Related papers: Contributions to Random Energy Models
The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on…
We consider the free energy of a mean-field quantum spin glass described by a $ p $-spin interaction and a transversal magnetic field. Recent rigorous results for the case $ p= \infty $, i.e. the quantum random energy model (QREM), are…
Within generalized random energy models, we study the effects of energy discreteness and of entropy extensivity in the low temperature phase. At zero temperature, discreteness of the energy induces replica symmetry breaking, in contrast to…
This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices. In the first part devoted to logREMs,…
We introduce a perceptron version of the Generalized Random Energy Model, and prove a quenched Sanov type large deviation principle for the empirical distribution of the random energies. The dual of the rate function has a representation…
In a previous work [A simplified Parisi Ansatz, Franchini, S., Commun. Theor. Phys., 73, 055601 (2021)] we introduced a simple method to compute the Random Overlap Structure of Aizenmann, Simm and Stars and the full RSB Parisi formula for…
It is widely held that the Random Energy Model (REM) describes the freezing transition of a variety of types of heteropolymers. We demonstrate that the hallmark property of REM, statistical independence of the energies of states over…
We derive the scaling limit for the Hierarchical Random Hopping dynamics for the non cascading 2-GREM at low temperatures and time scales where the dynamics is close to equilibrium. The {\em fine tuning} phenomenon plays a role (under…
We consider a model of directed polymers on regular trees with complex-valued random weights introduced by Cook and Derrida [CD90] and studied mathematically by Derrida, Evans and Speer [DES93]. In addition to the usual weak-disorder and…
We determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model (REM) and its hierarchical generalization, the GREM. Our…
We establish limit theorems that describe the asymptotic local and global geometric behaviour of random enriched trees considered up to symmetry. We apply these general results to random unlabelled weighted rooted graphs and uniform random…
The new Theorem on location of maximum of probability density functions of dimensionless second difference of the three adjacent energy levels for $N$-dimensional Gaussian orthogonal ensemble GOE($N$), $N$-dimensional Gaussian unitary…
In QM/MM indirect free energy simulation, QM/MM corrections can be obtained from integration of partial derivatives of alchemical Hamiltonians or from perturbation-based estimators including free energy perturbation (FEP) and acceptance…
Deep generative models (DGMs) are data-eager because learning a complex model on limited data suffers from a large variance and easily overfits. Inspired by the classical perspective of the bias-variance tradeoff, we propose regularized…
A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…
Large reasoning models (LRMs) have heterogeneous inference energy costs based on which model is used and how much it reasons. To reduce energy, it is important to choose the right LRM and operate it in the right way. As a result, the…
Global Autoregressive Models (GAMs) are a recent proposal [Parshakova et al., CoNLL 2019] for exploiting global properties of sequences for data-efficient learning of seq2seq models. In the first phase of training, an Energy-Based model…
We consider a sequence of random Hamiltonians $H_n(h,\sigma)=\sum^n_{i=1}h_i(\sigma_i-m)$, and study the asymptotic ($n\to \infty$) distribution of the energy levels $(H_n(h,\sigma))_{\sigma\in \{-1,1\}^n}$, where $h_1,h_2,\cdots$ are…
Energy-based models (EBMs) have experienced a resurgence within machine learning in recent years, including as a promising alternative for probabilistic regression. However, energy-based regression requires a proposal distribution to be…
We address the co-optimization of behind-the-meter (BTM) distributed energy resources (DER), including flexible demands, renewable distributed generation (DG), and battery energy storage systems (BESS) under net energy metering (NEM)…