Related papers: Low-resolution descriptions of model neural activi…
This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is…
Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…
Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but…
A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this…
We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…
Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…
Dense Associative Memories or Modern Hopfield Networks have many appealing properties of associative memory. They can do pattern completion, store a large number of memories, and can be described using a recurrent neural network with a…
To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most…
Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…
It is common to use networks to encode the architecture of interactions between entities in complex systems in the physical, biological, social, and information sciences. To study the large-scale behavior of complex systems, it is useful to…
Units of complex systems -- such as neurons in the brain or individuals in societies -- must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas…
Content-addressable memories such as Modern Hopfield Networks (MHN) have been studied as mathematical models of auto-association and storage/retrieval in the human declarative memory, yet their practical use for large-scale content storage…
Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between…