Memory Consolidation: Neural Data Analysis and Mathematical Modeling

Memory is crucial for our cognitive abilities such as perception and decision making. Understanding how the brain learns and remembers is, therefore, one of the most important problems of neuroscience. It has been suggested that consolidation of memory occurs in part during sleep. This memory function of sleep has been supported by experiments showing that behaviorally induced neural activity reactivates during sleep, a phenomenon called memory reactivation or memory replay. In the first half of this chapter, we will review how the brain’s electrical signals are used to identify the different stages of sleep, how memory is categorized into different types, and what data analysis techniques have been used to investigate memory consolidation during sleep. In the second half of the chapter, we will turn to mathematical modeling of the brain. While neural data analysis is the primary tool to investigate memory consolidation, mathematical modeling provides further insights into the mechanisms of memory consolidation. After a brief review of an approach that aims at modeling the detailed properties of a neuron, we will devote our discussion to another approach that focuses on an emergent property of neural networks. Combining the energy function in physics and Hebbian synapses in neuroscience, we will see that memory can be understood as the local minima of the energy and that the learning procedure generates both waking and sleep phases of neural networks. The chapter will be concluded by a discussion of the future directions of neural data analysis and mathematical modeling in memory consolidation study.