无序系统与神经网络
We introduce a two-parameter ensemble of random discrete-time Markov models that simultaneously captures critical slowing down and broken detailed balance. Extending a previously studied heterogeneous Markov ensemble, we incorporate…
Delayed generalization, termed grokking, in a machine learning calculation occurs when the increase in test accuracy is delayed relative to the training accuracy. This paper examines grokking in the context of a dense neural network trained…
Many-body localization (MBL) transition emerges at strong disorder in interacting systems, separating chaotic and reversible dynamics. Although the existence of MBL transition within the macroscopic limit in spin chains with a short-range…
Disordered materials occur naturally and also provide a broader design space than ordered or crystalline structures. We investigate a two-dimensional disordered network metamaterial constructed from a Delaunay triangulation of an underlying…
Typical mammal brains have some form of random connectivity between neurons. Reservoir computing, a neural network approach, uses random weights within its processing layer along with built-in recurrent connections and short-term, fading…
We use the transfer tensor method to analyze localization and transport in simple disordered systems, specifically the Anderson and Aubry-Andr\'e-Harper models. Emphasis is placed on the memory effects that emerge when ensemble-averaging…
We study harmonic chains with i.i.d. random spring constants $K_n$ and i.i.d. random masses $m_n$. We introduce a new combinatorial approach which allows to derive a compact approximate expression for the complex Lyapunov exponent, in terms…
Neural quantum states (NQS) are powerful ans\"atze in the variational Monte Carlo framework, yet their architectures are often treated as black boxes. We propose a physically transparent framework in which NQS are treated as neural…
Quantum criticality in the presence of strong quenched randomness remains a challenging topic in modern condensed matter theory. We show that the topology and anomaly associated with average symmetry can be used to predict certain…
Demonstrating quantum speedup for approximate optimization of classical spin glasses is of current interest. Such a demonstration must be done with respect to the best-known scaling of classical heuristics at a given optimality gap of a…
This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$ through the lens of renormalization group (RG) theory. The RG is based on a coarse-graining over the eigenvalues of matrix-like disorder,…
We study localization driven solely by interparticle interactions in moir\'e lattice systems without intrinsic disorder or externally imposed quasiperiodic potentials. We consider a one-dimensional bilayer with incommensurate lattice…
The construction of the Hamiltonian matrix \textbf{H} is an essential, yet computationally expensive step in \textit{ab-initio} device simulations based on density-functional theory (DFT). In homogeneous structures, the fact that a unit…
Quantum many-body systems pose a formidable computational challenge due to the exponential growth of their Hilbert space. While machine learning (ML) has shown promise as an alternative paradigm, most applications remain at the…
Probabilistic graphical models with frustration exhibit rugged energy landscapes that trap iterative optimization dynamics. These landscapes are shaped not only by local interactions, but crucially also by the global loop structure of the…
We study a variant of the pseudo-inverse learning rule for Hopfield-like Neural Networks, which allows the network to infer archetypal concepts on the basis of a limited number of examples. The mean-field replica theory for this model…
The spatial photonic Ising machine (SPIM) is a promising optical hardware solver for large-scale combinatorial optimization problems with dense interactions. As the SPIM can represent Ising problems with rank-one coupling matrices,…
Interest in studying the conductive properties of networks made from randomly distributed nanowires is due to their numerous technological applications. Although the sheet resistance of such networks can be calculated directly, the…
We study the effect of introducing separable quenched disorder on a non-equilibrium mean-field spin model exhibiting a phase transition to an oscillating state in the absence of disorder, due to non-reciprocal interactions. In the…
Systems with a complex dynamics like glasses or models of biological evolution are often pictured in terms of complex landscapes, with a large number of possible collective states. We show on the example of a stochastic spin model with…