Understanding quantum machine learning also requires rethinking generalization

Abstract

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the study of quantum models for machine learning tasks.

arXiv comment14+4 pages, 3 figures

References in corpus (62)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Machine learning and the physical sciences
• Barren plateaus in quantum neural network training landscapes
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum machine learning in feature Hilbert spaces
• Quantum Convolutional Neural Networks
• Machine learning phases of matter
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Strong quantum computational advantage using a superconducting quantum processor
• Parameterized quantum circuits as machine learning models
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Quantum algorithms: an overview
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• A class of quantum many-body states that can be efficiently simulated
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Data re-uploading for a universal quantum classifier
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• A rigorous and robust quantum speed-up in supervised machine learning
• Generalization in quantum machine learning from few training data
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Machine learning quantum phases of matter beyond the fermion sign problem
• Absence of Barren Plateaus in Quantum Convolutional Neural Networks
• Implementing a distance-based classifier with a quantum interference circuit
• Effect of barren plateaus on gradient-free optimization
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Training of Quantum Circuits on a Hybrid Quantum Computer
• Exploiting symmetry in variational quantum machine learning
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks
• Theory of overparametrization in quantum neural networks
• Group-Invariant Quantum Machine Learning
• Generalization in Quantum Machine Learning: a Quantum Information Perspective
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Fantastic Generalization Measures and Where to Find Them
• Computational advantage of quantum random sampling
• Training Quantum Embedding Kernels on Near-Term Quantum Computers
• Qibo: a framework for quantum simulation with hardware acceleration
• TensorCircuit: a Quantum Software Framework for the NISQ Era
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Universal discriminative quantum neural networks
• On the Quantum versus Classical Learnability of Discrete Distributions
• Out-of-distribution generalization for learning quantum dynamics
• Scaling of variational quantum circuit depth for condensed matter systems
• On the statistical complexity of quantum circuits
• Generalization despite overfitting in quantum machine learning models
• Quantum enhancements for deep reinforcement learning in large spaces
• Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems
• Style-based quantum generative adversarial networks for Monte Carlo events
• Expressivity of Quantum Neural Networks
• Variational Quantum Anomaly Detection: Unsupervised mapping of phase diagrams on a physical quantum computer
• Structural risk minimization for quantum linear classifiers
• Pseudo-dimension of quantum circuits
• Distributed quantum inner product estimation
• A super-polynomial quantum-classical separation for density modelling
• Effects of quantum resources on the statistical complexity of quantum circuits
• Expressivity of Variational Quantum Machine Learning on the Boolean Cube
• Decomposition of Matrix Product States into Shallow Quantum Circuits
• The power and limitations of learning quantum dynamics incoherently
• Rademacher complexity of noisy quantum circuits

Cited by in corpus (21)

• Does provable absence of barren plateaus imply classical simulability?
• Classically estimating observables of noiseless quantum circuits
• Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• A General Approach to Dropout in Quantum Neural Networks
• Training robust and generalizable quantum models
• What can we learn from quantum convolutional neural networks?
• Neural quantum kernels: training quantum kernels with quantum neural networks
• Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey
• Satellite image classification with neural quantum kernels
• Single-shot quantum machine learning
• Learning Fourier series with parametrized quantum circuits
• Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
• Generalization Bounds in Hybrid Quantum-Classical Machine Learning Models
• Towards Improved Quantum Machine Learning for Molecular Force Fields
• Quantum Curriculum Learning
• Double descent in quantum kernel methods
• Vortex Detection from Quantum Data
• Learning complexity gradually in quantum machine learning models
• Superior resilience to poisoning and amenability to unlearning in quantum machine learning
• Transfer entropy and O-information to detect grokking in tensor network multi-class classification problems