The rise of Artificial Intelligence (AI), driven by developments of deep learning and machine learning, has profoundly pervaded our society. However, the ever-growing demand of computing power, associated with huge energy consumption and high environmental impact, is unsustainable with current digital computing technologies. In the race toward future computing technologies, bio-inspired systems based on self-organizing memristive networks represents promising unconventional computing hardware platforms for emulating information processing capabilities of our brain [1-3]. However, the relationship between dynamics of these physical complex systems and their information processing capabilities represents a challenge.

In this framework, we have demonstrated that neuromorphic nanowire networks can be described as stochastic dynamical systems, where stimuli-dependent deterministic trajectories and stochastic effects can be holistically described by an Ornstein-Uhlenbeck process. Through a combined experimental and modelling approach, we showed that this unified modelling framework can describe main features of network dynamics including noise and jumps, and enable to correlate dynamics of these physical complex systems with their computational properties.

Figure 1a reports an image of the self-organizing nanowire network while Figure 1b-d reports examples of network dynamics in terms of the evolution of the conductance time trace as a function of time under voltage stimulation. As can be observed, network dynamics are characterized by deterministic trajectories and stochastic effects including noise and jumps. These effects can be holistically described through a unified mathematical framework as an Ornstein-Uhlenbeck process with noise and jumps, as can be observed in Figure 2 where an example of experimental and modeled time trace is compared.

This unified modeling approach allows to investigate the impact of deterministic and stochastic effects on computing, in the framework of the physical reservoir computing paradigm implemented through a time multiplexing scheme. Figure 3a reports an example of network prediction of the NARMA-2 benchmark task obtained by modeling the network as a stochastic dynamical system, while Figure 3b reports the prediction accuracy for different operating regimes in terms of bias voltage and input amplitude. The modeling approach enable not only to evaluate the best operational regime of the network, but also to disentangle the effect of deterministic and stochastic dynamics on computing capabilities.

We envision that these results can shed new light on the development of physical computing paradigms that takes into advantage of deterministic and stochastic dynamics on the same physical substrate, similarly to our brain.

The full paper can be found at https://www.nature.com/articles/s41467-025-58741-2. Codes exploited in this work are available on GitHub at https://github.com/MilanoGianluca/Self-organizing_neuromorphic_networks_as_stochastic_dynamical_systems), the code release is available on Zenodo (https://doi.org/10.5281/zenodo.15174744), and data of the work are available on Zenodo (https://doi.org/10.5281/zenodo.15050217).

References

[1] Milano, Gianluca, et al. "In materia reservoir computing with a fully memristive architecture based on self-organizing nanowire networks." Nature materials 21.2 (2022): 195-202.

[2] Milano, Gianluca, et al. "Tomography of memory engrams in self-organizing nanowire connectomes." Nature Communications14.1 (2023): 5723.

[3] Milano, Gianluca, et al. "Brain‐inspired structural plasticity through reweighting and rewiring in multi‐terminal self‐organizing memristive nanowire networks." Advanced Intelligent Systems2.8 (2020): 2000096.