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Volkan Cevher

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Related publications (249)

Page 2 of 13

How Gradient Descent Balances Features: A Dynamical Analysis For Two-Layer Neural Networks

Volkan Cevher, Fanghui Liu, Zhenyu Zhu

This paper investigates the fundamental regression task of learning k neurons (a.k.a. teachers) from Gaussian input, using two-layer ReLU neural networks with width m (a.k.a. students) and m, k = O(1), trained via gradient descent under proper initializati ...

2025

Scalable Semidefinite Programming

Volkan Cevher, Alp Yurtsever

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct algorithm for solving large SDP problems by economizing on both the storage an ...

2021

Smoothing technique for nonsmooth composite minimization with linear operator

Volkan Cevher, Van Quang Nguyen

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap technique. In addition t ...

2017

High Dimensional Bayesian Optimization via Additive Models with Overlapping Groups

Volkan Cevher, Paul Thierry Yves Rolland, Jonathan Mark Scarlett, Ilija Bogunovic

Bayesian optimization (BO) is a popular technique for sequential black-box function optimization, with applications including parameter tuning, robotics, environmental monitoring, and more. One of the most important challenges in BO is the development of a ...

2018

Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation

Volkan Cevher, Jonathan Mark Scarlett, Andreas Krause, Ilija Bogunovic

We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set ...

2016

Binary Sparse Coding of Convolutive Mixtures for Sound Localization and Separation via Spatialization

Volkan Cevher, Hervé Bourlard, Afsaneh Asaei, Saeid Haghighatshoar, Mohammadjavad Taghizadeh

We propose a sparse coding approach to address the problem of source-sensor localization and speech reconstruction. This approach relies on designing a dictionary of spatialized signals by projecting the microphone array recordings into the array manifolds ...

Institute of Electrical and Electronics Engineers2016

An inexact proximal path-following algorithm for constrained convex minimization

Volkan Cevher, Anastasios Kyrillidis, Quoc Tran Dinh

Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a ...

Siam Publications2014

Online performance guarantees for sparse recovery

Volkan Cevher

A K*-sparse vector x* ∈ RN produces measurements via linear dimensionality reduction as u = Φx* +n, where Φ ∈ RM×N (M

2011

Compressive sensing meets game theory

Volkan Cevher

We introduce the Multiplicative Update Selector and Estimator (MUSE) algorithm for sparse approximation in under-determined linear regression problems. Given ƒ = Φα* + μ, the MUSE provably and efficiently finds a k-sparse vector α̂ such that ∥Φα̂ − ƒ∥∞ ≤ ∥ ...

IEEE2011

Equivalence of synthesis and atomic formulations of sparse recovery

Volkan Cevher, Mitra Fatemi

Recovery of sparse signals from linear, dimensionality reducing measurements broadly fall under two well-known formulations, named the synthesis and the analysis a ́ la Elad et al. Recently, Chandrasekaran et al. introduced a new algorithmic sparse recover ...

Ieee2012

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

Bilinear Generalized Approximate Message Passing—Part I: Derivation

Volkan Cevher

In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its applica ...

Institute of Electrical and Electronics Engineers2014

Ultrasensitive hyperspectral imaging and biodetection enabled by dielectric metasurfaces

Volkan Cevher, Hatice Altug, Filiz Yesilköy, Andreas Tittl, Yasaman Jahani, Eduardo Romero Arvelo

Metasurfaces based on resonant subwavelength photonic structures enable novel ways of wavefront control and light focusing, underpinning a new generation of flat-optics devices. Recently emerged all-dielectric asymmetric metasurfaces, composed of arrays of ...

Nature Publishing Group2019

A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming

Volkan Cevher, Alp Yurtsever

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines the notions of smoothing and homotopy under the CGM framework, and provably achieves the optimal O(1/sqrt(k)) convergenc ...

ICML2018

Stochastic Three-Composite Convex Minimization

Volkan Cevher, Alp Yurtsever, Cong Bang Vu

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computati ...

2016

Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games

Volkan Cevher

Since Polyak's pioneering work, heavy ball (HB) momentum has been widely studied in minimization. However, its role in min-max games remains largely unexplored. As a key component of practical min-max algorithms like Adam, this gap limits their effectivene ...

2025

Understanding Deep Neural Function Approximation in Reinforcement Learning via ϵ-Greedy Exploration

Volkan Cevher, Fanghui Liu, Luca Viano

This paper provides a theoretical study of deep neural function approximation in reinforcement learning (RL) with the ϵ-greedy exploration under the online setting. This problem setting is motivated by the successful deep Q-networks (DQN) framework that fa ...

2022

Sparse Group Covers and Greedy Tree Approximations

Volkan Cevher, Luca Baldassarre

We consider the problem of finding a K-sparse approximation of a signal, such that the support of the approximation is the union of sets from a given collection, a.k.a. group structure. This problem subsumes the one of finding K-sparse tree approximations. ...

2015

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Volkan Cevher, Thomas Michaelsen Pethick, Wanyun Xie

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

2023

Stochastic Spectral Descent for Discrete Graphical Models

Volkan Cevher, Ya-Ping Hsieh, Edo Collins

Interest in deep probabilistic graphical models has increased in recent years, due to their state-of-the-art perfor- mance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a signif ...

Ieee-Inst Electrical Electronics Engineers Inc2016