Slow manifolds within network dynamics encode working memory efficiently and robustly

Heterogeneous Forgetting Rates and Greedy Allocation in Slot-Based Memory Networks Promotes Signal Retention

A key question in the neuroscience of memory encoding pertains to the mechanisms by which afferent stimuli are allocated within memory networks. This issue is especially pronounced in the domain of working memory, where capacity is finite. Presumably the brain must embed some "policy" by which to allocate these mnemonic resources in an online manner in order to maximally represent and store afferent information for as long as possible and without interference from subsequent stimuli. Here, we engage this question through a top-down theoretical modeling framework. We formally optimize a gating mechanism that projects afferent stimuli onto a finite number of memory slots within a recurrent network architecture. In the absence of external input, the activity in each slot attenuates over time (i.e., a process of gradual forgetting). It turns out that the optimal gating policy consists of a direct projection from sensory activity to memory slots, alongside an activity-dependent lateral inhibition. Interestingly, allocating resources myopically (greedily with respect to the current stimulus) leads to efficient utilization of slots over time. In other words, later-arriving stimuli are distributed across slots in such a way that the network state is minimally shifted and so prior signals are minimally "overwritten." Further, networks with heterogeneity in the timescales of their forgetting rates retain stimuli better than those that are more homogeneous. Our results suggest how online, recurrent networks working on temporally localized objectives without high-level supervision can nonetheless implement efficient allocation of memory resources over time.

Hamiltonian energy in a modified Hindmarsh-Rose model

This paper investigates the Hamiltonian energy of a modified Hindmarsh-Rose (HR) model to observe its effect on short-term memory. A Hamiltonian energy function and its variable function are given in the reduced system with a single node according to Helmholtz's theorem. We consider the role of the coupling strength and the links between neurons in the pattern formation to show that the coupling and cooperative neurons are necessary for generating the fire or a clear short-term memory when all the neurons are in sync. Then, we consider the effect of the degree and external stimulus from other neurons on the emergence and disappearance of short-term memory, which illustrates that generating short-term memory requires much energy, and the coupling strength could further reduce energy consumption. Finally, the dynamical mechanisms of the generation of short-term memory are concluded.

Multiplexing working memory and time in the trajectories of neural networks

Working memory (WM) and timing are generally considered distinct cognitive functions, but similar neural signatures have been implicated in both. To explore the hypothesis that WM and timing may rely on shared neural mechanisms, we used psychophysical tasks that contained either task-irrelevant timing or WM components. In both cases, the task-irrelevant component influenced performance. We then developed recurrent neural network (RNN) simulations that revealed that cue-specific neural sequences, which multiplexed WM and time, emerged as the dominant regime that captured the behavioural findings. During training, RNN dynamics transitioned from low-dimensional ramps to high-dimensional neural sequences, and depending on task requirements, steady-state or ramping activity was also observed. Analysis of RNN structure revealed that neural sequences relied primarily on inhibitory connections, and could survive the deletion of all excitatory-to-excitatory connections. Our results indicate that in some instances WM is encoded in time-varying neural activity because of the importance of predicting when WM will be used.

Synthesizing network dynamics for short-term memory of impulsive inputs

Illuminating the mechanisms that the brain uses to manage and coordinate its resources is a core question in neuroscience. In particular, circuits and networks in the brain are able to encode, store and recall large amounts of information, in the service of a wide range of functionality. How do the various dynamical mechanisms within these networks allow for such coordination? We consider the specific problem of how the dynamics of networks can enact a representation of input stimuli that is retained over time, i.e., a form of short-term memory. We utilize modeling and control-theoretic methods to approach these questions, treating the state trajectory of a dynamical system as an abstract memory trace of prior inputs. The inputs impinge on the network via a variable gain, which is to be synthesized by optimization. In order to perpetuate these memory traces of stimuli, we propose that this gain is adapted to optimize: i) the error between a ground truth representation of stimuli and the encoding of them; as well as ii) overwriting of prior information. Optimizing over these central tenets of memory, we obtain a 'policy' for adapting the input gain that is dependent on the state of the network. This derived policy yields a recurrent neural network between the policy and the neural circuits, affirming existing theories that the prefrontal cortex may hold subnetworks dedicated to working memory while actively engaging with other neural subnetworks.

Oscillatory Resonance and Dynamic Manifolds in Cortical Networks with Time Delay and Multiple External Stimuli

Rhythmic oscillation is crucial for information transmission and neural communication among different brain areas. Stochastic resonance (SR) can evoke different patterns of neural oscillation. However, the characteristics of network resonance and underlying dynamical mechanisms are still unclear. In this paper, a biological model of cortical network is established and its dynamical response to external periodic stimulation is investigated. We explore the oscillatory resonance of excitatory and inhibitory populations in cortical network. It is found that the intrinsic parameters of neural populations determine the extent of resonant activity, indicating that the firing rate exhibits coherent oscillation when the frequency of external stimulation is close to intrinsic frequency of neural population. In addition, the nonlinear dynamics of cortical network in oscillatory resonance can be represented by helical manifolds in low-dimensional state space. The geometry of neural manifolds reveals the periodic dynamics and state transition in oscillatory resonance. Moreover, time delay in chemical synapses can induce multiple resonances, which appear intermittently at integer multiples of the period of input signal. The dynamical response of neural population achieves maximal periodically, due to the transition of network states induced by time delay. Furthermore, mean-field theory is applied to analyze theoretical dynamic of cortical networks with time delay and demonstrate the effective transmission of stimulation information via oscillatory resonance in the brain. Consequently, the obtained results contribute to the improvement of neuromodulation for neurological disease from the viewpoint of the neural basis.