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Exploring the Interpretability of Quantum Neural Networks by Mutual Information

Xin Zhang, Xiaoyu Li, Chenguang Zhang +1 more

Jan 1, 20250 citations

Two-stage behavior of mutual information in quantum neural networks

Xin Zhang, Xiaoyu Li, Zhaoyang Dong +1 more

Physics Letters AOct 30, 20252 citations

Neural Network Renormalization Group

Shuo-Hui Li, Lei Wang

We present a variational renormalization group (RG) approach based on a reversible generative model with hierarchical architecture. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural network directly maps independent Gaussian noises to physical configurations following the inverse RG flow. The model has an exact and tractable likelihood, which allows unbiased training and direct access to the renormalized energy function of the latent variables. To train the model, we employ probability density distillation for the bare energy function of the physical problem, in which the training loss provides a variational upper bound of the physical free energy. We demonstrate practical usage of the approach by identifying mutually independent collective variables of the Ising model and performing accelerated hybrid Monte Carlo sampling in the latent space. Lastly, we comment on the connection of the present approach to the wavelet formulation of RG and the modern pursuit of information preserving RG.We present a variational renormalization group (RG) approach based on a reversible generative model with hierarchical architecture. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural network directly maps independent Gaussian noises to physical configurations following the inverse RG flow. The model has an exact and tractable likelihood, which allows unbiased training and direct access to the renormalized energy function of the latent variables. To train the model, we employ probability density distillation for the bare energy function of the physical problem, in which the training loss provides a variational upper bound of the physical free energy. We demonstrate practical usage of the approach by identifying mutually independent collective variables of the Ising model and performing accelerated hybrid Monte Carlo sampling in the latent space. Lastly, we comment on the connection of the present approach to the wavelet formulation of RG and the modern pursuit of information preserving RG.

arXiv:1802.02840Physical Review LettersDec 26, 2018140 citations

Information theory and renormalization group flows

Sergey M. Apenko

arXiv:0910.2097Physica A Statistical Mechanics and its ApplicationsAug 28, 201128 citations

Renormalization Group: Applications in Statistical Physics

Uwe Claus Täuber

arXiv:1112.1375Nuclear Physics B - Proceedings SupplementsJul 1, 201226 citations

Application of deep neural networks for computing the renormalization group flow of the two-dimensional ϕ 4 field theory

Yueqi Zhao, M. M. Fogler, Yi‐Zhuang You

Abstract We introduce RGFlow, a deep neural network–based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns real-space RG transformations from data without prior knowledge of the underlying model. In contrast to conventional approaches, RGFlow is bijective (information-preserving) and is optimized based on the principle of minimal mutual information. We demonstrate the method on two examples. The first one is a one-dimensional Gaussian model, where RGFlow is shown to learn the classical decimation rule. The second is the two-dimensional φ 4 theory, where the network successfully identifies a Wilson–Fisher-like critical point and provides an estimate of the correlation-length critical exponent.Abstract We introduce RGFlow, a deep neural network–based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns real-space RG transformations from data without prior knowledge of the underlying model. In contrast to conventional approaches, RGFlow is bijective (information-preserving) and is optimized based on the principle of minimal mutual information. We demonstrate the method on two examples. The first one is a one-dimensional Gaussian model, where RGFlow is shown to learn the classical decimation rule. The second is the two-dimensional φ 4 theory, where the network successfully identifies a Wilson–Fisher-like critical point and provides an estimate of the correlation-length critical exponent.

arXiv:2510.06508Machine Learning Science and TechnologyFeb 23, 20260 citations

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