Related papers: Finite size corrections to the Parisi overlap func…
The analysis of the solution with full replica symmetry breaking in the vicinity of $T_c$ of a general spin glass model with reflection symmetry is performed. The leading term in the order parameter function expansion is obtained. Parisi…
A fermionic random matrix model, which is a 0-dimensional version of the SYK model with replicas, is considered. The replica-off-diagonal correlation functions vanish at finite N, but we show that they do not vanish in the large N limit due…
Directed polymers on 1+1 dimensional lattices coupled to a heat bath at temperature $T$ are studied numerically for three ensembles of the site disorder. In particular correlations of the disorder as well as fractal patterning are…
Among the various machine learning methods solving partial differential equations, the Random Feature Method (RFM) stands out due to its accuracy and efficiency. In this paper, we demonstrate that the approximation error of RFM exhibits…
We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections in a crucial way depend on the parity of $N$; we…
We present a thorough numerical analysis of the relaxational dynamics of the Sherrington-Kirkpatrick spherical model with an additive non-disordered perturbation for large but finite sizes $N$. In the thermodynamic limit and at low…
We perform a systematic analytical study of finite size effects in separable recurrent neural network models with sequential dynamics, away from saturation. We find two types of finite size effects: thermal fluctuations, and…
We propose a new finite-size correction scheme for the formation energy of charged defects and impurities in one-dimensional systems within density functional theory. The energy correction in a supercell geometry is obtained by solving the…
This paper investigates how the degree of group fairness changes when the degree of individual fairness is actively controlled. As a metric quantifying individual fairness, we consider generalized entropy (GE) recently introduced into…
We revisit the gradient descent dynamics of the spherical Sherrington-Kirkpatrick ($p=2$) model with finite number of degrees of freedom. For fully random initial conditions we confirm that the relaxation takes place in three time regimes:…
It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size…
The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…
The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a $\sigma$-finite measure, and not necessarily a probability measure. Under this…
Family of replica matrices, related to general ultrametric spaces with general measures, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed. Replica symmetry breaking…
We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic…
Random Forests (RF) is a popular machine learning method for classification and regression problems. It involves a bagging application to decision tree models. One of the primary advantages of the Random Forests model is the reduction in…
A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (ERM). Gaussian equivalence theory (GET) has emerged as a…
We prove the existence of correlations between the equilibrium states at different temperatures of the multi-$p$-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models.…
For different reversible Markov kernels on finite state spaces, we look for families of probability measures for which the time evolution almost remains in their convex hull. Motivated by signal processing problems and metastability studies…
Disordered systems such as spin glasses have been used extensively as models for high-dimensional random landscapes and studied from the perspective of optimization algorithms. In a recent paper by L. Addario-Berry and the second author,…