Related papers: Dimensional Criticality at Grokking Across MLPs an…
One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…
Anderson localization is fundamentally controlled by dimensionality, yet the nature of the Anderson transition in continuously tunable noninteger dimensions remains largely unexplored. Here, we introduce a family of three-dimensional…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
We use the recently developed typical medium dynamical cluster (TMDCA) approach~[Ekuma \etal,~\textit{Phys. Rev. B \textbf{89}, 081107 (2014)}] to perform a detailed study of the Anderson localization transition in three dimensions for the…
Cross-domain shifts present a significant challenge for decision transformer (DT) policies. Existing cross-domain policy adaptation methods typically rely on a single simple filtering criterion to select source trajectory fragments and…
Joint clustering and feature learning methods have shown remarkable performance in unsupervised representation learning. However, the training schedule alternating between feature clustering and network parameters update leads to unstable…
Deep learning has been immensely successful at a variety of tasks, ranging from classification to AI. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understanding…
Graphs are a fundamental data structure for representing relational information in domains such as social networks, molecular systems, and knowledge graphs. However, graph learning models often suffer from limited generalization when…
Grokking in modular arithmetic has established itself as the quintessential fruit fly experiment, serving as a critical domain for investigating the mechanistic origins of model generalization. Despite its significance, existing research…
We study the dynamics of gradient flow with small weight decay on general training losses $F: \mathbb{R}^d \to \mathbb{R}$. Under mild regularity assumptions and assuming convergence of the unregularised gradient flow, we show that the…
We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…
Using classical density functional theory (DFT) in a modified mean-field approximation we investigate the fluid phase behavior of quasi-two dimensional dipolar fluids confined to a plane. The particles carry three-dimensional dipole moments…
The presence of nearby conformal field theories (CFTs) hidden in the complex plane of the tuning parameter was recently proposed as an elegant explanation for the ubiquity of "weakly first-order" transitions in condensed matter and…
We study the slow quenching dynamics (characterized by an inverse rate, $\tau^{-1}$) of a one-dimensional transverse Ising chain with nearest neighbor ferromagentic interactions across the quantum critical point (QCP) and analyze the…
We explore the dynamics of a tracer in an active particle harmonic chain, investigating the influence of interactions. Our analysis involves calculating mean-squared displacements (MSD) and space-time correlations through Green's function…
Transformer-based models have achieved remarkable success across a wide range of domains, yet our understanding of their training dynamics remains limited. In this work, we identify a recurrent focus-dilution cycle in attention learning and…
We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these…
Deep learning (DL) methods have emerged as a powerful tool for the inversion of geophysical data. When applied to field data, these models often struggle without additional fine-tuning of the network. This is because they are built on the…
The phenomenon of upper critical dimensionality d_c2 has been studied from the viewpoint of the scaling concepts. The Thouless number g(L) is not the only essential variable in scale transformations, because there is the second parameter…