Ilias Zadik

Stationary Points of a Shallow Neural Network with Quadratic Activations and the Global Optimality of the Gradient Descent Algorithm

Mathematics of Operations Research · 2024-02-20 · 3 citations

We consider the problem of training a shallow neural network with quadratic activation functions and the generalization power of such trained networks. Assuming that the samples are generated by a full rank matrix [Formula: see text] of the hidden network node weights, we obtain the following results. We establish that all full-rank approximately stationary solutions of the risk minimization problem are also approximate global optimums of the risk (in-sample and population). As a consequence, we…

Low-Degree Security of the Planted Random Subgraph Problem

Lecture notes in computer science · 2024-11-27 · 1 citations

On the Low-Temperature MCMC threshold: the cases of sparse tensor PCA, sparse regression, and a geometric rule

arXiv (Cornell University) · 2024-08-01 · 1 citations

Over the last years, there has been a significant amount of work studying the power of specific classes of computationally efficient estimators for multiple statistical parametric estimation tasks, including the estimators classes of low-degree polynomials, spectral methods, and others. Despite that, our understanding of the important class of MCMC methods remains quite poorly understood. For instance, for many models of interest, the performance of even zero-temperature (greedy-like) MCMC metho…

A second moment proof of the spread lemma

arXiv (Cornell University) · 2022-09-22 · 1 citations

This note concerns a well-known result which we term the ``spread lemma,'' which establishes the existence (with high probability) of a desired structure in a random set. The spread lemma was central to two recent celebrated results: (a) the improved bounds of Alweiss, Lovett, Wu, and Zhang (2019) on the Erdős-Rado sunflower conjecture; and (b) the proof of the fractional Kahn--Kalai conjecture by Frankston, Kahn, Narayanan and Park (2019). While the lemma was first proved (and later refined) by…

Node-Private Community Detection in Stochastic Block Models

ArXiv.org · 2026-04-10

We study community detection in stochastic block models under pure node-level differential privacy, a stringent notion that protects the participation of an individual together with all of their incident edges. This setting is substantially more challenging than edge-private community detection, since modifying a single node can affect linearly many observations. On the algorithmic side, we analyze a node-private estimator based on the exponential mechanism combined with an extension lemma, and…