The Context Maintenance and Retrieval (CMR) model, developed by Sean Polyn, Kenneth Norman, and Michael Kahana (2009), is an extension of the Temporal Context Model (TCM) that incorporates multiple sources of contextual information and a competitive accumulator retrieval mechanism. CMR provides a detailed account of the rich dynamics of free recall, including temporal clustering, semantic clustering, and source clustering.
Multi-Source Context
While TCM represents context primarily as a temporal signal, CMR extends the context vector to include multiple sub-regions representing different types of contextual information: temporal context (when the item was studied), source context (e.g., which task was performed during encoding), and semantic context (pre-experimental associations). The full context vector is a concatenation of these sub-regions:
Each sub-region evolves according to the same drift equation as in TCM, but with potentially different drift rates. Source context changes when the encoding task switches (e.g., from a size judgment to a pleasantness judgment), creating a contextual boundary that affects recall organization.
Semantic Associations
CMR incorporates pre-existing semantic associations through a pre-experimental weight matrix M^FT_pre that is added to the experimentally learned associations. When an item is recalled, it reinstates not only its temporal context but also the semantic context associated with it, biasing subsequent recalls toward semantically related items. This produces the semantic clustering effect: the tendency for semantically related items to be recalled together, even if they were studied in different positions.
Competitive Accumulator Retrieval
Unlike TCM, which uses a simple activation-based retrieval rule, CMR implements retrieval as a competitive leaky accumulator race. Each item in memory has an accumulator that gathers evidence at a rate proportional to its activation (determined by the match between the current context and the item's stored context). The first accumulator to reach a threshold is recalled. An additional accumulator represents the "stopping" option, which terminates recall when it wins the race:
where κ scales the input strength, λ is a leak (decay) rate, and γ is lateral inhibition between accumulators. This retrieval mechanism produces realistic inter-retrieval time distributions and naturally accounts for the acceleration of inter-retrieval times that precedes recall termination.
Empirical Predictions and Fits
CMR simultaneously fits multiple aspects of free recall data: the serial position curve, the probability of first recall as a function of position, the lag-recency function (conditional response probability as a function of temporal lag), semantic clustering scores, and source clustering scores. Polyn et al. (2009) demonstrated that the model captures the joint effects of temporal, semantic, and source information on recall dynamics, providing a more complete account than any single-mechanism model. Later extensions (CMR2, Lohnas et al., 2015) added mechanisms for recall of items from prior lists and for the dynamics of memory search across multiple lists.
The progression from TCM to CMR to CMR2 illustrates the productive cycle of model development in mathematical psychology. Each model preserves the core mechanisms of its predecessor while adding principled extensions to account for new empirical phenomena. CMR2 further extended the framework to account for prior-list intrusions and the dynamics of multi-list free recall, demonstrating the scalability of the temporal context approach.