Related papers: The simplest model of jamming
Generalized and Simulated Method of Moments are often used to estimate structural Economic models. Yet, it is commonly reported that optimization is challenging because the corresponding objective function is non-convex. For smooth…
Jamming is a common feature of out of equilibrium systems showing slow relaxation dynamics. Here we review our efforts in understanding jamming in granular materials using experiments and computer simulations. We first obtain an estimation…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
The behavior of the percolation threshold and the jamming coverage for isotropic random sequential adsorption samples has been studied by means of numerical simulations. A parallel algorithm that is very efficient in terms of its speed and…
In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by…
In a previous letter, we studied learning from stochastic examples by perceptrons with Ising weights in the framework of statistical mechanics. Under the one-step replica symmetry breaking ansatz, the behaviours of learning curves were…
When materials such as foams or emulsions are compressed, they display solid behaviour above the so-called `jamming' transition. Because compression is done out-of-equilibrium in the absence of thermal fluctuations, jamming appears as a new…
We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key…
We consider the persistent exclusion process in which a set of persistent random walkers interact via hard-core exclusion on a hypercubic lattice in $d$ dimensions. We work within the ballistic regime whereby particles continue to hop in…
In this research, we introduce the concept of "computational entanglement," a phenomenon observed in overparameterized feedforward linear networks that enables the network to achieve zero loss by fitting random noise, even on previously…
Jamming, or dynamical arrest, is a transition at which many particles stop moving in a collective manner. In nature it is brought about by, for example, increasing the packing density, changing the interactions between particles, or…
We study the binary and continuous negative-margin perceptrons as simple non-convex neural network models learning random rules and associations. We analyze the geometry of the landscape of solutions in both models and find important…
Via molecular dynamics simulations, we unveil the hysteretic nature of the jamming transition of soft repulsive frictionless spheres, as it occurs varying the volume fraction or the shear stress. In a given range of control parameters the…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of distributions, given one \emph{single} sample from each distribution. We study mean estimation and linear…
We consider a simple dynamic model of the vibrating screen operating in the parametric resonance (PR) mode. This model was used in the course of designing and setting of such a screen in LPMC. The PR-based screen compares favorably with…
Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer perceptrons). When they achieve good results in classification, we…
Like other critical phenomena, the jamming transition accompanies the divergence of the relaxation time $\tau$. A recent numerical study of frictionless spherical particles proves that $\tau$ is inversely proportional to the lowest non-zero…