Free recall scaling laws and short-term memory effects in a latching attractor network

The synaptic correlates of serial position effects in sequential working memory

Sequential working memory (SWM), referring to the temporary storage and manipulation of information in order, plays a fundamental role in brain cognitive functions. The serial position effect refers to the phenomena that recall accuracy of an item is associated to the order of the item being presented. The neural mechanism underpinning the serial position effect remains unclear. The synaptic mechanism of working memory proposes that information is stored as hidden states in the form of facilitated neuronal synapse connections. Here, we build a continuous attractor neural network with synaptic short-term plasticity (STP) to explore the neural mechanism of the serial position effect. Using a delay recall task, our model reproduces the the experimental finding that as the maintenance period extends, the serial position effect transitions from the primacy to the recency effect. Using both numerical simulation and theoretical analysis, we show that the transition moment is determined by the parameters of STP and the interval between presented stimulus items. Our results highlight the pivotal role of STP in processing the order information in SWM.

Multistability in neural systems with random cross-connections

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems using a firing rate model framework, in which clusters of similarly responsive neurons are represented as single units, which interact with each other through independent random connections. We explore the range of conditions in which multistability arises via recurrent input from other units while individual units, typically with some degree of self-excitation, lack sufficient self-excitation to become bistable on their own. We find many cases of multistability-defined as the system possessing more than one stable fixed point-in which stable states arise via a network effect, allowing subsets of units to maintain each others' activity because their net input to each other when active is sufficiently positive. In terms of the strength of within-unit self-excitation and standard deviation of random cross-connections, the region of multistability depends on the response function of units. Indeed, multistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the response function rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which produces Zipf's Law when enumerating the proportion of trials within which random initial conditions lead to a particular stable state of the system.

Multistability in neural systems with random cross-connections

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems, using a firing-rate model framework, in which clusters of neurons with net self-excitation are represented as units, which interact with each other through random connections. We focus on conditions in which individual units lack sufficient self-excitation to become bistable on their own. Rather, multistability can arise via recurrent input from other units as a network effect for subsets of units, whose net input to each other when active is sufficiently positive to maintain such activity. In terms of the strength of within-unit self-excitation and standard-deviation of random cross-connections, the region of multistability depends on the firing-rate curve of units. Indeed, bistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the firing-rate curve rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which can appear as Zipf's Law when sampled as the proportion of trials within which random initial conditions lead to a particular stable state of the system.

Mathematical models of learning and what can be learned from them

Learning is a multi-faceted phenomenon of critical importance and hence attracted a great deal of research, both experimental and theoretical. In this review, we will consider some of the paradigmatic examples of learning and discuss the common themes in theoretical learning research, such as levels of modeling and their corresponding relation to experimental observations and mathematical ideas common to different types of learning.