Nearly extensive sequential memory lifetime achieved by coupled nonlinear neurons

Many cognitive processes rely on the ability of the brain to hold sequences of events in short-term memory. Recent studies have revealed that such memory can be read out from the transient dynamics of a network of neurons. However, the memory performance of such a network in buffering past information has only been rigorously estimated in networks of linear neurons. When signal gain is kept low, so that neurons operate primarily in the linear part of their response nonlinearity, the memory lifetime is bounded by the square root of the network size. In this work, I demonstrate that it is possible to achieve a memory lifetime almost proportional to the network size, "an extensive memory lifetime", when the nonlinearity of neurons is appropriately utilized. The analysis of neural activity revealed that nonlinear dynamics prevented the accumulation of noise by partially removing noise in each time step. With this error-correcting mechanism, I demonstrate that a memory lifetime of order $N/\log N$ can be achieved.Comment: 21 pages, 5 figures, the manuscript has been accepted for publication in Neural Computatio

Computational role of sleep in memory reorganization

Sleep is considered to play an essential role in memory reorganization. Despite its importance, classical theoretical models did not focus on some sleep characteristics. Here, we review recent theoretical approaches investigating their roles in learning and discuss the possibility that non-rapid eye movement (NREM) sleep selectively consolidates memory, and rapid eye movement (REM) sleep reorganizes the representations of memories. We first review the possibility that slow waves during NREM sleep contribute to memory selection by using sequential firing patterns and the existence of up and down states. Second, we discuss the role of dreaming during REM sleep in developing neuronal representations. We finally discuss how to develop these points further, emphasizing the connections to experimental neuroscience and machine learning.Comment: Accepted for publication in Current Opinion in Neurobiolog

A Hopfield-like model with complementary encodings of memories

We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within concepts, and the second is sparse and exhibits no correlation among examples. The network stores each memory as a linear combination of its encodings. During retrieval, the network recovers sparse or dense patterns with a high or low activity threshold, respectively. As more memories are stored, the dense representation at low threshold shifts from examples to concepts, which are learned from accumulating common example features. Meanwhile, the sparse representation at high threshold maintains distinctions between examples due to the high capacity of sparse, decorrelated patterns. Thus, a single network can retrieve memories at both example and concept scales and perform heteroassociation between them. We obtain our results by deriving macroscopic mean-field equations that yield capacity formulas for sparse examples, dense examples, and dense concepts. We also perform network simulations that verify our theoretical results and explicitly demonstrate the capabilities of the network.Comment: 34 pages including 21 pages of appendices, 9 figure