Related papers: Identifying overparameterization in Quantum Circui…

A key component of a quantum machine learning model operating on classical inputs is the design of an embedding circuit mapping inputs to a quantum state. This paper studies a transfer learning setting in which classical-to-quantum…

This work analyzes transfer learning of the Variational Quantum Circuit (VQC). Our framework begins with a pretrained VQC configured in one domain and calculates the transition of 1-parameter unitary subgroups required for a new domain. A…

High-dimensional non-convex loss landscapes play a central role in the theory of Machine Learning. Gaining insight into how these landscapes interact with gradient-based optimization methods, even in relatively simple models, can shed light…

We study transfer learning for a linear regression task using several least-squares pretrained models that can be overparameterized. We formulate the target learning task as optimization that minimizes squared errors on the target dataset…

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide…

Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…

Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…

Recent research in neural networks and machine learning suggests that using many more parameters than strictly required by the initial complexity of a regression problem can result in more accurate or faster-converging models -- contrary to…

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and…

The variational quantum algorithm (VQA) with a parametrized quantum circuit is widely applicable to near-term quantum computing, but its fundamental issues that limit optimization performance have been reported in the literature. For…

Recently, there has been significant progress in understanding the convergence and generalization properties of gradient-based methods for training overparameterized learning models. However, many aspects including the role of small random…

Quantum machine learning has demonstrated significant potential in solving practical problems, particularly in statistics-focused areas such as data science and finance. However, challenges remain in preparing and learning statistical…

Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…

Different techniques have been used to prove several transference theorems of the form "nontrivial algorithms for a circuit class C yield circuit lower bounds against C". In this survey we revisit many of these results. We discuss how…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

Transformers serve as the foundational architecture for many successful large-scale models, demonstrating the ability to overfit the training data while maintaining strong generalization on unseen data, a phenomenon known as benign…

In the domain of variational quantum algorithms, quantum Fourier models (QFMs) provide a mathematically well defined structure for quantum machine learning (QML). There has been a substantial amount of work on the scalability and…

We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being…

Variational Quantum Circuits (VQCs) have emerged as a promising paradigm for quantum machine learning in the NISQ era. While parameter sharing in VQCs can reduce the parameter space dimensionality and potentially mitigate the barren plateau…

The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…