# Training deep physical neural networks with local physical information bottleneck

arXiv: https://arxiv.org/abs/2602.09569 · HTML: https://mlsanity.com/paper/2602.09569/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 65 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 27 of 27)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Greedy Layerwise Learning Can Scale to ImageNet](https://mlsanity.com/paper/1812.11446/) (2018)
- [Neuromorphic Silicon Photonic Networks](https://mlsanity.com/paper/1611.02272/) (2016)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Explaining a black-box using Deep Variational Information Bottleneck Approach](https://mlsanity.com/paper/1902.06918/) (2019)
- [The physics of optical computing](https://mlsanity.com/paper/2308.00088/) (2023)
- [Self-learning Machines based on Hamiltonian Echo Backpropagation](https://mlsanity.com/paper/2103.04992/) (2021)
- [Scaling Down Deep Learning with MNIST-1D](https://mlsanity.com/paper/2011.14439/) (2020)
- [From Tokens to Thoughts: How LLMs and Humans Trade Compression for Meaning](https://mlsanity.com/paper/2505.17117/) (2025)
- [Forward-Forward Training of an Optical Neural Network](https://mlsanity.com/paper/2305.19170/) (2023)
- [Silicon Photonic Architecture for Training Deep Neural Networks with Direct Feedback Alignment](https://mlsanity.com/paper/2111.06862/) (2021)
- [Hybrid training of optical neural networks](https://mlsanity.com/paper/2203.11207/) (2022)
- [Trainable and Dynamic Computing: Error Backpropagation through Physical Media](https://mlsanity.com/paper/1407.6637/) (2014)
- [Information decomposition in complex systems via machine learning](https://mlsanity.com/paper/2307.04755/) (2023)
- [LightOn Optical Processing Unit: Scaling-up AI and HPC with a Non von Neumann co-processor](https://mlsanity.com/paper/2107.11814/) (2021)
- [Model-free front-to-end training of a large high performance laser neural network](https://mlsanity.com/paper/2503.16943/) (2025)
- [Harnessing Synthetic Active Particles for Physical Reservoir Computing](https://mlsanity.com/paper/2307.15010/) (2023)
- [Perfecting Imperfect Physical Neural Networks with Transferable Robustness using Sharpness-Aware Training](https://mlsanity.com/paper/2411.12352/) (2024)

## Built on by (most cited first, 1 of 1)

- [Unifying Physical Backpropagation](https://mlsanity.com/paper/2608.11585/) (2026)

## Abstract (arXiv)

Deep learning has revolutionized modern society but faces growing energy and latency constraints. Deep physical neural networks (PNNs) are interconnected computing systems that directly exploit analog dynamics for energy-efficient, ultrafast AI execution. Realizing this potential, however, requires universal training methods tailored to physical intricacies. Here, we present the Physical Information Bottleneck (PIB), a general and efficient framework that integrates information theory and local learning, enabling deep PNNs to learn under arbitrary physical dynamics. By allocating matrix-based information bottlenecks to each unit, we demonstrate supervised, unsupervised, and reinforcement learning across electronic memristive chips and optical computing platforms. PIB also adapts to severe hardware faults and allows for parallel training via geographically distributed resources. Bypassing auxiliary digital models and contrastive measurements, PIB recasts PNN training as an intrinsic, scalable information-theoretic process compatible with diverse physical substrates.