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We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…

As NNs permeate various scientific and industrial domains, understanding the universality and reusability of their representations becomes crucial. At their core, these networks create intermediate neural representations, indicated as…

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…

Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…

The Hessian of a neural network captures parameter interactions through second-order derivatives of the loss. It is a fundamental object of study, closely tied to various problems in deep learning, including model design, optimization, and…

Retentive Network (RetNet) represents a significant advancement in neural network architecture, offering an efficient alternative to the Transformer. While Transformers rely on self-attention to model dependencies, they suffer from high…

In recent years, there has been increasing interest in developing models and tools to address the complex patterns of connectivity found in brain tissue. Specifically, this is due to a need to understand how emergent properties emerge from…

We develop of a line of work initiated by Curto and Itskov towards understanding the amount of information contained in the spike trains of hippocampal place cells via topology considerations. Previously, it was established that simply…

Sequential activation of neurons is a common feature of network activity during a variety of behaviors, including working memory and decision making. Previous network models for sequences and memory emphasized specialized architectures in…

The proposed analysis of the currently available experimental results concerning the neural cell activity in the brain area known as hippocampus suggests a particular mechanism of spatial information and memory processing. Below it is…

Biological flow networks adapt their network morphology to optimise flow while being exposed to external stimuli from different spatial locations in their environment. These adaptive flow networks retain a memory of the stimulus location in…

A wide range of networks, including small-world topology, can be modelled by the connectivity $\gamma$, and randomness $\omega$ of the links. Both learning and attractor abilities of a neural network can be measured by the mutual…

Neural processes (NPs) learn stochastic processes and predict the distribution of target output adaptively conditioned on a context set of observed input-output pairs. Furthermore, Attentive Neural Process (ANP) improved the prediction…

In this paper, we present a neural network system related to about memory and recall that consists of one neuron group (the "cue ball") and a one-layer neural net (the "recall net"). This system realizes the bidirectional memorization…

The potential for associative recall of diluted neuronal networks is investigated with respect to several biologically relevant configurations, more specifically the position of the cells along the input space and the spatial distribution…

Robotic and animal mapping systems share many of the same objectives and challenges, but differ in one key aspect: where much of the research in robotic mapping has focused on solving the data association problem, the grid cell neurons…

Recent studies point to the potential storage of a large number of patterns in the celebrated Hopfield associative memory model, well beyond the limits obtained previously. We investigate the properties of new fixed points to discover that…

Countless learning tasks require dealing with sequential data. Image captioning, speech synthesis, and music generation all require that a model produce outputs that are sequences. In other domains, such as time series prediction, video…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

Memory-based neural networks model temporal data by leveraging an ability to remember information for long periods. It is unclear, however, whether they also have an ability to perform complex relational reasoning with the information they…