# The effect of the number of parameters and the number of local feature patches on loss landscapes in distributed quantum neural networks

arXiv: https://arxiv.org/abs/2504.19239 · HTML: https://mlsanity.com/paper/2504.19239/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 27 Apr 2025.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [Bridging Mode Connectivity in Loss Landscapes and Adversarial Robustness](https://mlsanity.com/paper/2005.00060/) (2020)
- [Position Information in Transformers: An Overview](https://mlsanity.com/paper/2102.11090/) (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)
- [Exponentially Many Local Minima in Quantum Neural Networks](https://mlsanity.com/paper/2110.02479/) (2021)
- [High Dimensional Quantum Machine Learning With Small Quantum Computers](https://mlsanity.com/paper/2203.13739/) (2022)
- [An Invitation to Distributed Quantum Neural Networks](https://mlsanity.com/paper/2211.07056/) (2022)
- [Distributed Quantum Neural Networks via Partitioned Features Encoding](https://mlsanity.com/paper/2312.13650/) (2023)

## Abstract (arXiv)

Quantum neural networks hold promise for tackling computationally challenging tasks that are intractable for classical computers. However, their practical application is hindered by significant optimization challenges, arising from complex loss landscapes characterized by barren plateaus and numerous local minima. These problems become more severe as the number of parameters or qubits increases, hampering effective training. To mitigate these optimization challenges, particularly for classical data, we distribute overlapping local patches across multiple quantum neural networks, processing each patch with an independent quantum neural network, and aggregating their outputs for prediction. In this study, we investigate how the number of parameters and patches affects the loss landscape geometry of this distributed quantum neural network architecture via theoretical and empirical Hessian analyses and loss landscape visualization. Our results confirm that increasing the number of parameters tends to lead to deeper and sharper loss landscapes. Crucially, we theoretically derive and empirically demonstrate that increasing the number of patches significantly reduces the largest Hessian eigenvalue at minima. Furthermore, our analysis of the full Hessian eigenspectrum reveals a structure consisting of a bulk of near-zero eigenvalues and distinct outlier spikes corresponding to the number of classes, similar to classical deep learning models. These findings suggest that our distributed patch approach acts as a form of implicit structural regularization, promoting optimization stability and potentially enhancing generalization. Our study provides valuable insights into optimization challenges and highlights that the distributed patch approach is a promising strategy for developing more trainable and scalable quantum machine learning models for classical data tasks.