Timezone: »
Implicit-depth models such as Deep Equilibrium Networks have recently been shown to match or exceed the performance of traditional deep networks while being much more memory efficient. However, these models suffer from unstable convergence to a solution and lack guarantees that a solution exists. On the other hand, Neural ODEs, another class of implicit-depth models, do guarantee existence of a unique solution but perform poorly compared with traditional networks. In this paper, we develop a new class of implicit-depth model based on the theory of monotone operators, the Monotone Operator Equilibrium Network (monDEQ). We show the close connection between finding the equilibrium point of an implicit network and solving a form of monotone operator splitting problem, which admits efficient solvers with guaranteed, stable convergence. We then develop a parameterization of the network which ensures that all operators remain monotone, which guarantees the existence of a unique equilibrium point. Finally, we show how to instantiate several versions of these models, and implement the resulting iterative solvers, for structured linear operators such as multi-scale convolutions. The resulting models vastly outperform the Neural ODE-based models while also being more computationally efficient. Code is available at http://github.com/locuslab/monotoneopnet.
Author Information
Ezra Winston (Carnegie Mellon University)
J. Zico Kolter (Carnegie Mellon University / Bosch Center for AI)
Zico Kolter is an Assistant Professor in the School of Computer Science at Carnegie Mellon University, and also serves as Chief Scientist of AI Research for the Bosch Center for Artificial Intelligence. His work focuses on the intersection of machine learning and optimization, with a large focus on developing more robust, explainable, and rigorous methods in deep learning. In addition, he has worked on a number of application areas, highlighted by work on sustainability and smart energy systems. He is the recipient of the DARPA Young Faculty Award, and best paper awards at KDD, IJCAI, and PESGM.
Related Events (a corresponding poster, oral, or spotlight)
-
2020 Poster: Monotone operator equilibrium networks »
Tue Dec 8th 05:00 -- 07:00 PM Room Poster Session 1
More from the Same Authors
-
2020 Workshop: Machine Learning for Engineering Modeling, Simulation and Design »
Alex Beatson · Priya Donti · Amira Abdel-Rahman · Stephan Hoyer · Rose Yu · J. Zico Kolter · Ryan Adams -
2020 Poster: Community detection using fast low-cardinality semidefinite programming
 »
Po-Wei Wang · J. Zico Kolter -
2020 Poster: Deep Archimedean Copulas »
Chun Kai Ling · Fei Fang · J. Zico Kolter -
2020 Tutorial: (Track3) Deep Implicit Layers: Neural ODEs, Equilibrium Models, and Differentiable Optimization Q&A »
David Duvenaud · J. Zico Kolter · Matthew Johnson -
2020 Poster: Efficient semidefinite-programming-based inference for binary and multi-class MRFs »
Chirag Pabbaraju · Po-Wei Wang · J. Zico Kolter -
2020 Spotlight: Efficient semidefinite-programming-based inference for binary and multi-class MRFs »
Chirag Pabbaraju · Po-Wei Wang · J. Zico Kolter -
2020 Poster: Multiscale Deep Equilibrium Models »
Shaojie Bai · Vladlen Koltun · J. Zico Kolter -
2020 Poster: Denoised Smoothing: A Provable Defense for Pretrained Classifiers »
Hadi Salman · Mingjie Sun · Greg Yang · Ashish Kapoor · J. Zico Kolter -
2020 Oral: Multiscale Deep Equilibrium Models »
Shaojie Bai · Vladlen Koltun · J. Zico Kolter -
2020 Tutorial: (Track3) Deep Implicit Layers: Neural ODEs, Equilibrium Models, and Differentiable Optimization »
David Duvenaud · J. Zico Kolter · Matthew Johnson -
2019 Poster: Learning Stable Deep Dynamics Models »
J. Zico Kolter · Gaurav Manek -
2019 Poster: Adversarial Music: Real world Audio Adversary against Wake-word Detection System »
Juncheng Li · Shuhui Qu · Xinjian Li · Joseph Szurley · J. Zico Kolter · Florian Metze -
2019 Spotlight: Adversarial Music: Real world Audio Adversary against Wake-word Detection System »
Juncheng Li · Shuhui Qu · Xinjian Li · Joseph Szurley · J. Zico Kolter · Florian Metze -
2019 Poster: Differentiable Convex Optimization Layers »
Akshay Agrawal · Brandon Amos · Shane Barratt · Stephen Boyd · Steven Diamond · J. Zico Kolter -
2019 Poster: Uniform convergence may be unable to explain generalization in deep learning »
Vaishnavh Nagarajan · J. Zico Kolter -
2019 Poster: Deep Equilibrium Models »
Shaojie Bai · J. Zico Kolter · Vladlen Koltun -
2019 Spotlight: Deep Equilibrium Models »
Shaojie Bai · J. Zico Kolter · Vladlen Koltun -
2019 Oral: Uniform convergence may be unable to explain generalization in deep learning »
Vaishnavh Nagarajan · J. Zico Kolter -
2018 Poster: Differentiable MPC for End-to-end Planning and Control »
Brandon Amos · Ivan Jimenez · Jacob I Sacks · Byron Boots · J. Zico Kolter -
2018 Poster: End-to-End Differentiable Physics for Learning and Control »
Filipe de Avila Belbute-Peres · Kevin Smith · Kelsey Allen · Josh Tenenbaum · J. Zico Kolter -
2018 Spotlight: End-to-End Differentiable Physics for Learning and Control »
Filipe de Avila Belbute-Peres · Kevin Smith · Kelsey Allen · Josh Tenenbaum · J. Zico Kolter -
2018 Poster: Scaling provable adversarial defenses »
Eric Wong · Frank Schmidt · Jan Hendrik Metzen · J. Zico Kolter -
2018 Tutorial: Adversarial Robustness: Theory and Practice »
J. Zico Kolter · Aleksander Madry -
2017 Poster: Gradient descent GAN optimization is locally stable »
Vaishnavh Nagarajan · J. Zico Kolter -
2017 Oral: Gradient descent GAN optimization is locally stable »
Vaishnavh Nagarajan · J. Zico Kolter -
2017 Poster: Task-based End-to-end Model Learning in Stochastic Optimization »
Priya Donti · J. Zico Kolter · Brandon Amos -
2016 Poster: The Multiple Quantile Graphical Model »
Alnur Ali · J. Zico Kolter · Ryan Tibshirani -
2013 Workshop: Machine Learning for Sustainability »
Edwin Bonilla · Thomas Dietterich · Theodoros Damoulas · Andreas Krause · Daniel Sheldon · Iadine Chades · J. Zico Kolter · Bistra Dilkina · Carla Gomes · Hugo P Simao -
2011 Workshop: Machine Learning for Sustainability »
Thomas Dietterich · J. Zico Kolter · Matthew A Brown -
2011 Poster: The Fixed Points of Off-Policy TD »
J. Zico Kolter -
2011 Spotlight: The Fixed Points of Off-Policy TD »
J. Zico Kolter -
2010 Poster: Energy Disaggregation via Discriminative Sparse Coding »
J. Zico Kolter · Siddarth Batra · Andrew Y Ng -
2009 Mini Symposium: Machine Learning for Sustainability »
J. Zico Kolter · Thomas Dietterich · Andrew Y Ng -
2007 Spotlight: Hierarchical Apprenticeship Learning with Application to Quadruped Locomotion »
J. Zico Kolter · Pieter Abbeel · Andrew Y Ng -
2007 Poster: Hierarchical Apprenticeship Learning with Application to Quadruped Locomotion »
J. Zico Kolter · Pieter Abbeel · Andrew Y Ng