# Double descent in quantum kernel methods

arXiv: https://arxiv.org/abs/2501.10077 · HTML: https://mlsanity.com/paper/2501.10077/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 95 references that are in the map.
- First posted on arXiv 17 Jan 2025.

## Builds on (most cited first, 30 of 57)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [High-dimensional dynamics of generalization error in neural networks](https://mlsanity.com/paper/1710.03667/) (2017)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Harmless interpolation of noisy data in regression](https://mlsanity.com/paper/1903.09139/) (2019)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Scaling description of generalization with number of parameters in deep learning](https://mlsanity.com/paper/1901.01608/) (2019)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Understanding Double Descent Requires a Fine-Grained Bias-Variance Decomposition](https://mlsanity.com/paper/2011.03321/) (2020)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [A jamming transition from under- to over-parametrization affects loss landscape and generalization](https://mlsanity.com/paper/1810.09665/) (2018)
- [Limitations of Neural Collapse for Understanding Generalization in Deep Learning](https://mlsanity.com/paper/2202.08384/) (2022)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)

## Built on by (most cited first, 9 of 9)

- [Benign Overfitting with Quantum Kernels](https://mlsanity.com/paper/2503.17020/) (2025)
- [Double Descent and Overparameterization in Particle Physics Data](https://mlsanity.com/paper/2509.01397/) (2025)
- [Kernel-based optimization of measurement operators for quantum reservoir computers](https://mlsanity.com/paper/2602.14677/) (2026)
- [A PAC-Bayesian approach to generalization for quantum models](https://mlsanity.com/paper/2603.22964/) (2026)
- [Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potential](https://mlsanity.com/paper/2506.03779/) (2025)
- [Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach](https://mlsanity.com/paper/2602.18377/) (2026)
- [The interplay of robustness and generalization in quantum machine learning](https://mlsanity.com/paper/2506.08455/) (2025)
- [From Reachability to Learnability: Geometric Design Principles for Quantum Neural Networks](https://mlsanity.com/paper/2603.03071/) (2026)
- [Cautious optimism for deep parameterized quantum circuits](https://mlsanity.com/paper/2607.21409/) (2026)

## Abstract (arXiv)

The double descent phenomenon challenges traditional statistical learning theory by revealing scenarios where larger models do not necessarily lead to reduced performance on unseen data. While this counterintuitive behavior has been observed in a variety of classical machine learning models, particularly modern neural network architectures, it remains elusive within the context of quantum machine learning. In this work, we analytically demonstrate that linear regression models in quantum feature spaces can exhibit double descent behavior by drawing on insights from classical linear regression and random matrix theory. Additionally, our numerical experiments on quantum kernel methods across different real-world datasets and system sizes further confirm the existence of a test error peak, a characteristic feature of double descent. Our findings provide evidence that quantum models can operate in the modern, overparameterized regime without experiencing overfitting, potentially opening pathways to improved learning performance beyond traditional statistical learning theory.