Relax, No Need to Round: Integrality of Clustering Formulations. - Pranjal Awasthi; Afonso S. Bandeira; Moses Charikar; Ravishankar Krishnaswamy; Soledad Villar; Rachel A. Ward (ITCS, 2015)

On the tightness of an SDP relaxation of k-means. - Takayuki Iguchi; Dustin G. Mixon; Jesse Peterson; Soledad Villar (CoRR, 2015)

Clustering subgaussian mixtures with k-means. - Dustin G. Mixon; Soledad Villar; Rachel A. Ward (ITW, 2016)

Clustering subgaussian mixtures by semidefinite programming. - Dustin G. Mixon; Soledad Villar; Rachel A. Ward (CoRR, 2016)

A polynomial-time relaxation of the Gromov-Hausdorff distance. - Soledad Villar; Afonso S. Bandeira; Andrew J. Blumberg; Rachel A. Ward (CoRR, 2016)

A Note on Learning Algorithms for Quadratic Assignment with Graph Neural Networks. - Alex Nowak; Soledad Villar; Afonso S. Bandeira; Joan Bruna (CoRR, 2017)

Projected Power Iteration for Network Alignment. - Efe Onaran; Soledad Villar (CoRR, 2017)

Probably certifiably correct k-means clustering. - Takayuki Iguchi; Dustin G. Mixon; Jesse Peterson; Soledad Villar (Math. Program., 2017)

Revised Note on Learning Quadratic Assignment with Graph Neural Networks. - Alex Nowak; Soledad Villar; Afonso S. Bandeira; Joan Bruna (DSW, 2018)

SUNLayer: Stable denoising with generative networks. - Dustin G. Mixon; Soledad Villar (CoRR, 2018)

Utility Ghost: Gamified redistricting with partisan symmetry. - Dustin G. Mixon; Soledad Villar (CoRR, 2018)

On the equivalence between graph isomorphism testing and function approximation with GNNs. - Zhengdao Chen; Soledad Villar; Lei Chen 062; Joan Bruna (NeurIPS, 2019)

Experimental performance of graph neural networks on random instances of max-cut. - Weichi Yao; Afonso S. Bandeira; Soledad Villar (CoRR, 2019)

Fair redistricting is hard. - Richard Kueng; Dustin G. Mixon; Soledad Villar (Theor. Comput. Sci., 2019)

Efficient Belief Propagation for Graph Matching. - Efe Onaran; Soledad Villar (ICASSP, 2020)

Can Graph Neural Networks Count Substructures? - Zhengdao Chen; Lei Chen 062; Soledad Villar; Joan Bruna (NeurIPS, 2020)

MREC: a fast and versatile framework for aligning and matching point clouds with applications to single cell molecular data. - Andrew J. Blumberg; Mathieu Carrière; Michael A. Mandell; Raul Rabadan; Soledad Villar (CoRR, 2020)

SqueezeFit: Label-Aware Dimensionality Reduction by Semidefinite Programming. - Culver McWhirter; Dustin G. Mixon; Soledad Villar (IEEE Trans. Inf. Theory, 2020)

A Short Tutorial on The Weisfeiler-Lehman Test And Its Variants. - Ningyuan Teresa Huang; Soledad Villar (ICASSP, 2021)

Scalars are universal: Equivariant machine learning, structured like classical physics. - Soledad Villar; David W. Hogg; Kate Storey-Fisher; Weichi Yao; Ben Blum-Smith (NeurIPS, 2021)

Fitting very flexible models: Linear regression with large numbers of parameters. - David W. Hogg; Soledad Villar (CoRR, 2021)

Scalars are universal: Gauge-equivariant machine learning, structured like classical physics. - Soledad Villar; David W. Hogg; Kate Storey-Fisher; Weichi Yao; Ben Blum-Smith (CoRR, 2021)

A simple equivariant machine learning method for dynamics based on scalars. - Weichi Yao; Kate Storey-Fisher; David W. Hogg; Soledad Villar (CoRR, 2021)

MarkerMap: nonlinear marker selection for single-cell studies. - Nabeel Sarwar; Wilson Gregory; George A. Kevrekidis; Soledad Villar; Bianca Dumitrascu (CoRR, 2022)

From Local to Global: Spectral-Inspired Graph Neural Networks. - Ningyuan Huang; Soledad Villar; Carey E. Priebe; Da Zheng; Chengyue Huang; Lin Yang 011; Vladimir Braverman (CoRR, 2022)

Equivariant maps from invariant functions. - Ben Blum-Smith; Soledad Villar (CoRR, 2022)

Shuffled linear regression through graduated convex relaxation. - Efe Onaran; Soledad Villar (CoRR, 2022)

