The storage capacity of a directed graph and nodewise autonomous, ubiquitous learning.

The brain, an exceedingly intricate information processing system, poses a constant challenge to memory research, particularly in comprehending how it encodes, stores, and retrieves information. Cognitive psychology studies memory mechanism from behavioral experiment level and fMRI level, and neurobiology studies memory mechanism from anatomy and electrophysiology level. Current research findings are insufficient to provide a comprehensive, detailed explanation of memory processes within the brain. Numerous unknown details must be addressed to establish a complete information processing mechanism connecting micro molecular cellular levels with macro cognitive behavioral levels. Key issues include characterizing and distributing content within biological neural networks, coexisting information with varying content, and sharing limited resources and storage capacity. Compared with the hard disk of computer mass storage, it is very clear from the polarity of magnetic particles in the bottom layer, the division of tracks and sectors in the middle layer, to the directory tree and file management system in the high layer, but the understanding of memory is not sufficient. Biological neural networks are abstracted as directed graphs, and the encoding, storage, and retrieval of information within directed graphs at the cellular level are explored. A memory computational model based on active directed graphs and node-adaptive learning is proposed. First, based on neuronal local perspectives, autonomous initiative, limited resource competition, and other neurobiological characteristics, a resource-based adaptive learning algorithm for directed graph nodes is designed. To minimize resource consumption of memory content in directed graphs, two resource-occupancy optimization strategies-lateral inhibition and path pruning-are proposed. Second, this paper introduces a novel memory mechanism grounded in graph theory, which considers connected subgraphs as the physical manifestation of memory content in directed graphs. The encoding, storage, consolidation, and retrieval of the brain's memory system correspond to specific operations such as forming subgraphs, accommodating multiple subgraphs, strengthening connections and connectivity of subgraphs, and activating subgraphs. Lastly, a series of experiments were designed to simulate cognitive processes and evaluate the performance of the directed graph model. Experimental results reveal that the proposed adaptive connectivity learning algorithm for directed graphs in this paper possesses the following four features: (1) Demonstrating distributed, self-organizing, and self-adaptive properties, the algorithm achieves global-level functions through local node interactions; (2) Enabling incremental storage and supporting continuous learning capabilities; (3) Displaying stable memory performance, it surpasses the Hopfield network in memory accuracy, capacity, and diversity, as demonstrated in experimental comparisons. Moreover, it maintains high memory performance with large-scale datasets; (4) Exhibiting a degree of generalization ability, the algorithm's macroscopic performance remains unaffected by the topological structure of the directed graph. Large-scale, decentralized, and node-autonomous directed graphs are suitable simulation methods. Examining storage problems within directed graphs can reveal the essence of phenomena and uncover fundamental storage rules hidden within complex neuronal mechanisms, such as synaptic plasticity, ion channels, neurotransmitters, and electrochemical activities.