相关论文: Towards a theory of quantum gravity from neural ne…

We discuss a possibility that the entire universe on its most fundamental level is a neural network. We identify two different types of dynamical degrees of freedom: "trainable" variables (e.g. bias vector or weight matrix) and "hidden"…

We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable…

It was recently shown that the Madelung equations, that is, a hydrodynamic form of the Schr\"odinger equation, can be derived from a canonical ensemble of neural networks where the quantum phase was identified with the free energy of hidden…

When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such…

We discuss a quantum version of an artificial deep neural network where the role of neurons is taken over by qubits and the role of weights is played by unitaries. The role of the non-linear activation function is taken over by subsequently…

This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…

We present a unified geometric framework for modeling learning dynamics in physical, biological, and machine learning systems. The theory reveals three fundamental regimes, each emerging from the power-law relationship $g \propto…

Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…

Neural networks have emerged as a powerful way to approach many practical problems in quantum physics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantum many-body system, where the training is…

We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like…

At its core, Quantum Mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases. Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely…

We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics. By lifting neural parameters to a measure space and modeling training as Wasserstein…

This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…

We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…

In this paper, we study the dynamics of gradient descent in learning neural networks for classification problems. Unlike in existing works, we consider the linearly non-separable case where the training data of different classes lie in…

We demonstrate that the dynamics of neural networks trained with gradient descent and the dynamics of scalar fields in a flat, vacuum energy dominated Universe are structurally profoundly related. This duality provides the framework for…

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In this work, we combine topological deep generative models and…

We propose a neural network framework to preclude the need to define or observe incompletely or inaccurately defined states of a material in order to describe its response. The neural network design is based on the classical Coleman-Gurtin…