Related papers: Yet another exponential Hopfield model
The network embedding task is to represent the node in the network as a low-dimensional vector while incorporating the topological and structural information. Most existing approaches solve this problem by factorizing a proximity matrix,…
A Hopfield network is an auto-associative, distributive model of neural memory storage and retrieval. A form of error-correcting code, the Hopfield network can learn a set of patterns as stable points of the network dynamic, and retrieve…
We discuss how inference can be performed when data are sampled from the non-ergodic phase of systems with multiple attractors. We take as model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method…
Attention heads retrieve: given a query, they return a weighted average of stored values. We showed that this computation is one step of gradient descent on the modern Hopfield energy, and that Langevin sampling from the corresponding…
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…
Recently, Hopfield and Krotov introduced the concept of {\em dense associative memories} [DAM] (close to spin-glasses with $P$-wise interactions in a disordered statistical mechanical jargon): they proved a number of remarkable features…
We studied the computational properties of an attractor neural network (ANN) with different network topologies. Though fully connected neural networks exhibit, in general, a good performance, they are biologically unrealistic, as it is…
The demand for high-density data storage with ultrafast accessibility motivates the search for new memory implementations. Ideally such storage devices should be robust to input error and to unreliability of individual elements; furthermore…
Biologically-inspired computing models have made significant progress in recent years, but the conventional von Neumann architecture is inefficient for the large-scale matrix operations and massive parallelism required by these models. This…
Memory-augmented spiking neural networks (SNNs) promise energy-efficient neuromorphic computing, yet their generalization across sensory modalities remains unexplored. We present the first comprehensive cross-modal ablation study of memory…
Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that…
In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different…
The purpose of this study is to investigate how homophily, memory constraints, and adversarial disruptions collectively shape the resilience and adaptability of complex networks. To achieve this, we develop a new framework that integrates…
We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing…
Auto-associative neural networks (e.g., the Hopfield model implementing the standard Hebbian prescription) serve as a foundational framework for pattern recognition and associative memory in statistical mechanics. However, their…
Motivated by the geometric advantages of quaternions in representing rotations and postures, we propose a quaternion-valued supervised learning Hopfield-structured neural network (QSHNN) with a fully connected structure inspired by the…
Forming accurate memory of sequential stimuli is a fundamental function of biological agents. However, the computational mechanism underlying sequential memory in the brain remains unclear. Inspired by neuroscience theories and recent…
Learning new information without forgetting prior knowledge is central to human intelligence. In contrast, neural network models suffer from catastrophic forgetting: a significant degradation in performance on previously learned tasks when…
Hopfield networks and Boltzmann machines (BMs) are fundamental energy-based neural network models. Recent studies on modern Hopfield networks have broaden the class of energy functions and led to a unified perspective on general Hopfield…
The phenomenon of replica symmetry breaking is investigated for the retrieval phases of Hopfield-type network models. The basic calculation is done for the generalized version of the standard model introduced by Horner [1] and by…