Entropy, Combinatorial Dimensions and Random Averages. - Shahar Mendelson; Roman Vershynin (COLT, 2002)

Error Correction via Linear Programming. - Emmanuel J. Candès; Mark Rudelson; Terence Tao; Roman Vershynin (FOCS, 2005)

A Randomized Solver for Linear Systems with Exponential Convergence. - Thomas Strohmer; Roman Vershynin (APPROX-RANDOM, 2006)

Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements. - Mark Rudelson; Roman Vershynin (CISS, 2006)

Beyond Hirsch Conjecture: Walks on Random Polytopes and Smoothed Complexity of the Simplex Method. - Roman Vershynin (FOCS, 2006)

Algorithmic linear dimension reduction in the l_1 norm for sparse vectors - Anna C. Gilbert; Martin J. Strauss; Joel A. Tropp; Roman Vershynin (CoRR, 2006)

One sketch for all: fast algorithms for compressed sensing. - Anna C. Gilbert; Martin J. Strauss; Joel A. Tropp; Roman Vershynin (STOC, 2007)

Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms - Roman Vershynin (CoRR, 2007)

Sampling from large matrices: An approach through geometric functional analysis. - Mark Rudelson; Roman Vershynin (J. ACM, 2007)

Greedy signal recovery review. - Deanna Needell; Joel A. Tropp; Roman Vershynin (ACSCC, 2008)

Greedy signal recovery and uncertainty principles. - Deanna Needell; Roman Vershynin (Computational Imaging, 2008)

Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit. - Deanna Needell; Roman Vershynin (Found. Comput. Math., 2009)

Introduction to the non-asymptotic analysis of random matrices - Roman Vershynin (CoRR, 2010)

Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit. - Deanna Needell; Roman Vershynin (IEEE J. Sel. Top. Signal Process., 2010)

Uncertainty principles and vector quantization. - Yurii Lyubarskii; Roman Vershynin (IEEE Trans. Inf. Theory, 2010)

One-bit compressed sensing by linear programming - Yaniv Plan; Roman Vershynin (CoRR, 2011)

Introduction to the non-asymptotic analysis of random matrices. - Roman Vershynin (Compressed Sensing, 2012)

One-bit compressed sensing with non-Gaussian measurements - Albert Ai; Alex Lapanowski; Yaniv Plan; Roman Vershynin (CoRR, 2012)

Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach. - Yaniv Plan; Roman Vershynin (IEEE Trans. Inf. Theory, 2013)

Community detection in sparse networks via Grothendieck's inequality. - Olivier Guédon; Roman Vershynin (CoRR, 2014)

Optimization via Low-rank Approximation, with Applications to Community Detection in Networks. - Can M. Le; Elizaveta Levina; Roman Vershynin (CoRR, 2014)

Dimension Reduction by Random Hyperplane Tessellations. - Yaniv Plan; Roman Vershynin (Discret. Comput. Geom., 2014)

Invertibility of symmetric random matrices. - Roman Vershynin (Random Struct. Algorithms, 2014)

Sparse random graphs: regularization and concentration of the Laplacian. - Can M. Le; Elizaveta Levina; Roman Vershynin (CoRR, 2015)

Concentration and regularization of random graphs. - Can M. Le; Roman Vershynin (CoRR, 2015)

On the Effective Measure of Dimension in the Analysis Cosparse Model. - Raja Giryes; Yaniv Plan; Roman Vershynin (IEEE Trans. Inf. Theory, 2015)

Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization. - Jess Banks; Cristopher Moore; Roman Vershynin; Jiaming Xu 002 (CoRR, 2016)

A simple tool for bounding the deviation of random matrices on geometric sets. - Christopher Liaw; Abbas Mehrabian; Yaniv Plan; Roman Vershynin (CoRR, 2016)

Four lectures on probabilistic methods for data science. - Roman Vershynin (CoRR, 2016)

The Generalized Lasso With Non-Linear Observations. - Yaniv Plan; Roman Vershynin (IEEE Trans. Inf. Theory, 2016)

Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization. - Jess Banks; Cristopher Moore; Roman Vershynin; Nicolas Verzelen; Jiaming Xu 002 (ISIT, 2017)

Phase Retrieval via Randomized Kaczmarz: Theoretical Guarantees. - Yan Shuo Tan; Roman Vershynin (CoRR, 2017)

