Publications (17)
Finding stationary points on bounded-rank matrices: A geometric hurdle and a smooth remedy
Eitan Levin, Joe Kileel, Nicolas Boumal
We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delic…
Any-Dimensional Polynomial Optimization via de Finetti Theorems
Eitan Levin, Venkat Chandrasekaran
Polynomial optimization problems often arise in sequences indexed by dimension, and it is of interest to compute bounds on the optimal values of all problems in the sequence. Examp…
Multi-target detection with application to cryo-electron microscopy
Tamir Bendory, Nicolas Boumal, William Leeb +2
We consider the multi-target detection problem of recovering a set of signals that appear multiple times at unknown locations in a noisy measurement. In the low noise regime, one c…
Any-Dimensional Invariant Universality
Shengtai Yao, Eitan Levin, Mateo DÃaz
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The univer…
Limits of Weighted Graphs via Random Quotients
Eitan Levin, Venkat Chandrasekaran
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchange…
Any-Dimensional Learning by Sampling
Eitan Levin, Venkat Chandrasekaran
Many machine learning models are defined for inputs of different sizes, such as point clouds containing different numbers of points, sequences of tokens of different lengths, and g…
Any-dimensional equivariant neural networks
Eitan Levin, Mateo DÃaz
Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on…
Poset-Markov Channels: Capacity via Group Symmetry
Eray Unsal Atay, Eitan Levin, Venkat Chandrasekaran +1
Computing channel capacity is in general intractable because it is given by the limit of a sequence of optimization problems whose dimensionality grows to infinity. As a result, co…
A note on Douglas-Rachford, gradients, and phase retrieval
Eitan Levin, Tamir Bendory
The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retriev…
Direct reconstruction of two-dimensional currents in thin films from magnetic field measurements
Alexander Y. Meltzer, Eitan Levin, Eli Zeldov
Accurate determination of microscopic transport and magnetization currents is of central importance for the study of the electric properties of low dimensional materials and interf…
Dimension-Free Descriptions of Convex Sets
Eitan Levin, Venkat Chandrasekaran
Convex sets arising in a variety of applications are well-defined for every relevant dimension. Examples include the simplex and the spectraplex that correspond to probability dist…
Toward single particle reconstruction without particle picking: Breaking the detection limit
Tamir Bendory, Nicolas Boumal, William Leeb +2
Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method to resolve biological macro…
3D ab initio modeling in cryo-EM by autocorrelation analysis
Eitan Levin, Tamir Bendory, Nicolas Boumal +2
Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-EM) is the task of estimating the 3D structure of a molecule from a set of noisy 2D projections, taken from u…
Estimation of the Regularization Parameter in Linear Discrete Ill-Posed Problems Using the Picard parameter
Eitan Levin, Alexander Y. Meltzer
Accurate determination of the regularization parameter in inverse problems still represents an analytical challenge, owing mainly to the considerable difficulty to separate the unk…
On Transferring Transferability: Towards a Theory for Size Generalization
Eitan Levin, Yuxin Ma, Mateo DÃaz +1
Many modern learning tasks require models that can take inputs of varying sizes. Consequently, dimension-independent architectures have been proposed for domains where the inputs a…
The effect of smooth parametrizations on nonconvex optimization landscapes
Eitan Levin, Joe Kileel, Nicolas Boumal
We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for…
Stopping criterion for iterative regularization of large-scale ill-posed problems using the Picard parameter
Eitan Levin, Alexander Y. Meltzer
We propose a new stopping criterion for Krylov subspace iterative regularization of large-scale ill-posed inverse problems. Our stopping criterion accurately filters the data using…