Kolmogorov Complexity, Circuits, and the Strength of Formal Theories of Arithmetic. - Eric Allender; George Davie; Luke Friedman; Samuel B. Hopkins 001; Iddo Tzameret (Electron. Colloquium Comput. Complex., 2012)

Another proof of Wilmes' conjecture. - Sam Hopkins 001 (Discret. Math., 2014)

Tensor principal component analysis via sum-of-square proofs. - Samuel B. Hopkins 001; Jonathan Shi; David Steurer (COLT, 2015)

SoS and Planted Clique: Tight Analysis of MPW Moments at all Degrees and an Optimal Lower Bound at Degree Four. - Samuel B. Hopkins 001; Pravesh K. Kothari; Aaron Potechin (CoRR, 2015)

Tensor principal component analysis via sum-of-squares proofs. - Samuel B. Hopkins 001; Jonathan Shi; David Steurer (CoRR, 2015)

Speeding up sum-of-squares for tensor decomposition and planted sparse vectors. - Samuel B. Hopkins 001; Tselil Schramm; Jonathan Shi; David Steurer (CoRR, 2015)

Interlacing networks: Birational RSK, the octahedron recurrence, and Schur function identities. - Miriam Farber; Sam Hopkins 001; Wuttisak Trongsiriwat (J. Comb. Theory A, 2015)

A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem. - Boaz Barak; Samuel B. Hopkins 001; Jonathan A. Kelner; Pravesh Kothari; Ankur Moitra; Aaron Potechin (FOCS, 2016)

On the Integrality Gap of Degree-4 Sum of Squares for Planted Clique. - Samuel B. Hopkins 001; Pravesh Kothari; Aaron Henry Potechin; Prasad Raghavendra; Tselil Schramm (SODA, 2016)

Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors. - Samuel B. Hopkins 001; Tselil Schramm; Jonathan Shi; David Steurer (STOC, 2016)

Pattern Avoidance in Poset Permutations. - Sam Hopkins 001; Morgan Weiler (Order, 2016)

The Power of Sum-of-Squares for Detecting Hidden Structures. - Samuel B. Hopkins 001; Pravesh K. Kothari; Aaron Potechin; Prasad Raghavendra; Tselil Schramm; David Steurer (FOCS, 2017)

Efficient Bayesian Estimation from Few Samples: Community Detection and Related Problems. - Samuel B. Hopkins 001; David Steurer (FOCS, 2017)

Bayesian estimation from few samples: community detection and related problems. - Samuel B. Hopkins 001; David Steurer (CoRR, 2017)

Mixture models, robustness, and sum of squares proofs. - Samuel B. Hopkins 001; Jerry Li 001 (STOC, 2018)

Sub-Gaussian Mean Estimation in Polynomial Time. - Samuel B. Hopkins 001 (CoRR, 2018)

Statistical Inference and the Sum of Squares Method. - Samuel B. Hopkins 001 (2018)

How Hard is Robust Mean Estimation? - Samuel B. Hopkins 001; Jerry Li 001 (COLT, 2019)

A Robust Spectral Algorithm for Overcomplete Tensor Decomposition. - Samuel B. Hopkins 001; Tselil Schramm; Jonathan Shi (COLT, 2019)

Sum-of-Squares Meets Program Obfuscation, Revisited. - Boaz Barak; Samuel B. Hopkins 001; Aayush Jain; Pravesh Kothari; Amit Sahai (EUROCRYPT (1), 2019)

Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection. - Yihe Dong; Samuel B. Hopkins 001; Jerry Li 001 (NeurIPS, 2019)

Outlier-Robust Clustering of Gaussians and Other Non-Spherical Mixtures. - Ainesh Bakshi; Ilias Diakonikolas; Samuel B. Hopkins 001; Daniel Kane 001; Sushrut Karmalkar; Pravesh K. Kothari (FOCS, 2020)

Smoothed Complexity of 2-player Nash Equilibria. - Shant Boodaghians; Joshua Brakensiek; Samuel B. Hopkins 001; Aviad Rubinstein (FOCS, 2020)

Subexponential LPs Approximate Max-Cut. - Samuel B. Hopkins 001; Tselil Schramm; Luca Trevisan 001 (FOCS, 2020)

Estimating Rank-One Spikes from Heavy-Tailed Noise via Self-Avoiding Walks. - Jingqiu Ding; Samuel B. Hopkins 001; David Steurer (NeurIPS, 2020)

Robust and Heavy-Tailed Mean Estimation Made Simple, via Regret Minimization. - Samuel B. Hopkins 001; Jerry Li 001; Fred Zhang (NeurIPS, 2020)

Algorithms for heavy-tailed statistics: regression, covariance estimation, and beyond. - Yeshwanth Cherapanamjeri; Samuel B. Hopkins 001; Tarun Kathuria; Prasad Raghavendra; Nilesh Tripuraneni (STOC, 2020)