Deep Learning is Provably Robust to Symmetric Label Noise. - Carey E. Priebe; Ningyuan Huang; Soledad Villar; Cong Mu; Li Chen (CoRR, 2022)

Graph Neural Networks for Community Detection on Sparse Graphs. - Luana Ruiz; Ningyuan Huang; Soledad Villar (CoRR, 2022)

Sketch-and-solve approaches to k-means clustering by semidefinite programming. - Charles Clum; Dustin G. Mixon; Soledad Villar; Kaiying Xie (CoRR, 2022)

Dimensionality Reduction, Regularization, and Generalization in Overparameterized Regressions. - Ningyuan Teresa Huang; David W. Hogg; Soledad Villar (SIAM J. Math. Data Sci., 2022)

Prospective Learning: Principled Extrapolation to the Future. - Ashwin De Silva; Rahul Ramesh; Lyle H. Ungar; Marshall G. Hussain Shuler; Noah J. Cowan; Michael L. Platt; Chen Li; Leyla Isik; Seung-Eon Roh; Adam S. Charles; Archana Venkataraman; Brian Caffo; et al. (CoLLAs, 2023)

The Second Learning on Graphs Conference: Preface. - Soledad Villar; Benjamin Paul Chamberlain; Yuanqi Du; Hannes Stärk; Chaitanya K. Joshi; Andreea Deac; Iulia Duta; Joshua Robinson 001; Yanqiao Zhu 001; Kexin Huang; Michelle M. Li; Sofia Bourhim; et al. (LoG, 2023)

Fine-grained Expressivity of Graph Neural Networks. - Jan Böker; Ron Levie; Ningyuan Huang; Soledad Villar; Christopher Morris 001 (NeurIPS, 2023)

Approximately Equivariant Graph Networks. - Ningyuan Huang; Ron Levie; Soledad Villar (NeurIPS, 2023)

The passive symmetries of machine learning. - Soledad Villar; David W. Hogg; Weichi Yao; George A. Kevrekidis; Bernhard Schölkopf (CoRR, 2023)

GeometricImageNet: Extending convolutional neural networks to vector and tensor images. - Wilson Gregory; David W. Hogg; Ben Blum-Smith; Maria Teresa Arias; Kaze W. K. Wong; Soledad Villar (CoRR, 2023)

Dimensionless machine learning: Imposing exact units equivariance. - Soledad Villar; Weichi Yao; David W. Hogg; Ben Blum-Smith; Bianca Dumitrascu (J. Mach. Learn. Res., 2023)

Universal Transferability for GNNs Via Graphons. - Mauricio Velasco; Kaiying O'Hare; Bernardo Rychtenberg; Soledad Villar (IEEECONF, 2024)

A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphs. - Luana Ruiz; Ningyuan Teresa Huang; Soledad Villar (ICASSP, 2024)

Structuring Representation Geometry with Rotationally Equivariant Contrastive Learning. - Sharut Gupta; Joshua Robinson 001; Derek Lim; Soledad Villar; Stefanie Jegelka (ICLR, 2024)

Position: Is machine learning good or bad for the natural sciences? - David W. Hogg; Soledad Villar (ICML, 2024)

Graph neural networks and non-commuting operators. - Mauricio Velasco; Kaiying O'Hare; Bernardo Rychtenberg; Soledad Villar (NeurIPS, 2024)

Learning functions on symmetric matrices and point clouds via lightweight invariant features. - Ben Blum-Smith; Ningyuan Huang; Marco Cuturi; Soledad Villar (CoRR, 2024)

Is machine learning good or bad for the natural sciences? - David W. Hogg; Soledad Villar (CoRR, 2024)

Learning equivariant tensor functions with applications to sparse vector recovery. - Wilson Gregory; Josué Tonelli-Cueto; Nicholas F. Marshall; Andrew S. Lee; Soledad Villar (CoRR, 2024)

Thinner Latent Spaces: Detecting dimension and imposing invariance through autoencoder gradient constraints. - George A. Kevrekidis; Mauro Maggioni; Soledad Villar; Yannis G. Kevrekidis (CoRR, 2024)

Towards fully covariant machine learning. - Soledad Villar; David W. Hogg; Weichi Yao; George A. Kevrekidis; Bernhard Schölkopf (Trans. Mach. Learn. Res., 2024)

Empirical Power Analysis of a Statistical Test to Quantify Gerrymandering. - Ranthony A. Clark; Susan Glenn; Harlin Lee; Soledad Villar (CoRR, 2025)

Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equations. - Trung V. Phan; George A. Kevrekidis; Soledad Villar; Yannis G. Kevrekidis; Juan M. Bello-Rivas (CoRR, 2025)

On Transferring Transferability: Towards a Theory for Size Generalization. - Eitan Levin; Yuxin Ma; Mateo Díaz; Soledad Villar (CoRR, 2025)