Degree-Optimized Cumulative Polynomial Kolmogorov-Arnold Networks

We introduce cumulative polynomial Kolmogorov-Arnold networks (CP-KAN), a neural architecture combining Chebyshev polynomial basis functions and quadratic unconstrained binary optimization (QUBO). Our primary contribution involves reformulating the degree selection problem as a QUBO task, reducing the complexity from $O(D^N)$ to a single optimization step per layer. This approach enables efficient degree selection across neurons while maintaining computational tractability. The architecture performs well in regression tasks with limited data, showing good robustness to input scales and natural regularization properties from its polynomial basis. Additionally, theoretical analysis establishes connections between CP-KAN's performance and properties of financial time series. Our empirical validation across multiple domains demonstrates competitive performance compared to several traditional architectures tested, especially in scenarios where data efficiency and numerical stability are important. Our implementation, including strategies for managing computational overhead in larger networks is available in Ref.~\citep{cpkan_implementation}.

Enhanced Photonic Chip Design via Interpretable Machine Learning Techniques

Photonic chip design has seen significant advancements with the adoption of inverse design methodologies, offering flexibility and efficiency in optimizing device performance. However, the black-box nature of the optimization approaches, such as those used in inverse design in order to minimize a loss function or maximize coupling efficiency, poses challenges in understanding the outputs. This challenge is prevalent in machine learning-based optimization methods, which can suffer from the same lack of transparency. To this end, interpretability techniques address the opacity of optimization models. In this work, we apply interpretability techniques from machine learning, with the aim of gaining understanding of inverse design optimization used in designing photonic components, specifically two-mode multiplexers. We base our methodology on the widespread interpretability technique known as local interpretable model-agnostic explanations, or LIME. As a result, LIME-informed insights point us to more effective initial conditions, directly improving device performance. This demonstrates that interpretability methods can do more than explain models -- they can actively guide and enhance the inverse-designed photonic components. Our results demonstrate the ability of interpretable techniques to reveal underlying patterns in the inverse design process, leading to the development of better-performing components.

Sub-universal variational circuits for combinatorial optimization problems

Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic circuits designed for generating approximate solutions to combinatorial optimization problems constructed using two-bit stochastic matrices. Through a numerical study, we investigate the performance of our proposed variational circuits in solving the Max-Cut problem on various graphs of increasing sizes. Our classical algorithm demonstrates improved performance for several graph types to the quantum approximate optimization algorithm. Our findings suggest that evaluating the performance of quantum variational circuits against variational circuits with sub-universal gate sets is a valuable benchmark for identifying areas where quantum variational circuits can excel.

Explicability and Inexplicability in the Interpretation of Quantum Neural Networks

Interpretability of artificial intelligence (AI) methods, particularly deep neural networks, is of great interest due to the widespread use of AI-backed systems, which often have unexplainable behavior. The interpretability of such models is a crucial component of building trusted systems. Many methods exist to approach this problem, but they do not obviously generalize to the quantum setting. Here we explore the interpretability of quantum neural networks using local model-agnostic interpretability measures of quantum and classical neural networks. We introduce the concept of the band of inexplicability, representing the interpretable region in which data samples have no explanation, likely victims of inherently random quantum measurements. We see this as a step toward understanding how to build responsible and accountable quantum AI models.

An Invitation to Distributed Quantum Neural Networks

Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed techniques are often employed in training large models or large datasets either out of necessity or simply for speed. Quantum machine learning, on the other hand, is the interplay between machine learning and quantum computing. It seeks to understand the advantages of employing quantum devices in developing new learning algorithms as well as improving the existing ones. A set of architectures that are heavily explored in quantum machine learning are quantum neural networks. In this review, we consider ideas from distributed deep learning as they apply to quantum neural networks. We find that the distribution of quantum datasets shares more similarities with its classical counterpart than does the distribution of quantum models, though the unique aspects of quantum data introduces new vulnerabilities to both approaches. We review the current state of the art in distributed quantum neural networks, including recent numerical experiments and the concept of circuit cutting.