Autonomous and ubiquitous in-node learning algorithms of active directed graphs and its storage behavior

The brain’s memory system is extraordinarily complex, evidenced by the multitude of neurons involved and the intricate electrochemical activities within them, as well as the complex interactions among neurons. Memory research spans various levels, from cellular and molecular to cognitive behavioral studies, each with its own focus, making it challenging to fully describe the memory mechanism. Many details of how biological neuronal networks encode, store, and retrieve information remain unknown. In this study, we model biological neuronal networks as active directed graphs, where each node is self-adaptive and relies on local information for decision-making. To explore how these networks implement memory mechanisms, we propose a parallel distributed information access algorithm based on the node scale of the active directed graph. Here, subgraphs are seen as the physical realization of the information stored in the active directed graph. Unlike traditional algorithms with global perspectives, our algorithm emphasizes global node collaboration in resource utilization through local perspectives. While it may not achieve the global optimum like a global-view algorithm, it offers superior robustness, concurrency, decentralization, and biological feasibility. We also tested network capacity, fault tolerance, and robustness, finding that the algorithm performs better in sparser network structures.Author summary: In this paper, we delve into how biological neuronal networks encode, store, and retrieve information, aiming to model the brain’s memory system and propose practical algorithms for memory characterization and information storage at the algorithmic level. To characterize memory effectively, we must first identify its physical counterpart. We abstract the biological neuron network as an active directed graph, which serves as the framework for memory storage. According to the theory of memory engram and synaptic plasticity, memory is the co-activation of specific neuronal clusters and synaptic sets, which is reflected in the directed graph as the co-activation of specific point sets and edge sets. These activated point sets and edge sets are actually a connected subgraph of the whole active directed graph. Therefore, we propose to consider this connected subgraph as the physical counterpart of memory. We design a parallel distributed access algorithm based on the scale of the directed graph to explore whether this assumption meets the properties of stability, distinguishability, less interference, and incrementalism exhibited by memory. Our approach offers a more biologically realistic network model, focusing on the impact of connections between neurons and structure on memory rather than numerical characterization.