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Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
We study the emergence of glassy states after a sudden cooling in lattice models with short range interactions and without any a priori quenched disorder. The glassy state emerges whenever the equilibrium model possesses a sufficient number…
We introduce a Potts model with quenched, frustrated disorder, that enjoys of a gauge symmetry that forbids spontaneous magnetization, and allows the glassy phase to extend from $T_c$ down to T=0. We study numerical the 4 dimensional model…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
In this work, we study the finite time blow-up phenomenon of three types of semilinear wave systems with multiple speeds, posed on asymptotically Euclidean manifolds. We establish the upper bound estimates for the lifespan of solutions when…
The critical behaviour of the dynamical transition of glassy system is controlled by a Replica Symmetric action with n=1 replicas. The most divergent diagrams in the loop expansion correspond at all orders to the solutions of a stochastic…
We calculate moments of free energy's finite size correction for the transition point between ferromagnetic and spin glass phases. We find, that those moments scale with the number of spins with different critical indices, characteristic…
We discuss level crossing of the free-energy of TAP solutions under variations of external parameters such as magnetic field or temperature in mean-field spin-glass models that exhibit one-step Replica-Symmetry-Breaking (1RSB). We study the…
The multi-index matching is an NP-hard combinatorial optimization problem; for two indices it reduces to the well understood bipartite matching problem that belongs to the polynomial complexity class. We use the cavity method to solve the…
We consider the problem of model multiplicity in downstream decision-making, a setting where two predictive models of equivalent accuracy cannot agree on the best-response action for a downstream loss function. We show that even when the…
We propose a general formulation, called Multi-X, for multi-class multi-instance model fitting - the problem of interpreting the input data as a mixture of noisy observations originating from multiple instances of multiple classes. We…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…
We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter $p$. For $p=2$…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…
In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…
The number $\langle N_s\rangle$ of solutions of the equations of Thouless, Anderson and Palmer for p--spin interaction spin glass models is calculated. Below a critical temperature $T_c$ this number becomes exponentially large, as it is in…
The complexity of glasses makes it challenging to explain their dynamics. Machine Learning (ML) has emerged as a promising pathway for understanding glassy dynamics by linking their structural features to rearrangement dynamics. Support…
We propose a numerical methodology for the simultaneous numerical simulation of four states of matter; gas, liquid, elastoplastic solids and plasma. The distinct, interacting physical processes are described by a combination of…