# Self-Organising Memristive Networks as Physical Learning Systems

arXiv: https://arxiv.org/abs/2509.00747 · HTML: https://mlsanity.com/paper/2509.00747/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 186 references that are in the map.
- First posted on arXiv 31 Aug 2025.

## Builds on (most cited first, 20 of 20)

- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Edge Intelligence: Paving the Last Mile of Artificial Intelligence with Edge Computing](https://mlsanity.com/paper/1905.10083/) (2019)
- [Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing its Gradient Estimator Bias](https://mlsanity.com/paper/2006.03824/) (2020)
- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Brain-inspired learning in artificial neural networks: a review](https://mlsanity.com/paper/2305.11252/) (2023)
- [The physics of brain network structure, function, and control](https://mlsanity.com/paper/1809.06441/) (2018)
- [Memristors -- from In-memory computing, Deep Learning Acceleration, Spiking Neural Networks, to the Future of Neuromorphic and Bio-inspired Computing](https://mlsanity.com/paper/2004.14942/) (2020)
- [The hardware is the software](https://mlsanity.com/paper/2310.18335/) (2023)
- [Memristor models for machine learning](https://mlsanity.com/paper/1406.2210/) (2014)
- [25 years of criticality in neuroscience -- established results, open controversies, novel concepts](https://mlsanity.com/paper/1903.05129/) (2019)
- [The Computational Capacity of LRC, Memristive and Hybrid Reservoirs](https://mlsanity.com/paper/2009.00112/) (2020)
- [Training-free AI for Earth Observation Change Detection using Physics Aware Neuromorphic Networks](https://mlsanity.com/paper/2506.04285/) (2025)
- [Memristive Linear Algebra](https://mlsanity.com/paper/2407.20539/) (2024)
- [Uncontrolled learning: co-design of neuromorphic hardware topology for neuromorphic algorithms](https://mlsanity.com/paper/2408.05183/) (2024)
- [Dynamic Reservoir Computing with Physical Neuromorphic Networks](https://mlsanity.com/paper/2505.16813/) (2025)
- [Global minimization via classical tunneling assisted by collective force field formation](https://mlsanity.com/paper/2102.03385/) (2021)
- [A unifying approach to self-organizing systems interacting via conservation laws](https://mlsanity.com/paper/2507.02575/) (2025)
- [Learning Chaotic Dynamics with Neuromorphic Network Dynamics](https://mlsanity.com/paper/2506.10773/) (2025)

## Built on by (most cited first, 2 of 2)

- [How to Train Your Resistive Network: Generalized Equilibrium Propagation and Analytical Learning](https://mlsanity.com/paper/2602.03546/) (2026)
- [Thermal Anomaly Detection using Physics Aware Neuromorphic Networks: Comparison between Raw and L1C Sentinel-2 Data](https://mlsanity.com/paper/2604.18606/) (2026)

## Abstract (arXiv)

Learning with physical systems is an emerging paradigm that seeks to harness the intrinsic nonlinear dynamics of physical substrates for learning. The impetus for a paradigm shift in how hardware is used for computational intelligence stems largely from the unsustainability of artificial neural network software implemented on conventional transistor-based hardware. This Perspective highlights one promising approach using physical networks comprised of resistive memory nanoscale components with dynamically reconfigurable, self-organising electrical circuitry. Experimental advances have revealed the non-trivial interactions within these Self-Organising Memristive Networks (SOMNs), offering insights into their collective nonlinear and adaptive dynamics, and how these properties can be harnessed for learning using different hardware implementations. Theoretical approaches, including mean-field theory, graph theory, and concepts from disordered systems, reveal deeper insights into the dynamics of SOMNs, especially during transitions between different conductance states where criticality and other dynamical phase transitions emerge in both experiments and models. Furthermore, parallels between adaptive dynamics in SOMNs and plasticity in biological neuronal networks suggest the potential for realising energy-efficient, brain-like continual learning. SOMNs thus offer a promising route toward embedded edge intelligence, unlocking real-time decision-making for autonomous systems, dynamic sensing, and personalised healthcare, by embedding continuous learning in resource-constrained environments. The overarching aim of this Perspective is to show how the convergence of nanotechnology, statistical physics, complex systems, and self-organising principles offers a unique opportunity to advance a new generation of physical intelligence technologies.