Understanding Generalization in Quantum Machine Learning with Margins

• URL: http://arxiv.org/abs/2411.06919v1
• Date: Mon, 11 Nov 2024 12:22:18 GMT
• Title: Understanding Generalization in Quantum Machine Learning with Margins
• Authors: Tak Hur, Daniel K. Park,
• Abstract summary: We present a margin-based generalization bound for QML models. By connecting this margin-based metric to quantum information theory, we demonstrate how to enhance the generalization performance of QML.
• Score: 0.46040036610482665
• License:
• Abstract: Understanding and improving generalization capabilities is crucial for both classical and quantum machine learning (QML). Recent studies have revealed shortcomings in current generalization theories, particularly those relying on uniform bounds, across both classical and quantum settings. In this work, we present a margin-based generalization bound for QML models, providing a more reliable framework for evaluating generalization. Our experimental studies on the quantum phase recognition (QPR) dataset demonstrate that margin-based metrics are strong predictors of generalization performance, outperforming traditional metrics like parameter count. By connecting this margin-based metric to quantum information theory, we demonstrate how to enhance the generalization performance of QML through a classical-quantum hybrid approach when applied to classical data.

Related papers

• Optimizer-Dependent Generalization Bound for Quantum Neural Networks [5.641998714611475]
  Quantum neural networks (QNNs) play a pivotal role in addressing complex tasks within quantum machine learning. We investigate the generalization properties of QNNs through the lens of learning algorithm stability. Our work offers practical insights for applying QNNs in quantum machine learning.
  arXiv  Detail & Related papers  (2025-01-27T17:22:34Z)
• Benchmarking quantum machine learning kernel training for classification tasks [0.0]
  This study focuses on quantum kernel methods in the context of classification tasks. It examines the performance of Quantum Kernel Estimation (QKE) and Quantum Kernel Training (QKT) in connection with two quantum feature mappings. Experimental results indicate that quantum methods exhibit varying performance across different datasets.
  arXiv  Detail & Related papers  (2024-08-17T10:53:06Z)
• Separable Power of Classical and Quantum Learning Protocols Through the Lens of No-Free-Lunch Theorem [70.42372213666553]
  The No-Free-Lunch (NFL) theorem quantifies problem- and data-independent generalization errors regardless of the optimization process. We categorize a diverse array of quantum learning algorithms into three learning protocols designed for learning quantum dynamics under a specified observable. Our derived NFL theorems demonstrate quadratic reductions in sample complexity across CLC-LPs, ReQu-LPs, and Qu-LPs. We attribute this performance discrepancy to the unique capacity of quantum-related learning protocols to indirectly utilize information concerning the global phases of non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2024-05-12T09:05:13Z)
• Information-theoretic generalization bounds for learning from quantum data [5.0739329301140845]
  We propose a general mathematical formalism for describing quantum learning by training on classical-quantum data. We prove bounds on the expected generalization error of a quantum learner in terms of classical and quantum information-theoretic quantities. Our work lays a foundation for a unifying quantum information-theoretic perspective on quantum learning.
  arXiv  Detail & Related papers  (2023-11-09T17:21:38Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Do Quantum Circuit Born Machines Generalize? [58.720142291102135]
  We present the first work in the literature that presents the QCBM's generalization performance as an integral evaluation metric for quantum generative models. We show that the QCBM is able to effectively learn the reweighted dataset and generate unseen samples with higher quality than those in the training set.
  arXiv  Detail & Related papers  (2022-07-27T17:06:34Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• Clustering and enhanced classification using a hybrid quantum autoencoder [0.0]
  We propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space. This variational QML algorithm learns to identify, and classically represent, their essential distinguishing characteristics. The analysis and employment of the HQA model are presented in the context of amplitude encoded states.
  arXiv  Detail & Related papers  (2021-07-26T06:50:31Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.