Hippocampal networks are believed to be a major center of associative learning due to the central role of the hippocampus in learning and memory, as well as the relatively high levels of recurrent connectivity and synaptic plasticity. The lack of topographic structure in hippocampus has made it a natural inspiration for associative memory models, such as the Hopfield model, for encoding memories in unstructured recurrent networks. At the same time, studies in rodents have uncovered the critical role of hippocampus in spatial navigation and, more recently, time-tracking. In contrast to associative memory encoding, these functions have been successfully modeled using spatially structured networks. How can these viewpoints be reconciled? The central goal of this research is to develop a mathematical theory of memory encoding in spatially structured networks, and to study the neural codes that arise from such networks. Specifically, the research will develop mathematical theory to answer the following questions: (1) How can overlapping memory patterns be encoded precisely as attractors of an unstructured neural network, without introducing unwanted "spurious states"? (2) How can memories be encoded in a spatially structured network, such as a bump attractor network, while maintaining functions that depend on the network's spatial organization? (3) Aside from error correction, what are the advantages of redundancy in a neural code, such as the hippocampal place field code, that is characterized by heavily overlapping receptive fields? This last question will also be explored via the analysis of cortical and hippocampal data sets provided by collaborating labs.
The hippocampus is often thought of as a "Swiss knife" in the brain. Decades of experimental work have uncovered its essential role in learning and memory, as well as in spatial navigation. From a theoretical standpoint, it is puzzling how the same neural network can achieve such disparate functions. In particular, mathematical models of memory encoding are fundamentally quite different from models of spatial navigation. This work will integrate these two major types of neural network models, with the goal of understanding how the hippocampus can support multiple important functions. At its core, the research will advance the mathematical theory behind our understanding of network-level computation in the brain.
