Related papers: Liquid Hopfield model: retrieval and localization …

Liquid mixtures can separate into phases with distinct composition. This phenomenon has recently come back to prominence due to its role in complex biological liquids, such as the cytoplasm, which contain thousands of components. For simple…

We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging…

The central question that we address is: How can structured information be stored in a hierarchical Hopfield model involving hidden layers? To this end, we develop a formalism of strokes and concepts that allows us to appropriately…

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…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which…

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…

Reasoning is the ability to integrate internal states and external inputs in a meaningful and semantically consistent flow. Contemporary machine learning (ML) systems increasingly rely on such sequential reasoning, from language…

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…

Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological,…

When a simple or complex liquid recedes from a smooth solid substrate it often leaves a homogeneous or structured deposit behind. In the case of a receding non-volatile pure liquid the deposit might be a liquid film or an arrangement of…

In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a…

We consider $L$-directional associative memories, composed of $L$ Hopfield networks, displaying imitative Hebbian intra-network interactions and anti-imitative Hebbian inter-network interactions, where couplings are built over a set of…

We propose a model describing liquid-solid phase coexistence in mixed lipid membranes by including explicitly the occurrence of a rippled phase. For a single component membrane, we employ a previous model in which the membrane thickness is…

Hydration of hydrophobic solutes in water is the cause of different phenomena, including the hydrophobic heat-capacity anomaly, which are not yet fully understood. Because of its topicality, there has recently been growing interest in the…

Structuring latent representations in a hierarchical manner enables models to learn patterns at multiple levels of abstraction. However, most prevalent image understanding models focus on visual similarity, and learning visual hierarchies…

In this paper, we explore the interplay between topological structures and phase retrieval in the context of projective Hilbert spaces. This work provides not only a deeper understanding and a new classification of the phase retrieval…

Living organisms rely on molecular networks, such as gene circuits and signaling pathways, for information processing and robust decision-making in crowded, noisy environments. Recent advances show that interacting biomolecules…

By solving the Young Laplace equation of capillary hydrostatics one can accurately determine equilibrium shapes of droplets on relatively smooth solid surfaces. The solution, however of the Young Laplace equation becomes tricky when a…

Chemical reactions and biological processes are often governed by the structure and transport dynamics of the interface between two liquid phases. Despite their importance, our microscopic understanding of liquid-liquid interfaces has been…