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Cortical circuits exhibit intricate recurrent architectures that are remarkably similar across different brain areas. Such stereotyped structure suggests the existence of common computational principles. However, such principles have…
Many cognitive models, including those for predicting the time of future events, can be mapped onto a particular form of neural representation in which activity across a population of neurons is restricted to manifolds that specify the…
The high motility of synaptic weights raises the question of how the brain can retain its functionality in the face of constant synaptic remodeling. Here we used the whisker system of rats and mice to study the interplay between synaptic…
Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions…
Throughout the literature on Neural Cellular Automata (NCAs), it is often taken for granted that the systems learn attractors. This is shown through evolving the system for many timesteps and noting visual similarity to the goal state.…
The activation/repression of a given gene is typically regulated by multiple transcription factors (TFs) that bind at the gene regulatory region and recruit RNA polymerase (RNAP). The interactions between the promoter region and TFs and…
Neuronal activity is found to lie on low-dimensional manifolds embedded within the high-dimensional neuron space. Variants of principal component analysis are frequently employed to assess these manifolds. These methods are, however,…
Continuous attractor networks (CANs) are a well-established class of models for representing low-dimensional continuous variables such as head direction, spatial position, and phase. In canonical spatial domains, transitions along the…
We present introductory considerations and analysis toward computing applications based on the recently introduced deterministic logic scheme with random spike (pulse) trains [Phys. Lett. A 373 (2009) 2338-2342]. Also, in considering the…
Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
Short-term synaptic plasticity (STSP) affects the efficiency of synaptic transmission for persistent presynaptic activities. We consider attractor neural networks, for which the attractors are given, in the absence of STSP, by cell…
The human brain is autonomously active. To understand the functional role of this self-sustained neural activity, and its interplay with the sensory data input stream, is an important question in cognitive system research and we review here…
Many cognitive processes, including working memory, recruit multiple distributed interacting brain regions to encode information. How to understand the underlying cognition function mechanism of working memory is a challenging problem,…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
Animals survive in dynamic environments changing at arbitrary timescales, but such data distribution shifts are a challenge to neural networks. To adapt to change, neural systems may change a large number of parameters, which is a slow…
How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been…
Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit…
Gating mechanisms are widely used in neural network models, where they allow gradients to backpropagate more easily through depth or time. However, their saturation property introduces problems of its own. For example, in recurrent models…
Multiplicative gating is widely used in neural architectures and has recently been applied to attention layers to improve performance and training stability in large language models. Despite the success of gated attention, the mathematical…