Research areas
- mathematics and optimization of deep neural networks
- numerical methods for nonlinear Partial Differential Equations and Optimal Transportation
- Multi-Resolution Continuous Normalizing Flows Vikram Voleti, Chris Finlay, Adam Oberman, Christopher Pal arxiv
- EuclidNets: An Alternative Operation for Efficient Inference of Deep Learning Models Xinlin Li and Mariana Parazeres and Adam M. Oberman and Alireza Ghaffari and Masoud Asgharian and Vahid Partovi Nia arXiv.2212.11803
- On the Generalization of Representations in Reinforcement Learning. Charline Le Lan, Stephen Tu, Adam Oberman, Rishabh Agarwal, Marc G. Bellemare: AISTATS 2022: 4132-4157 https://arxiv.org/abs/2203.00543
- FairCal: Fairness Calibration for Face Verification. Tiago Salvador, Stephanie Cairns, Vikram Voleti, Noah Marshall, Adam M. Oberman. ICLR 2022 https://arxiv.org/abs/2106.03761
- EuclidNets: Combining Hardware and Architecture Design for Efficient Training and Inference. Mariana Oliveira Prazeres, Xinlin Li, Adam M. Oberman, Vahid Partovi Nia. ICPRAM 2022: 141-151 https://arxiv.org/abs/2212.11803
- A Reproducible and Realistic Evaluation of Partial Domain Adaptation Methods. Tiago Salvador, Kilian Fatras, Ioannis Mitliagkas, and Adam Oberman. NeurIPS Distribution Shifts Workshop, 2022 https://arxiv.org/abs/2210.01210
- ImageNet-Cartoon and ImageNet-Drawing: two domain shift datasets for ImageNet. Tiago Salvador and Adam M. Oberman. ICML Shift Happens Workshop, 2022
- Score-based Denoising Diffusion with Non-Isotropic Gaussian Noise Models. Vikram Voleti, Christopher Pal, Adam Oberman. NeurIPS 2022 Workshop on Score-Based Methods https://arxiv.org/abs/2210.12254
- Improving Continuous Normalizing Flows using a Multi-Resolution Framework. Voleti, Vikram, Chris Finlay, Adam M. Oberman, and Christopher Pal. In ICML Workshop on Invertible Neural Networks, Normalizing Flows, and Explicit Likelihood Models.
- Stochastic Gradient Descent with Polyak's Learning Rate Mariana Prazeres, Adam Oberman Journal of Scientific Computing 89.1 (2021): 1-16. arxiv
- (workshop) Learning normalizing flows from Entropy-Kantorovich potentials Chris Finlay, Augusto Gerolin, Adam M Oberman, Aram-Alexandre Pooladian arxiv INNF+ 2021 workshop (2021)
- (Journal) Scaleable input gradient regularization for adversarial robustness Chris Finlay, Adam Oberman, Machine Learning with Applications (MLWA), 3 2021 arxiv github
- "Methods and systems for computing an output of a neural network layer". US Patent application 17/317,833 (filed May 11, 2021)
- (Journal and Conference) Nesterov's method with decreasing learning rate leads to accelerated stochastic gradient descent, Maxime Laborde, Adam Oberman arxiv (Older version: A Lyapunov analysis for accelerated gradient method: from deterministic to stochastic case, Maxime Laborde, Adam Oberman AISTATS 2020 (Proceedings of Machine Learning Research)
- (Conference) Calibrated Top-1 Uncertainty Estimates for classification by score based models Adam Oberman Chris Finlay, Alexander Iannantuono, Tiago Salvador arxiv spotlight presentation at Spotlight Talk at UDL ICML Workshop (140 accepted papers, 6 contributed talks, 8 spotlight talks).
