Related papers: Information and Topology in Attractor Neural Netwo…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

We study the effect of varying wiring in excitable random networks in which connection weights change with activity to mold local resistance or facilitation due to fatigue. Dynamic attractors, corresponding to patterns of activity, are then…

Networks offer a powerful approach to modeling complex systems by representing the underlying set of pairwise interactions. Link prediction is the task that predicts links of a network that are not directly visible, with profound…

We draw upon a previously largely untapped literature on human collective intelligence as a source of inspiration for improving deep learning. Implicit in many algorithms that attempt to solve Deep Reinforcement Learning (DRL) tasks is the…

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…

A prevalent assumption regarding real-world data is that it lies on or close to a low-dimensional manifold. When deploying a neural network on data manifolds, the required size, i.e., the number of neurons of the network, heavily depends on…

We define bipartite and monopartite relational networks of chemical elements and compounds using two different datasets of inorganic chemical and material compounds, as well as study their topology. We discover that the connectivity between…

In recent years, graph theory has been widely employed to probe several language properties. More specifically, the so-called word adjacency model has been proven useful for tackling several practical problems, especially those relying on…

The richness in the content of various information networks such as social networks and communication networks provides the unprecedented potential for learning high-quality expressive representations without external supervision. This…

The analysis of complex systems such as neural networks is made particularly difficult by the overwhelming number of their interacting components. In the absence of prior knowledge, identifying a small but informative subset of network…

Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

We consider a finite structured population of mobile individuals that strategically explore a network using a Markov movement model and interact with each other via a public goods game. We extend the model of Erovenko et al. (2019) from…

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…

The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…

We consider neural networks (NNs) where the final layer is down-scaled by a fixed hyperparameter $\gamma$. Recent work has identified $\gamma$ as controlling the strength of feature learning. As $\gamma$ increases, network evolution changes…

Neuro-symbolic reasoning systems face fundamental challenges in maintaining semantic coherence while satisfying physical and logical constraints. Building upon our previous work on Ontology Neural Networks, we present an enhanced framework…

Many recent methods for unsupervised or self-supervised representation learning train feature extractors by maximizing an estimate of the mutual information (MI) between different views of the data. This comes with several immediate…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…

We study a model of spiking neurons, with recurrent connections that result from learning a set of spatio-temporal patterns with a spike-timing dependent plasticity rule and a global inhibition. We investigate the ability of the network to…