• Corpus ID: 218502627

Complex Amplitude-Phase Boltzmann Machines

@article{Li2020ComplexAB,
  title={Complex Amplitude-Phase Boltzmann Machines},
  author={Zengyi Li and Friedrich T. Sommer},
  journal={ArXiv},
  year={2020},
  volume={abs/2005.01862}
}
We extend the framework of Boltzmann machines to a network of complex-valued neurons with variable amplitudes, referred to as Complex Amplitude-Phase Boltzmann machine (CAP-BM). The model is capable of performing unsupervised learning on the amplitude and relative phase distribution in complex data. The sampling rule of the Gibbs distribution and the learning rules of the model are presented. Learning in a Complex Amplitude-Phase restricted Boltzmann machine (CAP-RBM) is demonstrated on… 

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References

SHOWING 1-10 OF 14 REFERENCES
Complex-Valued Restricted Boltzmann Machine for Direct Learning of Frequency Spectra
TLDR
A new energy-based probabilistic model where a restricted Boltzmann machine (RBM) is extended to deal with complex-valued visible units and it is demonstrated that the proposed CRBM can directly encode complex spectra of speech signals without decoupling imaginary number or phase from the complex-value data.
Lending direction to neural networks
Robust computation with rhythmic spike patterns
TLDR
The link established between rhythmic firing patterns and complex attractor dynamics has implications for the interpretation of spike patterns seen in neuroscience and can serve as a framework for computation in emerging neuromorphic devices.
Complex-Valued Deep Boltzmann Machines
  • C. Popa
  • Computer Science
    2018 International Joint Conference on Neural Networks (IJCNN)
  • 2018
TLDR
This paper presents the full deduction of the learning algorithm for DBMs with values in the complex domain, both in terms of average log-probability and classification error for the deep neural network models initialized using complex-valued DBMs.
A Learning Algorithm for Boltzmann Machines
Deep Complex Networks
TLDR
This work relies on complex convolutions and present algorithms for complex batch-normalization, complex weight initialization strategies for complex-valued neural nets and uses them in experiments with end-to-end training schemes and demonstrates that such complex- valued models are competitive with their real-valued counterparts.
Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network
We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a
On Complex Valued Convolutional Neural Networks
TLDR
A variation of the CNN model with complex valued input and weights is presented, and it is demonstrated that the complex model is significantly less vulnerable to overfitting and detects meaningful phase structure in the data.
Training restricted Boltzmann machines using approximations to the likelihood gradient
TLDR
A new algorithm for training Restricted Boltzmann Machines is introduced, which is compared to some standard Contrastive Divergence and Pseudo-Likelihood algorithms on the tasks of modeling and classifying various types of data.
A Practical Guide to Training Restricted Boltzmann Machines
TLDR
This guide is an attempt to share expertise at training restricted Boltzmann machines with other machine learning researchers.
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