mlsanityData to 7 Oct 2026

Training Deep Boltzmann Networks with Sparse Ising Machines

arXiv 2303.10728 ↗First posted 19 Mar 2023cs.ET cs.LG cs.NEcited by 23

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Abstract (arXiv)

The slowing down of Moore's law has driven the development of unconventional computing paradigms, such as specialized Ising machines tailored to solve combinatorial optimization problems. In this paper, we show a new application domain for probabilistic bit (p-bit) based Ising machines by training deep generative AI models with them. Using sparse, asynchronous, and massively parallel Ising machines we train deep Boltzmann networks in a hybrid probabilistic-classical computing setup. We use the full MNIST and Fashion MNIST (FMNIST) dataset without any downsampling and a reduced version of CIFAR-10 dataset in hardware-aware network topologies implemented in moderately sized Field Programmable Gate Arrays (FPGA). For MNIST, our machine using only 4,264 nodes (p-bits) and about 30,000 parameters achieves the same classification accuracy (90%) as an optimized software-based restricted Boltzmann Machine (RBM) with approximately 3.25 million parameters. Similar results follow for FMNIST and CIFAR-10. Additionally, the sparse deep Boltzmann network can generate new handwritten digits and fashion products, a task the 3.25 million parameter RBM fails at despite achieving the same accuracy. Our hybrid computer takes a measured 50 to 64 billion probabilistic flips per second, which is at least an order of magnitude faster than superficially similar Graphics and Tensor Processing Unit (GPU/TPU) based implementations. The massively parallel architecture can comfortably perform the contrastive divergence algorithm (CD-n) with up to n = 10 million sweeps per update, beyond the capabilities of existing software implementations. These results demonstrate the potential of using Ising machines for traditionally hard-to-train deep generative Boltzmann networks, with further possible improvement in nanodevice-based realizations.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 20 of its 82 references that are in the map. First posted on arXiv 19 Mar 2023.

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20 of 82 references.

References · 20

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  3. 2021Carbon Emissions and Large Neural Network Trainingcited by 561
  4. 2016Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagationcited by 251
  5. 2015Application of Quantum Annealing to Training of Deep Neural Networkscited by 37
  6. 2022Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learningcited by 26
  7. 2021Massively Parallel Probabilistic Computing with Sparse Ising Machinescited by 24
  8. 2020Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Qcited by 18
  9. 2022Gaussian-Bernoulli RBMs Without Tearscited by 17
  10. 2023Thermodynamic AI and the fluctuation frontiercited by 15
  11. 2023A full-stack view of probabilistic computing with p-bits: devices, architectures and algorithmscited by 13
  12. 2018Scrambled Linear Pseudorandom Number Generatorscited by 12
8 more
  1. 2021Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learningcited by 11
  2. 2022Efficient Optimization with Higher-Order Ising Machinescited by 10
  3. 2019High Performance Monte Carlo Simulation of Ising Model on TPU Clusterscited by 7
  4. 2020A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learningcited by 7
  5. 2016Sparsely-Connected Neural Networks: Towards Efficient VLSI Implementation of Deep Neural Networkscited by 6
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  7. 2013Joint Training Deep Boltzmann Machines for Classificationcited by 2
  8. 2016Deep Restricted Boltzmann Networkscited by 1

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Citing papers per year: 2023: 5; 2024: 2; 2025: 11; 2026: 5.

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  1. 2024Training of Physical Neural Networkscited by 47
  2. 2023Training an Ising Machine with Equilibrium Propagationcited by 29
  3. 2023CMOS + stochastic nanomagnets: heterogeneous computers for probabilistic inference and learningcited by 10
  4. 2025An efficient probabilistic hardware architecture for diffusion-like modelscited by 8
  5. 2023Training Multi-layer Neural Networks on Ising Machinecited by 3
  6. 2025Learning at the Speed of Physics: Equilibrium Propagation on Oscillator Ising Machinescited by 3
  7. 2025Local Learning Rules for Out-of-Equilibrium Physical Generative Modelscited by 2
  8. 2025Formalized Hopfield Networks and Boltzmann Machinescited by 2
  9. 2026Generative Models on Analog Hardware with Dynamicscited by 2
  10. 2023Machine Learning Quantum Systems with Magnetic p-bitscited by 1
  11. 2025Probabilistic Quantum SVM Training on Ising Machinecited by 1
  12. 2025Nonlocal Monte Carlo via Reinforcement Learningcited by 1
11 more
  1. 2026From Independent to Correlated Diffusion: Generalized Generative Modeling with Probabilistic Computerscited by 1
  2. 2026A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computingcited by 1
  3. 2023Improved Sparse Ising Optimizationcited by 0
  4. 2024Mean-Field Assisted Deep Boltzmann Learning with Probabilistic Computerscited by 0
  5. 2025Bayesian Reasoning Enabled by Spin-Orbit Torque Magnetic Tunnel Junctionscited by 0
  6. 2025Efficient Optimization Accelerator Framework for Multistate Ising Problemscited by 0
  7. 2025Quantum Boltzmann Machines using Parallel Annealing for Medical Image Classificationcited by 0
  8. 2025Photonic restricted Boltzmann machine for content generation taskscited by 0
  9. 2025Probabilistic Computers for Neural Quantum Statescited by 0
  10. 2026Optimizing Energy-based Neural Network Training with Coherent Ising Machinecited by 0
  11. 2026Scaling Up Thermodynamic AI Modelscited by 0