无序系统与神经网络

We investigate the impact of line-edge roughness on current-driven domain wall dynamics in ferromagnetic racetracks. Modeling the edge disorder as a spatially correlated Ornstein-Uhlenbeck process, we demonstrate that even minimal…

These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…

We study the statistics of rewired random regular graphs (RRGs) in a mixed ensemble, where the average number of triangles is controlled by the fugacity $\lambda$, while the number of vertices and the vertex degree are fixed. This model…

Combinatorial optimization problems are central to both practical applications and the development of optimization methods. While classical and quantum algorithms have been refined over decades, machine learning--assisted approaches are…

We investigate the localization transition of interacting particles in a one-dimensional correlated disorder system. The disorder which we investigate allows for vanishing backwards scattering processes. We derive by two renormalization…

Conventional molecular dynamics (MD) simulation approaches, such as $\textit{ab initio}$ MD (AIMD) and empirical force field MD (EFFMD), face significant trade-offs between physical accuracy and computational efficiency. This work presents…

Associative memory retrieves complete patterns from partial or corrupted inputs and constitutes a primitive form of generative inference. Classical Hopfield networks (CHN) provide a canonical framework for associative memory but suffer from…

Setting the learning rate (LR) for a deep learning model is a critical part of successful training. Choosing LRs is often done empirically with trial and error. In this work, we explore a solvable model of optimal LR schedules for a…

Many-body localized (MBL) systems are known to thermalize in periodically driven systems. In this work, we demonstrate that under proper driving protocol, this thermalization this thermalization can be resisted such that the MBL phase turns…

Models of many-body localization (MBL) exhibit slow numerical drifts towards delocalization with increasing system size, for which no satisfactory theory exists. Numerics indicates that these drifts are driven by the proliferation of…

Deep neural networks owe their expressive power to nonlinear activation functions. The effective field theory of signal propagation at initialization reveals a few distinct universality classes of activations that exhibit different depth…

Topological states of matter in disordered systems without translation symmetry have attracted great interest in recent years. These states with topological characters are not only robust against certain disorders, but also can be…

We derive a novel deterministic equivalence for the two-point function of a random matrix resolvent. Using this result, we give a unified derivation of the performance of a wide variety of high-dimensional linear models trained with…

We study the thermodynamic memory capacity of modern Hopfield networks (Dense Associative Memory models) with continuous states under geometric constraints, extending classical analyses of pairwise associative memory. We derive…

Disordered spatial networks describe structures and interactions across multiple length scales. The scattering and interference of waves within these networks result in structural phase transitions, localization, diffusion, and band gaps.…

Large nonlinear recurrent neural networks with random couplings generate high-dimensional, potentially chaotic activity whose structure is of interest in neuroscience and other fields. A fundamental object encoding the collective structure…

We study the number entropy and quasiparticle width in one-dimensional quasiperiodic many-body localized (MBL) systems and observe slow dynamics that have previously been investigated in detail only in random systems. In contrast,…

The Sachdev-Ye-Kitaev (SYK) model is a disordered quantum mean-field model studied in condensed matter physics and the holographic theory of black holes. Its structural properties can be derived heuristically using a combination of the…

Ultrastable glasses, amorphous solids with exceptionally low-energy states and enhanced kinetic, thermodynamic and mechanical stability, have long been a subject of intense experimental interest. Over the past decade, their computational…

The reservoir computing based on the thin film embedded with magnetic impurities in the presence of the long-range (the dipole-dipole) interaction is numerically investigated. We simulated the magnetization dynamics by taking into account…