# Do Quantum Neural Networks have Simplicity Bias?

arXiv: https://arxiv.org/abs/2407.03266 · HTML: https://mlsanity.com/paper/2407.03266/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 3 Jul 2024.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [Is SGD a Bayesian sampler? Well, almost](https://mlsanity.com/paper/2006.15191/) (2020)
- [Deep neural networks have an inbuilt Occam's razor](https://mlsanity.com/paper/2304.06670/) (2023)
- [Neural networks are a priori biased towards Boolean functions with low entropy](https://mlsanity.com/paper/1909.11522/) (2019)

## Built on by (most cited first, 3 of 3)

- [Quantum Neural Networks in Practice: A Comparative Study with Classical Models from Standard Data Sets to Industrial Images](https://mlsanity.com/paper/2411.19276/) (2024)
- [Exploiting the equivalence between quantum neural networks and perceptrons](https://mlsanity.com/paper/2407.04371/) (2024)
- [Model selection in hybrid quantum neural networks with applications to quantum transformer architectures](https://mlsanity.com/paper/2603.21749/) (2026)

## Abstract (arXiv)

One hypothesis for the success of deep neural networks (DNNs) is that they are highly expressive, which enables them to be applied to many problems, and they have a strong inductive bias towards solutions that are simple, known as simplicity bias, which allows them to generalise well on unseen data because most real-world data is structured (i.e. simple). In this work, we explore the inductive bias and expressivity of quantum neural networks (QNNs), which gives us a way to compare their performance to those of DNNs. Our results show that it is possible to have simplicity bias with certain QNNs, but we prove that this type of QNN limits the expressivity of the QNN. We also show that it is possible to have QNNs with high expressivity, but they either have no inductive bias or a poor inductive bias and result in a worse generalisation performance compared to DNNs. We demonstrate that an artificial (restricted) inductive bias can be produced by intentionally restricting the expressivity of a QNN. Our results suggest a bias-expressivity tradeoff. Our conclusion is that the QNNs we studied can not generally offer an advantage over DNNs, because these QNNs either have a poor inductive bias or poor expressivity compared to DNNs.