Neural Network Theory
Neural Networks have witnessed extensive integration across diverse domains within physics. However, our focus shifts towards the inverse problem: How can neural networks benefit from physics? This line of inquiry holds immense potential for the field of interpretable machine learning and explainable AI.
Learning with a neural network involves algorithmically assimilating information into a model. However, the process of neural learning remains largely elusive, given the challenge of understanding how to extract information from its complex inner workings. This lack of interpretability is a major hurdle in many AI applications, as it makes it difficult to trust and debug these powerful models.
Here's where the physics analogy comes in. Analogous to dynamical systems in statistical physics, describing neural network training involves an extensive number of degrees of freedom – essentially the vast number of connections and weights within the network. This complexity makes it challenging to understand the learning process in detail. However, physics offers a powerful approach: describing complex systems through macroscopic quantities.
To that end, we introduce Collective Variables for neural networks [1]. These variables capture the essential aspects of the learning process, tracing out the microscopic details (individual weights and connections) to describe and analyze the learning process at every stage. By applying this physics-inspired approach, we aim to construct a macroscopic theory of learning to achieve a more interpretable understanding of neural networks. Working towards a solution to this central issue of machine learning, we want to build and optimize systems that are not only powerful but also understandable and trustworthy.
Responsible People: Konstantin Nikolaou & Samuel Tovey
[1] Samuel Tovey et al 2023 Mach. Learn.: Sci. Technol. 4 035040
Machine-learned Interatomic Potential
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Reinforcement Learning
Published soon
Quantum Machine Learning
It has been shown that Quantum Computers possess the potential to surpass classical computers in tasks that exceed a certain level of complexity. In many machine learning tasks, problems are projected into a higher-dimensional space where models can effectively learn a given task. By integrating quantum computing with machine learning, we enter the realm of Quantum Machine Learning, where researchers aim to leverage the exponentially large Hilbert space to potentially outperform classical machine learning models.
In Quantum Machine Learning, computations are executed on quantum circuits, altering the quantum state of the multi-qubit system. Specifically, during the training of Quantum Machine Learning models, parameters on the quantum circuit are adjusted to best fit a given training dataset.
Our focus lies in exploring the capabilities of quantum neural networks for time series predictions. Time series data encompasses various types, including simple analytical functions, chaotic time series data, or real-life data such as stock market data. We aim to investigate the quantum models' potential to discern correlations within a given time series dataset and predict future data points.
Furthermore, we are delving into the potential of utilizing quantum systems, such as spin chains or quantum circuits, as Quantum Reservoirs for time series prediction and anomaly detection within time series data.
Research questions we are pursuing include:
- How do quantum models compare to classical models in terms of time series prediction capability?
- Which quantum time series model best captures the sequential property of time series?
- How can we best exploit the exponentially large Hilbert space?
- Can we improve Quantum models by performing random measurements of the Quantum state?
- How does training the parameters on the circuit compare to treating the circuit as a quantum reservoir?
Responsible People: Tobias Fellner, Samuel Tovey
