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Ising machines are a promising non-von-Neumann computational concept forneural network training and combinatorial optimization. However, while variousneural networks can be implemented with Ising machines, their inability toperform fast statistical sampling makes them inefficient for training neuralnetworks compared to digital computers. Here, we introduce a universal conceptto achieve ultrafast statistical sampling with analog Ising machines byinjecting noise. With an opto-electronic Ising machine, we experimentallydemonstrate that this can be used for accurate sampling of Boltzmanndistributions and for unsupervised training of neural networks, with equalaccuracy as software-based training. Through simulations, we find that Isingmachines can perform statistical sampling orders-of-magnitudes faster thansoftware-based methods. This enables the use of Ising machines beyondcombinatorial optimization and makes them into efficient tools for machinelearning and other applications.

Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning