Remembering events in the past is crucial to intelligent behaviour. Flexible memory retrieval, beyond simple recall, requires a model of how events relate to one another. Two key brain systems are implicated in this process: the hippocampal episodic memory (EM) system and the prefrontal working memory (WM) system. While an understanding of the hippocampal system, from computation to algorithm and representation, is emerging, less is understood about how the prefrontal WM system can give rise to flexible computations beyond simple memory retrieval, and even less is understood about how the two systems relate to each other. Here we develop a mathematical theory relating the algorithms and representations of EM and WM by showing a duality between storing memories in synapses versus neural activity. In doing so, we develop a formal theory of the algorithm and representation of prefrontal WM as structured, and controllable, neural subspaces (termed activity slots). By building models using this formalism, we elucidate the differences, similarities, and trade-offs between the hippocampal and prefrontal algorithms. Lastly, we show that several prefrontal representations in tasks ranging from list learning to cue dependent recall are unified as controllable activity slots. Our results unify frontal and temporal representations of memory, and offer a new basis for understanding the prefrontal representation of WM

Neural computations are currently conceptualised using two separate approaches: sorting neurons into functional sub-populations or examining distributed collective dynamics. Whether and how these two aspects interact to shape computations is currently unclear. Using a novel approach to extract computational mechanisms from recurrent networks trained on neuroscience tasks, we show that the collective dynamics and sub-population structure play fundamentally complementary roles. Although various tasks can be implemented in networks with fully random population structure, we found that flexible input–output mappings instead require a non-random population structure that can be described in terms of multiple sub-populations. Our analyses revealed that such a sub-population organisation enables flexible computations through a mechanism based on gain-controlled modulations that flexibly shape the collective dynamics.

Neural computations are currently investigated using two separate approaches: sorting neurons into functional subpopulations or examining the low-dimensional dynamics of collective activity. Whether and how these two aspects interact to shape computations is currently unclear. Using a novel approach to extract computational mechanisms from networks trained on neuroscience tasks, here we show that the dimensionality of the dynamics and subpopulation structure play fundamentally com- plementary roles. Although various tasks can be implemented by increasing the dimensionality in networks with fully random population structure, flexible input–output mappings instead require a non-random population structure that can be described in terms of multiple subpopulations. Our analyses revealed that such a subpopulation structure enables flexible computations through a mechanism based on gain-controlled modulations that flexibly shape the collective dynamics. Our results lead to task-specific predictions for the structure of neural selectivity, for inactivation experiments and for the implication of different neurons in multi-tasking.