Free recall is a standard memory task in which a subject is presented with a sequence of items and, after presentation, asked to retrieve as many as possible in any order. Understanding free recall is not only a question of retrieval capacity, but also of retrieval structure: recalled items appear in clusters, transitions are highly non-random, and retrieval depends strongly on temporal position. We introduce the Tree of Memory (TOM), a computational model in which memory is represented by a hierarchical episodic data structure (episodic tree) augmented with a sparse semantic graph. Experience is organized across multiple temporal scales in different levels of the hierarchy, and recall is modeled as a probabilistic search process over this representation. Specifically, retrieval proceeds through a stochastic depth-first traversal of the episodic tree, interleaved with local exploration of semantic edges whenever an item is reached.
We characterize distinct asymptotic recall regimes and show that the expected number of retrieved items grows logarithmically or as a sublinear power law, depending on how the probability of traversing deeper levels of the memory hierarchy scales with list length. We also study how the same memory representation supports different retrieval algorithms. This allows us to ask how changes in search strategy and auxiliary structure affect recall efficiency. One variant introduces additional semantic links that guide retrieval through a learned sequence, yielding linear recall in list length with high probability. Another uses a small set of pointers to recently formed subtrees, enabling efficient retrieval of entire temporal chunks. These variants highlight explicit trade-offs between recall performance, representation complexity, scalability, and auxiliary memory. Simulations further show that TOM reproduces canonical empirical signatures of free recall. Together, these results suggest that hierarchical representations and probabilistic graph search provide a compact computational framework for understanding both spontaneous and strategy-driven memory retrieval.