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Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i.e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in predictive error across tasks.
Author Information
Michael Poli (Stanford University)
Stefano Massaroli (Mila - Quebec AI Institute)
Federico Berto (KAIST)
Jinkyoo Park (KAIST)
Tri Dao (Stanford University)
Christopher Ré (Stanford)
Stefano Ermon (Stanford)
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Volodymyr Kuleshov · Stefano Ermon -
2016 : Invited Talk: You've been using asynchrony wrong your whole life! (Chris Re, Stanford) »
Christopher Ré -
2016 Poster: Cyclades: Conflict-free Asynchronous Machine Learning »
Xinghao Pan · Maximilian Lam · Stephen Tu · Dimitris Papailiopoulos · Ce Zhang · Michael Jordan · Kannan Ramchandran · Christopher Ré · Benjamin Recht -
2016 Poster: Solving Marginal MAP Problems with NP Oracles and Parity Constraints »
Yexiang Xue · zhiyuan li · Stefano Ermon · Carla Gomes · Bart Selman -
2016 Poster: Generative Adversarial Imitation Learning »
Jonathan Ho · Stefano Ermon -
2016 Poster: Variational Bayes on Monte Carlo Steroids »
Aditya Grover · Stefano Ermon -
2016 Poster: Sub-sampled Newton Methods with Non-uniform Sampling »
Peng Xu · Jiyan Yang · Farbod Roosta-Khorasani · Christopher Ré · Michael Mahoney -
2016 Poster: Adaptive Concentration Inequalities for Sequential Decision Problems »
Shengjia Zhao · Enze Zhou · Ashish Sabharwal · Stefano Ermon -
2015 Poster: Asynchronous stochastic convex optimization: the noise is in the noise and SGD don't care »
Sorathan Chaturapruek · John Duchi · Christopher Ré -
2015 Poster: Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width »
Christopher M De Sa · Ce Zhang · Kunle Olukotun · Christopher Ré -
2015 Spotlight: Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width »
Christopher M De Sa · Ce Zhang · Kunle Olukotun · Christopher Ré · Christopher Ré -
2015 Poster: Taming the Wild: A Unified Analysis of Hogwild-Style Algorithms »
Christopher M De Sa · Ce Zhang · Kunle Olukotun · Christopher Ré · Christopher Ré -
2014 Workshop: 4th Workshop on Automated Knowledge Base Construction (AKBC) »
Sameer Singh · Fabian M Suchanek · Sebastian Riedel · Partha Pratim Talukdar · Kevin Murphy · Christopher Ré · William Cohen · Tom Mitchell · Andrew McCallum · Jason E Weston · Ramanathan Guha · Boyan Onyshkevych · Hoifung Poon · Oren Etzioni · Ari Kobren · Arvind Neelakantan · Peter Clark -
2014 Poster: Parallel Feature Selection Inspired by Group Testing »
Yingbo Zhou · Utkarsh Porwal · Ce Zhang · Hung Q Ngo · XuanLong Nguyen · Christopher Ré · Venu Govindaraju -
2013 Workshop: Big Learning : Advances in Algorithms and Data Management »
Xinghao Pan · Haijie Gu · Joseph Gonzalez · Sameer Singh · Yucheng Low · Joseph Hellerstein · Derek G Murray · Raghu Ramakrishnan · Michael Jordan · Christopher Ré -
2013 Poster: Embed and Project: Discrete Sampling with Universal Hashing »
Stefano Ermon · Carla Gomes · Ashish Sabharwal · Bart Selman -
2012 Poster: Density Propagation and Improved Bounds on the Partition Function »
Stefano Ermon · Carla Gomes · Ashish Sabharwal · Bart Selman -
2011 Poster: Accelerated Adaptive Markov Chain for Partition Function Computation »
Stefano Ermon · Carla Gomes · Ashish Sabharwal · Bart Selman -
2011 Spotlight: Accelerated Adaptive Markov Chain for Partition Function Computation »
Stefano Ermon · Carla Gomes · Ashish Sabharwal · Bart Selman