- (Conference) How to train your neural ODE: the world of Jacobian and kinetic regularization Chris Finlay, Jorn-Henrik Jacobsen, Levon Nurbekyan, Adam Oberman arxiv ICML 2020
- (Conference) A principled approach for generating adversarial images under non-smooth dissimilarity metrics Aram-Alexandre Pooladian, Chris Finlay, Tim Hoheisel, Adam Oberman AISTATS 2020 (Proceedings of Machine Learning Research) arxiv
- (Journal and Conference) No collision transportation maps, Levon Nurbekyan, Alexander Iannantuono, Adam M. Oberman NeurIPS 2019 OTML workshop Journal of Scientific Computing 2020 arxiv
- (Journal) A regularization interpretation of the proximal point method for weakly convex functions Tim Hoheisel, Maxime Laborde, Adam Oberman Journal of Dynamics and Games 2020
- (Conference) Partial differential equation regularization for supervised machine learning, Adam Oberman 75 Years of Mathematicas of Computation Symposium (2020) AMS Contemporary Math arxiv
- (Journal) A Partial Differential Equation Obstacle problem for the Level Set Approach to Visibility Adam Oberman, Tiago Salvador; Journal Sci Computing (2020) arxiv
- (Conference) The LogBarrier adversarial attack: making effective use of decision boundary information Chris Finlay, Aram-Alexander Pooladian, Adam Oberman ICCV 2019 arxiv
- (Journal) Improved accuracy of monotone finite difference schemes on point clouds and regular grids Chris Finlay, Adam M. Oberman; SIAM SISC 2019 arxiv
- Parle: parallelizing stochastic gradient descent Pratik Chaudhari, Carlo Baldassi, Riccardo Zecchina, Stefano Soatto, Ameet Talwalkar, Adam Oberman SysML 2018 arxiv
- Stochastic Backward Euler: An Implicit Gradient Descent Algorithm for k-means Clustering Penghang Yin, Minh Pham, Adam Oberman, Stanley Osher; Journal of Scientific Computing 2018 arxiv
- Deep Relaxation: partial differential equations for optimizing deep neural networks Pratik Chaudhari, Adam M. Oberman, Stanley Osher, Stefano Soatto, Guillame Carlier; Research in Math Sciences 2018 arxiv
- Approximate Homogenization of fully nonlinear elliptic PDEs Chris Finlay and Adam M. Oberman; Journal of Scientific Computing 2018, arxiv
- Approximate Homogenization of convex nonlinear elliptic PDEs Chris Finlay and Adam M. Oberman; Comm Math Sci 2018, arxiv
- Numerical methods for motion of level sets by affine curvature Adam M. Oberman and Tiago Salvador; IMA Journal of Numerical Analysis, 2017. journal arxiv
- A partial differential equation for the rank one convex envelope Adam M. Oberman and Yuanlong Ruan; Archive for Rational Mechanics and Analysis arxiv ;
- A partial differential equation for the uniformly quasiconvex envelope Bilal Abbasi and Adam M. Oberman 2017; IMA Journal of Numerical Analysis journal arxiv
- Computing the quasiconvex envelope using a nonlocal solver Bilal Abbasi and Adam M. Oberman 2017; Journal of Scientific Computing arxiv
- Anomaly detection and classification for streaming data using partial differential equations Bilal Abbasi, Jeff Calder and Adam M Oberman, 2017; SIAM journal of Applied Math arxiv
- Numerical Methods for the two-Hessian elliptic partial differential equation Brittany D. Froese, Adam M. Oberman, Tiago Salvador; IMA Journal of Numerical Analysis, May 2016 journal arxiv
- A multigrid solver for the three dimensional Monge-Ampère equation Jun Liu, Brittany D. Froese, Adam M. Oberman, Mingqing Xiao; International Journal of Computer Mathematics, November 2016; journal arxiv
- Adaptive finite difference methods for nonlinear elliptic and parabolic partial differential equations with free boundaries Adam M. Oberman, Ian Zwiers; Journal of Scientific Computing, November 2015 arxiv JSC
- Filtered schemes for Hamilton-Jacobi equations: a simple construction of convergent accurate difference schemes with Tiago Salvador; Journal of Computational Physics Volume 284, 1 March 2015, pages 367-388; arxiv JCP
- Numerical methods for matching for teams and Wasserstein barycenters G. Carlier, A. Oberman and É. Oudet; ESAIM: Mathematical Modelling and Numerical Analysis (M2AN) 6 2015 1621-1642; arxiv M2AN
- Nonlinear elliptic PDEs on graphs with Juan Manfredi and Alex Sviridov; Differential and Integral Equations Volume 28 Numbers 1-2, January/February 2015. DIE Journal version, arxiv
- Solution of Optimal Transportation Problems Using a Multigrid Linear Programming Approach Adam M. Oberman, Yuanlong Ruan, 2020 Vol 38, pages 933-951, arxiv Journal of Computational Mathematics
- Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach Adam M. Oberman and Yanghong Huang; SIAM Journal of Numerical Analysis 2014 Volume 52, Issue 6, pp. 2599-3180 SINUM ; arxiv
- (with Jean-David Benamou and Brittany Froese) Numerical solution of the Optimal Transportation Problem using the Monge-Ampère equation Journal of Computational Physics Volume 260, 1 March 2014, Pages 107–126 arxiv ; JCP version
