Related papers: Spectral Bias in Variational Quantum Machine Learn…

Quantum machine learning models based on parameterized circuits can be viewed as Fourier series approximators. However, they often struggle to learn functions with multiple frequency components, particularly high-frequency or non-dominant…

In this work, we highlight an unforeseen behavior of the expressivity of Parameterized Quantum Circuits (PQCs) for machine learning. A large class of these models, seen as Fourier Series which frequencies are derived from the encoding…

This article presents an argument for why quantum computers could unlock new methods for machine learning. We argue that spectral methods, in particular those that learn, regularise, or otherwise manipulate the Fourier spectrum of a machine…

Quantum neural networks constitute a key class of near-term quantum learning models, yet their training dynamics remain not fully understood. Here, we present a unified theoretical framework for the frequency principle (F-principle) that…

CNNs exhibit many behaviors different from humans, one of which is the capability of employing high-frequency components. This paper discusses the frequency bias phenomenon in image classification tasks: the high-frequency components are…

Spectral bias implies an imbalance in training dynamics, whereby high-frequency components may converge substantially more slowly than low-frequency ones. To alleviate this issue, we propose a cross-attention-based architecture that…

An intriguing phenomenon observed during training neural networks is the spectral bias, which states that neural networks are biased towards learning less complex functions. The priority of learning functions with low complexity might be at…

Quantum machine learning is arguably one of the most explored applications of near-term quantum devices. Much focus has been put on notions of variational quantum machine learning where parameterized quantum circuits (PQCs) are used as…

The mechanism governing the training dynamics of Quantum Neural Networks (QNNs) remains under-explored. In classical Deep Neural Networks (DNNs), training is dominated by "Spectral Bias," i.e. prioritizing learning low-frequency components…

Spectral bias is an important observation of neural network training, stating that the network will learn a low frequency representation of the target function before converging to higher frequency components. This property is interesting…

Despite their ability to represent highly expressive functions, deep learning models seem to find simple solutions that generalize surprisingly well. Spectral bias -- the tendency of neural networks to prioritize learning low frequency…

Understanding deep learning is increasingly emergent as it penetrates more and more into industry and science. In recent years, a research line from Fourier analysis sheds lights on this magical "black box" by showing a Frequency Principle…

Parameterized Quantum Circuits (PQCs) have been acknowledged as a leading strategy to utilize near-term quantum advantages in multiple problems, including machine learning and combinatorial optimization. When applied to specific tasks, the…

The vulnerability of deep neural networks to adversarial samples has been a major impediment to their broad applications, despite their success in various fields. Recently, some works suggested that adversarially-trained models emphasize…

Recent works have shown that traditional Neural Network (NN) architectures display a marked frequency bias in the learning process. Namely, the NN first learns the low-frequency features before learning the high-frequency ones. In this…

Variational quantum algorithms have received substantial theoretical and empirical attention. As the underlying variational quantum circuit (VQC) can be represented by Fourier series that contain an exponentially large spectrum in the…

VQC can be understood through the lens of Fourier analysis. It is already well-known that the function space represented by any circuit architecture can be described through a truncated Fourier sum. We show that the spectrum available to…

Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit…

Variational quantum algorithms (VQAs) and their applications in the field of quantum machine learning through parametrized quantum circuits (PQCs) are thought to be one major way of leveraging noisy intermediate-scale quantum computing…

In this paper, we use spectral analysis to investigate transfer learning and study model sensitivity to frequency shortcuts in medical imaging. By analyzing the power spectrum density of both pre-trained and fine-tuned model gradients, as…