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Tree of Memory: A Mathematical Model of Hierarchical Episodic Recall

Creative Commons 'BY' version 4.0 license
Abstract

Understanding free recall requires models that explain not only how many items are retrieved, but also how retrieval is organized—with clustered output, structured transitions, and strong dependence on temporal position. We introduce the Tree of Memory (TOM), in which recall unfolds as a probabilistic search over an explicitly hierarchical episodic representation, coupled with a minimal semantic association structure. The episodic component represents experience across temporal scales encoded in different hierarchical layers. Recall proceeds via probabilistic depth-first traversal of the episodic tree, interleaved with semantic exploration triggered upon item retrieval. The framework admits explicit mathematical characterizations of recall-capacity scaling regimes: depending on the scaling of attention-weighted episodic accessibility, the expected number of recalled items grows sublinearly with list length. In simulations, TOM reproduces canonical free-recall signatures, thereby providing a principled framework to study how hierarchical episodic organization, attention, and semantic associations jointly shape free recall.