- (with Brittany Froese) Convergent Filtered Schemes for the Monge–Ampère Partial Differential Equation SIAM Journal on Numerical Analysis, 51(1):423–444, 2013. journal ; arxiv
- Finite Difference Methods for the infinity Laplace and p-Laplace equations Journal of Computational and Applied Mathematics, Volume 254, 15 December 2013, Pages 65–80 arxiv ; journal
- A numerical method for variational problems with convexity constraints. SIAM Journal on Scientific Computing Vol. 35, No. 1, A378-A396 arxiv ; SISC
- (with Brittany Froese) Convergent finite difference solvers for viscosity solutions of the elliptic Monge-Ampère equation in dimensions two and higher SIAM Journal on Numerical Analysis, 49(4):1692–1714, 2012. arxiv ; journal ;
- (with Rustum Choksi and Yves van Gennip) Anisotropic Total Variation Regularized L1-Approximation and Denoising/Deblurring of 2D Bar Codes Inverse Problems and Imaging, 5(3):591-617, 2011. arxiv.org ; Article
- (with Brittany Froese) Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation J. Comput. Phys. 230(3):818-834, 2011. Article ; arxiv.org
- (with Stan Osher, Ryo Takei, and Richard Tsai) Numerical methods for anisotropic Mean Curvature flow based on a discrete time variational formulation Comm. Math. Sci. 9(3) :637-662, 2011 Cam Report ; Article
- (with Luis Silvestre) The Dirichlet Problem for the Convex Envelope, Trans. Amer. Math. Soc 363(11) 5871-5886, 2011. Journal
- Convergence Rates for Difference Schemes for Polyhedral Nonlinear Parabolic Equations, . J. Comput. Math. Vol. 28, No.4, 2010, 474–488. Journal Version
- (with Jean-David Benamou and Brittany Froese) Two Numerical Methods for the Elliptic Monge-Ampère Equation, ESAIM: M2AN, Volume 44 (2010), Number 4, pp 737-758 Article ; journal link
- (with Brittany Froese) Numerical Averaging of Non-Divergence Structure Elliptic Operators, Comm. Math. Sci, Vol. 7 (2009), No. 4, pp 785-804 journal link
- (with Ryo Takei and Alexander Vladimirsky) Homogenization of Metric Hamilton-Jacobi Equations, SIAM Multiscale Modeling and Simulation, Vol. 8 Number 1 (2009) 269-295 Article ; journal link
- (with Diogo Gomes) Viscosity Solutions Methods for Converse KAM Theory, ESAIM: M2AN, Vol. 42 (2008) 1047-1064. journal link ;
- Computing the convex envelope using a nonlinear partial differential equation, Mathematical Models and Methods in Applied Sciences (M3AS), Vol. 18. No 5 (2008) 759-780 journal link
- Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian, Discrete and Continuous Dynamical Systems series B (DCDS B) Volume 10, Number 1, July 2008 (221-238) Project Page ; journal link ; Eigenvalues.pdf
- An explicit solution of the Lipschitz extension problem, Proc. Amer. Math. Soc. 136 (2008) 4329-4338. journal link ;
- The convex envelope is the solution of a nonlinear obstacle problem, Proc. Amer. Math. Soc. 135 (2007), no. 6, 1689–1694 journal link
- Convergent Difference Schemes for Nonlinear Elliptic and Parabolic Equations: Hamilton-Jacobi Equations and Free Boundary Problems, SIAM Journal on Numerical Analysis, Vol 44 (2006) No. 2 pp. 879-895. journal link
- A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions, Mathematics of Computation, 74 (2005) Number 251, 1217-1230. journal link
- A convergent monotone difference scheme for motion of level sets by mean curvature, Numerische Mathematik, Volume 99 (2004) Number 2 pages 365-379. journal link ;
- (with Robert McCann) Exact semigeostrophic flows in an elliptical basin, Nonlinearity, Volume 17 pages 1891-1922 (2004). journal link
- (with Diogo Gomes) Computing the effective Hamiltonian using a variational approach, SIAM Journal on Control and Optimization, Volume 43 (2004) Number 3 pages 793-812. journal link
- (with T. Zariphopoulou) Pricing early exercise contracts in incomplete markets, Computational Management Science, Vol 1 Issue 1 December (2003) pages 75-107. journal link
- (with P. Constantin, A. Kiselev, and L. Ryzhik) Bulk burning rate in passive-reactive diffusion, Archive for Rational Mechanics, 154 (2000), 53-91. journal link
- Improved Predictive Uncertainty using Corruption-based Calibration Tiago Salvador, Vikram Voleti, Alexander Iannantuono, Adam Oberman arxiv
- Lischitz regularized deep neural networks generalize and are adversarially robust, Chris Finlay, Jeff Calder, Bilal Abbasi, Adam M. Oberman arxiv
- Farkas layers: don't shift the data, fix the geometry, Aram-Alexandre Pooladian, Chris Finlay, Adam M. Oberman arxiv
- Deterministic Gaussian Averaged Networks, Ryan Campbell, Chris Finlay, Adam M Oberman arxiv
- Finite difference methods for fractional Laplacians Adam M. Oberman and Yanghong Huang arxiv
- Approximate Convex Hulls: sketching the convex hull using curvature Robert Graham, Adam M. Oberman arxiv