# A method for quantifying the generalization capabilities of generative models for solving Ising models

arXiv: https://arxiv.org/abs/2405.03435 · HTML: https://mlsanity.com/paper/2405.03435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 6 May 2024.

## Builds on (most cited first, 15 of 15)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Neural Architecture Search without Training](https://mlsanity.com/paper/2006.04647/) (2020)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [A Survey on Neural Architecture Search](https://mlsanity.com/paper/1905.01392/) (2019)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [On Evaluation Metrics for Graph Generative Models](https://mlsanity.com/paper/2201.09871/) (2022)
- [On the ability of neural nets to express distributions](https://mlsanity.com/paper/1702.07028/) (2017)
- [Do Quantum Circuit Born Machines Generalize?](https://mlsanity.com/paper/2207.13645/) (2022)
- [How Well Do WGANs Estimate the Wasserstein Metric?](https://mlsanity.com/paper/1910.03875/) (2019)
- [Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks](https://mlsanity.com/paper/2105.05650/) (2021)
- [Towards a theory of machine learning](https://mlsanity.com/paper/2004.09280/) (2020)
- [Towards Deepening Graph Neural Networks: A GNTK-based Optimization Perspective](https://mlsanity.com/paper/2103.03113/) (2021)
- [Message Passing Variational Autoregressive Network for Solving Intractable Ising Models](https://mlsanity.com/paper/2404.06225/) (2024)
- [Quasi-orthogonality and intrinsic dimensions as measures of learning and generalisation](https://mlsanity.com/paper/2203.16687/) (2022)

## Abstract (arXiv)

For Ising models with complex energy landscapes, whether the ground state can be found by neural networks depends heavily on the Hamming distance between the training datasets and the ground state. Despite the fact that various recently proposed generative models have shown good performance in solving Ising models, there is no adequate discussion on how to quantify their generalization capabilities. Here we design a Hamming distance regularizer in the framework of a class of generative models, variational autoregressive networks (VAN), to quantify the generalization capabilities of various network architectures combined with VAN. The regularizer can control the size of the overlaps between the ground state and the training datasets generated by networks, which, together with the success rates of finding the ground state, form a quantitative metric to quantify their generalization capabilities. We conduct numerical experiments on several prototypical network architectures combined with VAN, including feed-forward neural networks, recurrent neural networks, and graph neural networks, to quantify their generalization capabilities when solving Ising models. Moreover, considering the fact that the quantification of the generalization capabilities of networks on small-scale problems can be used to predict their relative performance on large-scale problems, our method is of great significance for assisting in the Neural Architecture Search field of searching for the optimal network architectures when solving large-scale Ising models.