Related papers: Capacity of an associative memory model on random …

We study the relation between the growth rate of a graph property and the entropy of the graph limits that arise from graphs with that property. In particular, for hereditary classes we obtain a new description of the colouring number,…

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

Graph neural networks (GNNs) have been extensively studied for prediction tasks on graphs. As pointed out by recent studies, most GNNs assume local homophily, i.e., strong similarities in local neighborhoods. This assumption however limits…

Two potential bottlenecks on the expressiveness of recurrent neural networks (RNNs) are their ability to store information about the task in their parameters, and to store information about the input history in their units. We show…

We consider events over the probability space generated by the degree sequences of multiple independent Erd\H{o}s-R\'enyi random graphs, and consider an approximation probability space where such degree sequences are deemed to be sequences…

We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…

A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield…

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…

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…

An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns…

We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…

The weight space of an artificial neural network can be systematically explored using tools from statistical mechanics. We employ a combination of a hybrid Monte Carlo algorithm which performs long exploration steps, a ratchet-based…

Designing neural network architectures is a task that lies somewhere between science and art. For a given task, some architectures are eventually preferred over others, based on a mix of intuition, experience, experimentation and luck. For…

In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…

Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…

Graph serves as a powerful tool for modeling data that has an underlying structure in non-Euclidean space, by encoding relations as edges and entities as nodes. Despite developments in learning from graph-structured data over the years, one…

We study the storage of multiple phase-coded patterns as stable dynamical attractors in recurrent neural networks with sparse connectivity. To determine the synaptic strength of existent connections and store the phase-coded patterns, we…

Generating graph structures is a challenging problem due to the diverse representations and complex dependencies among nodes. In this paper, we introduce Graph Variational Recurrent Neural Network (GraphVRNN), a probabilistic autoregressive…

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…

Human learners are adept at grasping the complex relationships underlying incoming sequential input. In the present work, we formalize complex relationships as graph structures derived from temporal associations in motor sequences. Next, we…