相关论文: Constraints for the order parameters in analogical…

We consider two models of Hopfield-like associative memory with $q$-valued neurons: Potts-glass neural network (PGNN) and parametrical neural network (PNN). In these models neurons can be in more than two different states. The models have…

The common thread behind the recent Nobel Prize in Physics to John Hopfield and those conferred to Giorgio Parisi in 2021 and Philip Anderson in 1977 is disorder. Quoting Philip Anderson: "more is different". This principle has been…

We introduce Graph Hopfield Networks, whose energy function couples associative memory retrieval with graph Laplacian smoothing for node classification. Gradient descent on this joint energy yields an iterative update interleaving Hopfield…

We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free…

Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the…

Despite the recent success of artificial neural networks, more biologically plausible learning methods may be needed to resolve the weaknesses of backpropagation trained models such as catastrophic forgetting and adversarial attacks.…

Macroscopic spin ensembles possess brain-like features such as non-linearity, plasticity, stochasticity, selfoscillations, and memory effects, and therefore offer opportunities for neuromorphic computing by spintronics devices. Here we…

Looking to overcome the limitations of traditional networks, the network science community has lately given much attention to the so-called higher-order networks, where group interactions are modeled alongside pairwise ones. While degree…

We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse…

The aim of this thesis is to compare the capacity of different models of neural networks. We start by analysing the problem solving capacity of a single perceptron using a simple combinatorial argument. After some observations on the…

Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This…

In this short note, we reify the connection between work on the storage capacity problem in wide two-layer treelike neural networks and the rapidly-growing body of literature on kernel limits of wide neural networks. Concretely, we observe…

Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model. On the other hand, associative memories for sparse patterns, such…

The relativistic Hopfield model constitutes a generalization of the standard Hopfield model that is derived by the formal analogy between the statistical-mechanic framework embedding neural networks and the Lagrangian mechanics describing a…

We use the Binary Intrinsic Dimension (BID), a geometrical measure designed for binary data, to analyze the Hopfield model, a paradigmatic spin system from statistical mechanics, machine learning and neuroscience. The BID allows us to…

Graph convolutional neural networks (GCNNs) have become a machine learning workhorse for screening the chemical space of crystalline materials in fields such as catalysis and energy storage, by predicting properties from structures.…

In this work we consider the {\em analog bipartite spin-glass} (or {\em real-valued restricted Boltzmann machine} in a neural network jargon), whose variables (those quenched as well as those dynamical) share standard Gaussian…

We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap $R^{1,2}$…

The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking…

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists…