The Trouble with von Koch Curves Built from ngons. - Tamás Keleti; Elliot Paquette (Am. Math. Mon., 2010)

The Threshold for Integer Homology in Random d-Complexes. - Christopher Hoffman; Matthew Kahle; Elliot Paquette (Discret. Comput. Geom., 2017)

Universality for the conjugate gradient and MINRES algorithms on sample covariance matrices. - Elliot Paquette; Thomas Trogdon (CoRR, 2020)

Surjectivity of near-square random matrices. - Hoi H. Nguyen; Elliot Paquette (Comb. Probab. Comput., 2020)

SGD in the Large: Average-case Analysis, Asymptotics, and Stepsize Criticality. - Courtney Paquette; Kiwon Lee; Fabian Pedregosa; Elliot Paquette (COLT, 2021)

Dynamics of Stochastic Momentum Methods on Large-scale, Quadratic Models. - Courtney Paquette; Elliot Paquette (NeurIPS, 2021)

Trajectory of Mini-Batch Momentum: Batch Size Saturation and Convergence in High Dimensions. - Kiwon Lee; Andrew N. Cheng; Elliot Paquette; Courtney Paquette (NeurIPS, 2022)

Implicit Regularization or Implicit Conditioning? Exact Risk Trajectories of SGD in High Dimensions. - Courtney Paquette; Elliot Paquette; Ben Adlam; Jeffrey Pennington (NeurIPS, 2022)

Fitting an ellipsoid to a quadratic number of random points. - Afonso S. Bandeira; Antoine Maillard; Shahar Mendelson; Elliot Paquette (CoRR, 2023)

Differentially Private Linear Regression with Linked Data. - Shurong Lin; Elliot Paquette; Eric D. Kolaczyk (CoRR, 2023)

Hitting the High-Dimensional Notes: An ODE for SGD learning dynamics on GLMs and multi-index models. - Elizabeth Collins-Woodfin; Courtney Paquette; Elliot Paquette; Inbar Seroussi (CoRR, 2023)

Halting Time is Predictable for Large Models: A Universality Property and Average-Case Analysis. - Courtney Paquette; Bart van Merriënboer; Elliot Paquette; Fabian Pedregosa (Found. Comput. Math., 2023)

Uniqueness in Nuclear Norm Minimization: Flatness of the Nuclear Norm Sphere and Simultaneous Polarization. - Tim Hoheisel; Elliot Paquette (J. Optim. Theory Appl., 2023)

The High Line: Exact Risk and Learning Rate Curves of Stochastic Adaptive Learning Rate Algorithms. - Elizabeth Collins-Woodfin; Inbar Seroussi; Begoña García Malaxechebarría; Andrew W. Mackenzie; Elliot Paquette; Courtney Paquette (NeurIPS, 2024)

4+3 Phases of Compute-Optimal Neural Scaling Laws. - Elliot Paquette; Courtney Paquette; Lechao Xiao; Jeffrey Pennington (NeurIPS, 2024)

A Clipped Trip: the Dynamics of SGD with Gradient Clipping in High-Dimensions. - Noah Marshall; Ke Liang Xiao; Atish Agarwala; Elliot Paquette (CoRR, 2024)

Exact Risk Curves of signSGD in High-Dimensions: Quantifying Preconditioning and Noise-Compression Effects. - Ke Liang Xiao; Noah Marshall; Atish Agarwala; Elliot Paquette (CoRR, 2024)

To Clip or not to Clip: the Dynamics of SGD with Gradient Clipping in High-Dimensions. - Noah Marshall; Ke Liang Xiao; Atish Agarwala; Elliot Paquette (ICLR, 2025)

Dimension-adapted Momentum Outscales SGD. - Damien Ferbach; Katie Everett; Gauthier Gidel; Elliot Paquette; Courtney Paquette (CoRR, 2025)