相关论文: Dimensional Criticality at Grokking Across MLPs an…
Graph Neural Networks (GNNs) conventionally rely on standard Laplacian or adjacency matrices for structural message passing. In this work, we substitute the traditional Laplacian with a Doubly Stochastic graph Matrix (DSM), derived from the…
A critical vulnerability of supervised deep learning in high-dimensional tabular domains is "generalization collapse": models form precise decision boundaries around known training distributions but fail catastrophically when encountering…
A random growth lattice filling model of percolation with touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty sites and…
We study the well-known grokking phenomena in neural networks (NNs) using a 3-layer MLP trained on 1 k-sample subset of MNIST, with and without weight decay, and discover a novel third phase -- \emph{anti-grokking} -- that occurs very late…
Graph Neural Network (GNN) has demonstrated extraordinary performance in classifying graph properties. However, due to the selection bias of training and testing data (e.g., training on small graphs and testing on large graphs, or training…
We study non-interacting systems with a power-law quasiparticle dispersion $\xi_{\bf k}\propto k^\alpha$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2\alpha$ there exists a…
We study dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads. We use an influence functional for quantum Nyquist noise to describe the crossover for the dephasing time $\Tph (T)$…
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity.…
We propose that learning in deep neural networks proceeds in two phases: a rapid curve fitting phase followed by a slower compression or coarse graining phase. This view is supported by the shared temporal structure of three phenomena:…
Unsupervised anomaly detection of multivariate time series is a challenging task, given the requirements of deriving a compact detection criterion without accessing the anomaly points. The existing methods are mainly based on reconstruction…
Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent…
We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized…
Nearly magnetic metals often have layered lattice structures, consisting of coupled planes. In such a situation, physical properties will display, upon decreasing temperature or energy, a dimensional crossover from two-dimensional (2d) to…
We implement an efficient strong-disorder renormalization-group (SDRG) procedure to study disordered tight-binding models in any dimension and on the Erdos-Renyi random graphs, which represent an appropriate infinite dimensional limit. Our…
Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…
If a system undergoing phase transitions exhibits some characteristics of both first and second order, it is said to be of 'mixed order' or to display the Thouless effect. Such a transition is present in a simple model of a dynamic social…
Estimating a fractal dimension from a finite stochastic trajectory is a finite-size scaling problem: the apparent box-counting exponent is shaped by an occupancy crossover between the resolved range of scales and the finite number of…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate…
We use high-dimensional bosonization to derive an effective field theory that describes the Pomeranchuck transition in isotropic two-dimensional Fermi liquids. We find that the transition is triggered by the softening of an eigenmode that…