Message Passing Variational Autoregressive Network for Solving Intractable Ising Models

• URL: http://arxiv.org/abs/2404.06225v1
• Date: Tue, 9 Apr 2024 11:27:07 GMT
• Title: Message Passing Variational Autoregressive Network for Solving Intractable Ising Models
• Authors: Qunlong Ma, Zhi Ma, Jinlong Xu, Hairui Zhang, Ming Gao,
• Abstract summary: Many deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Here we propose a variational autoregressive architecture with a message passing mechanism, which can effectively utilize the interactions between spin variables. The new network trained under an annealing framework outperforms existing methods in solving several prototypical Ising spin Hamiltonians, especially for larger spin systems at low temperatures.
• Score: 6.261096199903392
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Learning a probability distribution of energy configuration or finding the ground states of a disordered, fully connected Ising model is essential for statistical mechanics and NP-hard problems. Despite tremendous efforts, a neural network architecture with the ability to high-accurately solve these fully connected and extremely intractable problems on larger systems is still lacking. Here we propose a variational autoregressive architecture with a message passing mechanism, which can effectively utilize the interactions between spin variables. The new network trained under an annealing framework outperforms existing methods in solving several prototypical Ising spin Hamiltonians, especially for larger spin systems at low temperatures. The advantages also come from the great mitigation of mode collapse during the training process of deep neural networks. Considering these extremely difficult problems to be solved, our method extends the current computational limits of unsupervised neural networks to solve combinatorial optimization problems.

Related papers

• Graph Neural Networks for Learning Equivariant Representations of Neural Networks [55.04145324152541]
  We propose to represent neural networks as computational graphs of parameters. Our approach enables a single model to encode neural computational graphs with diverse architectures. We showcase the effectiveness of our method on a wide range of tasks, including classification and editing of implicit neural representations.
  arXiv  Detail & Related papers  (2024-03-18T18:01:01Z)
• A hybrid approach for solving the gravitational N-body problem with Artificial Neural Networks [0.0]
  We study the use of Artificial Neural Networks (ANNs) to replace expensive parts of the integration of planetary systems. We compare the results of the numerical integration of a planetary system with asteroids with those obtained by a Hamiltonian Neural Network and a conventional Deep Neural Network.
  arXiv  Detail & Related papers  (2023-10-31T12:20:20Z)
• Addressing caveats of neural persistence with deep graph persistence [54.424983583720675]
  We find that the variance of network weights and spatial concentration of large weights are the main factors that impact neural persistence. We propose an extension of the filtration underlying neural persistence to the whole neural network instead of single layers. This yields our deep graph persistence measure, which implicitly incorporates persistent paths through the network and alleviates variance-related issues.
  arXiv  Detail & Related papers  (2023-07-20T13:34:11Z)
• Rational Neural Network Controllers [0.0]
  Recent work has demonstrated the effectiveness of neural networks in control systems (known as neural feedback loops) One of the big challenges of this approach is that neural networks have been shown to be sensitive to adversarial attacks. This paper considers rational neural networks and presents novel rational activation functions, which can be used effectively in robustness problems for neural feedback loops.
  arXiv  Detail & Related papers  (2023-07-12T16:35:41Z)
• How neural networks learn to classify chaotic time series [77.34726150561087]
  We study the inner workings of neural networks trained to classify regular-versus-chaotic time series. We find that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models.
  arXiv  Detail & Related papers  (2023-06-04T08:53:27Z)
• Spiking neural network for nonlinear regression [68.8204255655161]
  Spiking neural networks carry the potential for a massive reduction in memory and energy consumption. They introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. A framework for regression using spiking neural networks is proposed.
  arXiv  Detail & Related papers  (2022-10-06T13:04:45Z)
• Consistency of Neural Networks with Regularization [0.0]
  This paper proposes the general framework of neural networks with regularization and prove its consistency. Two types of activation functions: hyperbolic function(Tanh) and rectified linear unit(ReLU) have been taken into consideration.
  arXiv  Detail & Related papers  (2022-06-22T23:33:39Z)
• Building Compact and Robust Deep Neural Networks with Toeplitz Matrices [93.05076144491146]
  This thesis focuses on the problem of training neural networks which are compact, easy to train, reliable and robust to adversarial examples. We leverage the properties of structured matrices from the Toeplitz family to build compact and secure neural networks.
  arXiv  Detail & Related papers  (2021-09-02T13:58:12Z)
• Creating Powerful and Interpretable Models withRegression Networks [2.2049183478692584]
  We propose a novel architecture, Regression Networks, which combines the power of neural networks with the understandability of regression analysis. We demonstrate that the models exceed the state-of-the-art performance of interpretable models on several benchmark datasets.
  arXiv  Detail & Related papers  (2021-07-30T03:37:00Z)
• Firefly Neural Architecture Descent: a General Approach for Growing Neural Networks [50.684661759340145]
  Firefly neural architecture descent is a general framework for progressively and dynamically growing neural networks. We show that firefly descent can flexibly grow networks both wider and deeper, and can be applied to learn accurate but resource-efficient neural architectures. In particular, it learns networks that are smaller in size but have higher average accuracy than those learned by the state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-02-17T04:47:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.