无序系统与神经网络

The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…

We study a minimal model of disordered systems, the random field Ising model (RFIM) on a generalized Petersen Graph, GP(N,k). This graph has a connected inner and outer loop, where both the loops consist of N nodes constituting a total of…

We identify fundamental limitations in machine learning by demonstrating that non-trivial mixed-state phases of matter are computationally hard to learn. Focusing on unsupervised learning of distributions, we show that autoregressive neural…

Transformer architectures are typically described in algorithmic and statistical terms, leaving their internal mechanics without a familiar structural language for researchers trained in physical theories. To bridge this gap, we develop a…

Performing machine learning with analog signals offers advantages in speed and energy efficiency, but sensitivity to component and measurement imperfections often foils training without a system-specific companion digital model. Here we…

We explore interpretations of the power-law banded random matrix (PLBRM) ensemble as Hamiltonians of one-dimensional quantum many-body systems. We introduce and compare a number of labeling schemes for assigning random matrix basis indices…

Sampling the parameter space of artificial neural networks according to a Boltzmann distribution provides insight into the geometry of low-loss solutions and offers an alternative to conventional loss minimization for training. However,…

Extreme-value fluctuations at quantum critical points remain poorly understood in the presence of strong correlations and openness. At the integer quantum Hall transition in the open Chalker--Coddington network, we show that the maximal…

Geoenergy projects (CO2 storage, geothermal, subsurface H2 generation/storage, critical minerals from subsurface fluids, or nuclear waste disposal) increasingly follow a petroleum-style funnel from screening and appraisal to operations,…

Dynamical Mean Field Theory (DMFT) provides an asymptotic description of the dynamics of macroscopic observables in certain disordered systems. Originally pioneered in the context of spin glasses by Sompolinsky and Zippelius (1982), it has…

We investigate associative-memory behavior in a reconfigurable particle packing programmed by purely local cyclic driving. The system is a two-dimensional bidisperse Lennard--Jones particle assembly with periodic boundaries evolved under…

Neural quantum states (NQS) provide flexible and compact wavefunction parameterizations for numerical studies of quantum many-body physics. In particular, NQS aim to circumvent the exponential scaling of the Hilbert space by compressing…

A model for studying the ultrametricity of the energy landscape in a disordered heteropolymer is presented. It is treated as a simplified model of a protein molecule in which amino acid residues are modeled as point masses. Pairwise…

We develop variational continuous unitary transformations (VCUTs), which integrate Wegner-Wilson flow equations with tensor network techniques to approximately diagonalize many-body localized (MBL) Hamiltonians. The diagonalizing unitary is…

Modern neural networks are heavily overparameterized, and pruning, which removes redundant neurons or connections, has emerged as a key approach to compressing them without sacrificing performance. However, while practical pruning methods…

We develop a microscopic theory of thermalisation for a thermometer coupled to a many-body bath beyond standard Markovian and Fermi-golden-rule assumptions. By modeling interaction matrix elements in the non-interacting basis as independent…

The Aubry-Andr\'e model describes a system with quasiperiodic lattice modulation. In one dimension the AAH model is known to exhibit a sharp metal to insulator transition at a self-dual critical point at which all the states in the spectrum…

We study disorder effects in the extended Su-Schrieffer-Heeger (SSH) model using a convolutional neural network (CNN) trained on reduced correlation matrices (RCMs) of disorder-free systems to predict winding number phase diagrams in…

With the growing prevalence of AI, demand increases for hardware that mimics the brain's ability to extract structure from limited data. In the retina, ganglion cells detect features from sparse inputs via lateral inhibition, where neurons…

Graph neural networks (GNNs) are increasingly applied to hard optimization problems, often claiming superiority over classical heuristics. However, such claims risk being unsolid due to a lack of standard benchmarks on truly hard instances.…