Robustly Learning any Clusterable Mixture of Gaussians. - Ilias Diakonikolas; Samuel B. Hopkins 001; Daniel Kane 001; Sushrut Karmalkar (CoRR, 2020)

Statistical Query Algorithms and Low Degree Tests Are Almost Equivalent. - Matthew S. Brennan; Guy Bresler; Samuel B. Hopkins 001; Jerry Li 001; Tselil Schramm (COLT, 2021)

Counterexamples to New Circular Security Assumptions Underlying iO. - Samuel B. Hopkins 001; Aayush Jain; Huijia Lin (CRYPTO (2), 2021)

The Franz-Parisi Criterion and Computational Trade-offs in High Dimensional Statistics. - Afonso S. Bandeira; Ahmed El Alaoui; Samuel B. Hopkins 001; Tselil Schramm; Alexander S. Wein; Ilias Zadik (NeurIPS, 2022)

Privacy Induces Robustness: Information-Computation Gaps and Sparse Mean Estimation. - Kristian Georgiev; Samuel B. Hopkins 001 (NeurIPS, 2022)

Efficient mean estimation with pure differential privacy via a sum-of-squares exponential mechanism. - Samuel B. Hopkins 001; Gautam Kamath 001; Mahbod Majid (STOC, 2022)

Matrix discrepancy from Quantum communication. - Samuel B. Hopkins 001; Prasad Raghavendra; Abhishek Shetty (STOC, 2022)

Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributions. - Gavin Brown 003; Samuel B. Hopkins 001; Adam Smith 006 (COLT, 2023)

The Full Landscape of Robust Mean Testing: Sharp Separations between Oblivious and Adaptive Contamination. - Clément L. Canonne; Samuel B. Hopkins 001; Jerry Li 001; Allen Liu; Shyam Narayanan (FOCS, 2023)

Robustness Implies Privacy in Statistical Estimation. - Samuel B. Hopkins 001; Gautam Kamath 001; Mahbod Majid; Shyam Narayanan (STOC, 2023)

Towards Practical Robustness Auditing for Linear Regression. - Daniel Freund 001; Samuel B. Hopkins 001 (CoRR, 2023)

A quasi-polynomial time algorithm for Multi-Dimensional Scaling via LP hierarchies. - Ainesh Bakshi; Vincent Cohen-Addad; Samuel B. Hopkins 001; Rajesh Jayaram; Silvio Lattanzi (CoRR, 2023)

Insufficient Statistics Perturbation: Stable Estimators for Private Least Squares Extended Abstract. - Gavin Brown 003; Jonathan Hayase; Samuel B. Hopkins 001; Weihao Kong; Xiyang Liu; Sewoong Oh; Juan C. Perdomo; Adam Smith 006 (COLT, 2024)

Beyond Catoni: Sharper Rates for Heavy-Tailed and Robust Mean Estimation. - Shivam Gupta 002; Samuel B. Hopkins 001; Eric C. Price (COLT, 2024)

Adversarially-Robust Inference on Trees via Belief Propagation. - Samuel B. Hopkins 001; Anqi Li (COLT, 2024)

Insufficient Statistics Perturbation: Stable Estimators for Private Least Squares. - Gavin Brown 003; Jonathan Hayase; Samuel B. Hopkins 001; Weihao Kong; Xiyang Liu; Sewoong Oh; Juan C. Perdomo; Adam Smith 006 (CoRR, 2024)

Metric Embeddings Beyond Bi-Lipschitz Distortion via Sherali-Adams. - Ainesh Bakshi; Vincent Cohen-Addad; Rajesh Jayaram; Sam Hopkins 001; Silvio Lattanzi (COLT, 2025)

Robustness Auditing for Linear Regression: To Singularity and Beyond. - Ittai Rubinstein; Samuel B. Hopkins 001 (ICLR, 2025)

SoS Certifiability of Subgaussian Distributions and Its Algorithmic Applications. - Ilias Diakonikolas; Samuel B. Hopkins 001; Ankit Pensia; Stefan Tiegel (STOC, 2025)

SoS Certificates for Sparse Singular Values and Their Applications: Robust Statistics, Subspace Distortion, and More. - Ilias Diakonikolas; Samuel B. Hopkins 001; Ankit Pensia; Stefan Tiegel (STOC, 2025)

Rescaled Influence Functions: Accurate Data Attribution in High Dimension. - Ittai Rubinstein; Samuel B. Hopkins 001 (CoRR, 2025)

Additive Approximation Schemes for Low-Dimensional Embeddings. - Prashanti Anderson; Ainesh Bakshi; Samuel B. Hopkins 001 (CoRR, 2025)