In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and computational model of learning and memory based on a small set of bio-plausible functions that include coincidence detection, signal modulation, and reward/penalty mechanisms. Our theoretical approach proposes that these basic functions are sufficient to establish and modulate an information space over which computation can be carried out, generating signal gradients usable for inference and behavior. The computational method used to test this is a structurally dynamic cellular automaton with continuous-valued cell states and a series of recursive steps propagating over an undirected graph with the memory function embedded entirely in the creation and modulation of graph edges. The experimental results show: that the toy model can make near-optimal choices to re-discover a reward state after a single training run; that it can avoid complex penalty configurations; that signal modulation and network plasticity can generate exploratory behaviors in sparse reward environments; that the model generates context-dependent memory representations; and that it exhibits high computational efficiency because of its minimal, single-pass training requirements combined with flexible and contextual memory representation.
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