Related papers: Dynamic Manifold Hopfield Networks for Context-Dep…
By embedding physical intuition, network architectures enforce fundamental properties, such as energy conservation laws, leading to plausible predictions. Yet, scaling these models to intrinsically high-dimensional systems remains a…
Traditional predictive coding networks, inspired by theories of brain function, consistently achieve promising results across various domains, extending their influence into the field of computer vision. However, the performance of the…
Well characterized sequences of dynamical states play an important role for motor control and associative neural computation in the brain. Autonomous dynamics involving sequences of transiently stable states have been termed associative…
Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…
Associative memory architectures such as the Hopfield network have long been important conceptual and theoretical models for neuroscience and artificial intelligence. However, translating these abstract models into spiking neural networks…
Understanding natural symmetries is key to making sense of our complex and ever-changing world. Recent work has shown that neural networks can learn such symmetries directly from data using Hamiltonian Neural Networks (HNNs). But HNNs…
Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks.…
Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
In this paper, we explore the dynamics of structured complex-valued Hopfield neural networks (CvHNNs), which arise when the synaptic weight matrix possesses specific structural properties. We begin by analyzing CvHNNs with a Hermitian…
Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…
A large number of studies have shown the existence of metabolic covalent modifications in different molecular structures, able to store biochemical information that is not encoded by the DNA. Some of these covalent mark patterns can be…
Associative Memories like the famous Hopfield Networks are elegant models for describing fully recurrent neural networks whose fundamental job is to store and retrieve information. In the past few years they experienced a surge of interest…
The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…
Current deep neural networks (DNNs) used in materials modeling often lack explicit physical structure and clear analytical formulations tailored to material systems, which can limit their interpretability. In this work, we integrate…
We propose an algorithm grounded in dynamical systems theory that generalizes manifold learning from a global state representation, to a network of local interacting manifolds termed a Generative Manifold Network (GMN). Manifolds are…
In this research paper novel real/complex valued recurrent Hopfield Neural Network (RHNN) is proposed. The method of synthesizing the energy landscape of such a network and the experimental investigation of dynamics of Recurrent Hopfield…