# Training single-electron and single-photon stochastic physical neural networks

arXiv: https://arxiv.org/abs/2604.10861 · HTML: https://mlsanity.com/paper/2604.10861/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Builds on (most cited first, 14 of 14)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [An optical neural network using less than 1 photon per multiplication](https://mlsanity.com/paper/2104.13467/) (2021)
- [Estimator Meets Equilibrium Perspective: A Rectified Straight Through Estimator for Binary Neural Networks Training](https://mlsanity.com/paper/2308.06689/) (2023)
- [Dual adaptive training of photonic neural networks](https://mlsanity.com/paper/2212.06141/) (2022)
- [Asymmetrical estimator for training encapsulated deep photonic neural networks](https://mlsanity.com/paper/2405.18458/) (2024)

## Abstract (arXiv)

The computational demands of deep learning motivate the investigation of alternative approaches to computation. One alternative is physical neural networks~(PNNs), in which learning and inference are performed directly via physical processes. Stochastic PNNs arise when the underlying neurons are realized by the dynamics of a stochastic activation switch. Here we propose novel electronic and photonic stochastic neurons. The electronic realization is implemented by single-electron tunneling through a quantum dot. The photonic realization is implemented via a single-photon source driving one of two modes coupled via a controllable beam-splitter-like interaction. In the electronic case, the charge state of the quantum dot forms the basis for the stochastic neuron, whereas in the photonic case the occupation of the undriven mode serves as the basis for the stochastic neuron. Training of stochastic PNNs is performed with models of stochastic neurons, as well as with coherently-driven, single-photon detector stochastic neurons previously introduced. Several training strategies for MNIST handwritten digit classification have been investigated using single-hidden-layer stochastic PNNs, including varying the number of trials in each layer to control forward pass stochasticity and employing either true probability or empirical outputs in the backward pass to evaluate their influence on gradient estimation. We show that when empirical outputs are used in the backward pass, the network achieves more than 97% test accuracy with few trials per layer. Despite the simplicity of the model architecture, high test accuracy is maintained in the presence of a high degree of noise and model uncertainty. The results demonstrate the potential of embracing stochastic PNNs for deep learning.