Related papers: Lattice physics approaches for neural networks
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of…
Network science provides a universal framework for modeling complex systems, contrasting the reductionist approach generally adopted in physics. In a prototypical study, we utilize network models created from spectroscopic data of atoms to…
Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…
Activity in neocortex exhibits a range of behaviors, from irregular to temporally precise, and from weakly to strongly correlated. So far there has been no single theoretical framework that could explain all these behaviors, leaving open…
Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems, and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only…
We present a new exact renormalization approach for quantum lattice models leading to long-range interactions. The renormalization scheme is based on wavelets with an infinite support in such a way that the excitation spectrum at the fixed…
Technological advances have dramatically expanded our ability to probe multi-neuronal dynamics and connectivity in the brain. However, our ability to extract a simple conceptual understanding from complex data is increasingly hampered by…
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…
We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two…
Understanding how decision making changes across the lifespan is a central challenge for neuroscience, yet research on cognitive aging has remained largely disconnected from the theoretical and computational advances that now shape modern…
We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
This essay, derived from a lecture at "The Physics Modeling of Thought" workshop in Berlin in winter 2023, explores the mutually beneficial relationship between theoretical neuroscience and statistical physics through the lens of efficient…
It has long been known that photonic science and especially photonic communications can raise the speed of technologies and producing manufacturing. More recently, photonic science has also been interested in its capabilities to implement…
Artificial and natural neural network models are a new toolkit which could be potentially have been used for clarifying of complex brain functions. To attend this goal, such models need to be neurobiologically realistic. However, although…
Connecting neural activity to function is a common aim in neuroscience. How to define and conceptualize function, however, can vary. Here I focus on grounding this goal in the specific question of how a given change in behavior is produced…
Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…