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

Deep learning has achieved tremendous success with independent and identically distributed (i.i.d.) data. However, the performance of neural networks often degenerates drastically when encountering out-of-distribution (OoD) data, i.e., when…

We study biased random walkers on lattices with randomly dispersed static traps in one, two and three dimensions. As the external bias is increased from zero the system undergoes a phase transition, most clearly manifested in the asymptotic…

Using Brownian Dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order, (in the infinite chain…

The dynamical percolation transition of two dimensional Axial Next Nearest Neighbour Ising (ANNNI) model to pulsed magnetic field has been studied by finite size scaling analysis (by Monte Carlo simulation) for various values of frustration…

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network…

One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too…

Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…

Extensive numerical simulations in the past decades proved that the critical exponents of the jamming of frictionless spherical particles remain unchanged in two and three dimensions. This implies that the upper critical dimension is…

The grokking phenomenon as reported by Power et al. ( arXiv:2201.02177 ) refers to a regime where a long period of overfitting is followed by a seemingly sudden transition to perfect generalization. In this paper, we attempt to reveal the…

Lightning, the most colossal discharge in nature, and flux avalanches in quantum superconductors--phenomena separated by twenty orders of magnitude in scale--display striking fractal similarity. We demonstrate that this is no mere analogy…

We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neural networks (DNNs). DNNs show remarkable generalization…

Grokking describes a delayed generalization phenomenon in which a neural network achieves perfect training accuracy long before validation accuracy improves, followed by an abrupt transition to strong generalization. Existing detection…

The full parameter space of the transition from Townsend to glow discharge is investigated numerically in one space dimension in the classical model: with electrons and positive ions drifting in the local electric field, impact ionization…

We investigate the static critical behaviour of a uniaxial magnetic layer, with finite thickness L in one direction, yet infinitely extended in the remaining d dimensions. The magnetic dipole-dipole interaction is taken into account. We…

Deep learning on graphs has shown remarkable success across numerous applications, including social networks, bio-physics, traffic networks, and recommendation systems. Regardless of their successes, current methods frequently depend on the…

We study dimensionally restricted non-perturbative causal set quantum dynamics in $2$ and $3$ spacetime dimensions with non-trivial global spatial topology. The causal set sample space is generated from causal embeddings into spacetime…

Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on…

We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in…

Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of…

We demonstrate that conventional artificial deep neural networks operating near the phase boundary of the signal propagation dynamics, also known as the edge of chaos, exhibit universal scaling laws of absorbing phase transitions in…