examined. We compare the test accuracies of the models over the datasets Banknote
Authentication, Breast Cancer Wisconsin, MNIST and AudioMNIST. The results show that the classical neural networks and the hybrid transfer learning approaches perform better than our model, which matches our expectations that the classical part in transfer learning plays the major role in the overall performance. Compared to a variational quantum circuit with amplitude embedding, no significant dierence can be observed, so that our model is a reasonable alternative to this.

Author:

Jonas Maurer

Advisors:

Claudia Linnhoff-Popien, Michael Kölle, Philipp Altmann, Leo Sünkel

Student Thesis | Published October 2023 | Copyright © QAR-Lab
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Approximating Quadratic Unconstrained Binary Optimization Problems using Graph Convolutional Neural Networks

Abstract:

The quantum annealing hardware currently available has not yet reached the stage to successfully compete with ecient heuristics on classical machines, due to limitations in size and connectivity. Confronted with this challenge, the approach to approximate QUBO matrices by removing certain entries before solving them on the quantum hardware has been introduced. This is done to reduce the size and the complexity of the embedding, anticipating benefits with regard to the size of the solvable problems as well as the quality of the solutions.
We will extend this approach by using artificial neural networks to generate suitable approximations based on the structure of the matrix. The proposed model consists of two separate networks, a graph convolutional neural network to compute features for the nodes in the QUBO graph and a second fully connected network to derive a decision, whether the connection between two nodes should be removed from the matrix. A genetic algorithm was employed to train the model, using instances of seven dierent problems. Problem specific phase transitions were taken into account to confront the model with
easy and hard problem instances.
The trained models were subsequently evaluated using classical and quantum solvers, comparing the performance of the approximated matrix with the original matrix, another approximation strategy and classical approaches. The experiments provided satisfying results for certain problems, as the approximated matrices were partially able to produce even better results than the original matrices. In other respects, it became apparent, that this approach is not applicable to all problems.

Author:

Felix Ferdinand Mindt

Advisors:

Claudia Linnhoff-Popien, David Bucher, Sebastian Zielinski

Student Thesis | Published October 2023 | Copyright © QAR-Lab
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