  Recent research has provided a wealth of evidence highlighting the pivotal
role of high-order interdependencies in supporting the information-processing
capabilities of distributed complex systems. These findings may suggest that
high-order interdependencies constitute a powerful resource that is, however,
challenging to harness and can be readily disrupted. In this paper we contest
this perspective by demonstrating that high-order interdependencies can not
only exhibit robustness to stochastic perturbations, but can in fact be
enhanced by them. Using elementary cellular automata as a general testbed, our
results unveil the capacity of dynamical noise to enhance the statistical
regularities between agents and, intriguingly, even alter the prevailing
character of their interdependencies. Furthermore, our results show that these
effects are related to the high-order structure of the local rules, which
affect the system's susceptibility to noise and characteristic times-scales.
These results deepen our understanding of how high-order interdependencies may
spontaneously emerge within distributed systems interacting with stochastic
environments, thus providing an initial step towards elucidating their origin
and function in complex systems like the human brain.
