Related papers: Categorical Hopfield Networks
In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…
We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…
The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…
Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…
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…
In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel…
This paper aims to solve a distributed resource allocation problem with binary local constraints. The problem is formulated as a binary program with a cost function defined by the summation of agent costs plus a global mismatch/penalty…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
Neural population activity in cortical and hippocampal circuits can be flexibly reorganized by context, suggesting that cognition relies on dynamic manifolds rather than static representations. However, how such dynamic organization can be…
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…
Recent works have highlighted the need for a new dynamical paradigm in the modeling of brain function and evolution. Specifically, these models should incorporate non-constant and asymmetric synaptic weights $T_{ij}$ in the neuron-neuron…
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…
Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
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…
I aim to show that models, classification or generating functions, invariances and datasets are algorithmically equivalent concepts once properly defined, and provide some concrete examples of them. I then show that a) neural networks (NNs)…
We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not…
While Hopfield networks are known as paradigmatic models for memory storage and retrieval, modern artificial intelligence systems mainly stand on the machine learning paradigm. We show that it is possible to formulate a teacher-student…
Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…