Concentration and regularization of random graphs. - Can M. Le; Elizaveta Levina; Roman Vershynin (Random Struct. Algorithms, 2017)

Polynomial Time and Sample Complexity for Non-Gaussian Component Analysis: Spectral Methods. - Yan Shuo Tan; Roman Vershynin (COLT, 2018)

On Neuronal Capacity. - Pierre Baldi; Roman Vershynin (NeurIPS, 2018)

The capacity of feedforward neural networks. - Pierre Baldi; Roman Vershynin (Neural Networks, 2019)

Polynomial Threshold Functions, Hyperplane Arrangements, and Random Tensors. - Pierre Baldi; Roman Vershynin (SIAM J. Math. Data Sci., 2019)

Memory capacity of neural networks with threshold and ReLU activations. - Roman Vershynin (CoRR, 2020)

Memory Capacity of Neural Networks with Threshold and Rectified Linear Unit Activations. - Roman Vershynin (SIAM J. Math. Data Sci., 2020)

A theory of capacity and sparse neural encoding. - Pierre Baldi; Roman Vershynin (Neural Networks, 2021)

The Quarks of Attention. - Pierre Baldi; Roman Vershynin (CoRR, 2022)

Private measures, random walks, and synthetic data. - March Boedihardjo; Thomas Strohmer; Roman Vershynin (CoRR, 2022)

AVIDA: Alternating method for Visualizing and Integrating Data. - Kathryn Dover; Zixuan Cang; Anna Ma; Qing Nie; Roman Vershynin (CoRR, 2022)

Private Sampling: A Noiseless Approach for Generating Differentially Private Synthetic Data. - March Boedihardjo; Thomas Strohmer; Roman Vershynin (SIAM J. Math. Data Sci., 2022)

Algorithmically Effective Differentially Private Synthetic Data. - Yiyun He; Roman Vershynin; Yizhe Zhu (COLT, 2023)

Covariance loss, Szemeredi regularity, and differential privacy. - March Boedihardjo; Thomas Strohmer; Roman Vershynin (CoRR, 2023)

Differentially private low-dimensional representation of high-dimensional data. - Yiyun He; Thomas Strohmer; Roman Vershynin; Yizhe Zhu (CoRR, 2023)

Online Stochastic Gradient Descent with Arbitrary Initialization Solves Non-smooth, Non-convex Phase Retrieval. - Yan Shuo Tan; Roman Vershynin (J. Mach. Learn. Res., 2023)

Privacy of Synthetic Data: A Statistical Framework. - March Boedihardjo; Thomas Strohmer; Roman Vershynin (IEEE Trans. Inf. Theory, 2023)

AVIDA: An alternating method for visualizing and integrating data. - Kathryn Dover; Zixuan Cang; Anna Ma; Qing Nie; Roman Vershynin (J. Comput. Sci., 2023)

The quarks of attention: Structure and capacity of neural attention building blocks. - Pierre Baldi; Roman Vershynin (Artif. Intell., 2023)

An Algorithm for Streaming Differentially Private Data. - Girish Kumar; Thomas Strohmer; Roman Vershynin (CoRR, 2024)

Online Differentially Private Synthetic Data Generation. - Yiyun He; Roman Vershynin; Yizhe Zhu (CoRR, 2024)

Metric geometry of the privacy-utility tradeoff. - March Boedihardjo; Thomas Strohmer; Roman Vershynin (CoRR, 2024)

Differentially Private Synthetic High-dimensional Tabular Stream. - Girish Kumar; Thomas Strohmer; Roman Vershynin (CoRR, 2024)

Covariance's Loss is Privacy's Gain: Computationally Efficient, Private and Accurate Synthetic Data. - March Boedihardjo; Thomas Strohmer; Roman Vershynin (Found. Comput. Math., 2024)

Hamiltonicity of sparse pseudorandom graphs. - Asaf Ferber; Jie Han 002; Dingjia Mao; Roman Vershynin (Comb. Probab. Comput., 2025)

LLM Watermarking Using Mixtures and Statistical-to-Computational Gaps. - Pedro Abdalla; Roman Vershynin (CoRR, 2025)

Thinning to improve two-sample discrepancy. - Gleb Smirnov; Roman Vershynin (CoRR, 2025)