相关论文: Dimensional Criticality at Grokking Across MLPs an…

We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in Random Boolean…

Graph Neural Networks (GNNs) are susceptible to distribution shifts, creating vulnerability and security issues in critical domains. There is a pressing need to enhance the generalizability of GNNs on out-of-distribution (OOD) test data.…

The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram which includes a coupling mu to the order of the vertices. Monte Carlo renormalization group and…

Gradient descent dynamics in complex energy landscapes, i.e. featuring multiple minima, finds application in many different problems, from soft matter to machine learning. Here, we analyze one of the simplest examples, namely that of soft…

One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…

Deep learning has been demonstrated with tremendous success in recent years. Despite so, its performance in practice often degenerates drastically when encountering out-of-distribution (OoD) data, i.e. training and test data are sampled…

Odd diffusion breaks time-reversal symmetry in overdamped systems through transverse probability currents while preserving equilibrium steady states. In this work, we develop a dynamical density functional theory (DDFT) for dense…

Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural…

Non-thermal dynamical critical behavior can arise in isolated quantum systems brought out of equilibirum by a change in time of their parameters. While this phenomenon has been studied in a variety of systems in the case of a sudden quench,…

Deep learning is widely applied in computer-aided pathological diagnosis, which alleviates the pathologist workload and provide timely clinical analysis. However, most models generally require large-scale annotated data for training, which…

We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime. We prove limit theorems for the trajectories of summary statistics (i.e., finite-dimensional functions) of SGD as the…

These lecture notes provide an overview of the renormalization group (RG) as a successful framework to understand critical phenomena above the upper critical dimension $d_{\rm uc}$. After an introduction to the scaling picture of continuous…

The superconducting transition is studied within the one-loop renormalization group in fixed dimension $D=3$ and at the critical point. A tricritical behavior is found, and for $\kappa > \kappa_c$, an attractive charged fixed point,…

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To…

We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase.…

Jamming transition is traditionally regarded as a geometric transition governed by static contact networks. Recently, dynamic phase transitions of athermal particles under periodic shearing provide a new lens on this problem, leading to a…

We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…

We present Link Density (LD) computed from the Recurrence Network (RN) of a time series data as an effective measure that can detect dynamical transitions in a system. We illustrate its use using time series from the standard Rossler system…

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to…