Timezone: »
Recent methods in geometric deep learning have introduced various neural networks to operate over data that lie on Riemannian manifolds. These methods are often inspired by and directly generalize standard Euclidean neural networks. However, extending Euclidean networks is difficult and has only been done for a select few manifolds. In this work, we examine the residual neural network (ResNet) and show how to extend this construction to general Riemannian manifolds in a geometrically principled manner. Originally introduced to help solve the vanishing gradient problem, ResNets have become ubiquitous in machine learning due to their beneficial learning properties, excellent empirical results, and easy-to-incorporate nature when building varied neural networks. We find that our Riemannian ResNets mirror these desirable properties: when compared to existing manifold neural networks designed to learn over hyperbolic space and the manifold of symmetric positive definite matrices, we outperform both kinds of networks in terms of relevant testing metrics and training dynamics.
Author Information
Isay Katsman (Cornell University)
Eric Chen (Cornell University)
Sidhanth Holalkere (Cornell University)
Aaron Lou (Stanford University)
Ser Nam Lim (Meta AI)
Christopher De Sa (Cornell)
More from the Same Authors
-
2021 : Equivariant Manifold Flows »
Isay Katsman -
2023 Poster: Graph Inductive Biases in Transformers without Message Passing »
Liheng Ma · Chen Lin · Derek Lim · Adriana Romero Soriano · Puneet Dokania · Mark Coates · Phil Torr · Ser Nam Lim -
2023 Poster: Reflected Diffusion Models »
Aaron Lou · Stefano Ermon -
2022 : MCTensor: A High-Precision Deep Learning Library with Multi-Component Floating-Point »
Tao Yu · Wentao Guo · Canal Li · Tiancheng Yuan · Christopher De Sa -
2022 : Neural Geometric Embedding Flows »
Aaron Lou · Yang Song · Jiaming Song · Stefano Ermon -
2022 Poster: Low-Precision Stochastic Gradient Langevin Dynamics »
Ruqi Zhang · Andrew Wilson · Christopher De Sa -
2022 Spotlight: Low-Precision Stochastic Gradient Langevin Dynamics »
Ruqi Zhang · Andrew Wilson · Christopher De Sa -
2021 Poster: Variance Reduced Training with Stratified Sampling for Forecasting Models »
Yucheng Lu · Youngsuk Park · Lifan Chen · Yuyang Wang · Christopher De Sa · Dean Foster -
2021 Spotlight: Variance Reduced Training with Stratified Sampling for Forecasting Models »
Yucheng Lu · Youngsuk Park · Lifan Chen · Yuyang Wang · Christopher De Sa · Dean Foster -
2021 Poster: Low-Precision Reinforcement Learning: Running Soft Actor-Critic in Half Precision »
Johan Björck · Xiangyu Chen · Christopher De Sa · Carla Gomes · Kilian Weinberger -
2021 Spotlight: Low-Precision Reinforcement Learning: Running Soft Actor-Critic in Half Precision »
Johan Björck · Xiangyu Chen · Christopher De Sa · Carla Gomes · Kilian Weinberger -
2021 Poster: Optimal Complexity in Decentralized Training »
Yucheng Lu · Christopher De Sa -
2021 Oral: Optimal Complexity in Decentralized Training »
Yucheng Lu · Christopher De Sa -
2020 Poster: Moniqua: Modulo Quantized Communication in Decentralized SGD »
Yucheng Lu · Christopher De Sa -
2020 Poster: Differentiating through the Fréchet Mean »
Aaron Lou · Isay Katsman · Qingxuan Jiang · Serge Belongie · Ser Nam Lim · Christopher De Sa -
2019 Poster: Distributed Learning with Sublinear Communication »
Jayadev Acharya · Christopher De Sa · Dylan Foster · Karthik Sridharan -
2019 Oral: Distributed Learning with Sublinear Communication »
Jayadev Acharya · Christopher De Sa · Dylan Foster · Karthik Sridharan -
2019 Poster: SWALP : Stochastic Weight Averaging in Low Precision Training »
Guandao Yang · Tianyi Zhang · Polina Kirichenko · Junwen Bai · Andrew Wilson · Christopher De Sa -
2019 Poster: A Kernel Theory of Modern Data Augmentation »
Tri Dao · Albert Gu · Alexander J Ratner · Virginia Smith · Christopher De Sa · Christopher Re -
2019 Poster: Improving Neural Network Quantization without Retraining using Outlier Channel Splitting »
Ritchie Zhao · Yuwei Hu · Jordan Dotzel · Christopher De Sa · Zhiru Zhang -
2019 Oral: SWALP : Stochastic Weight Averaging in Low Precision Training »
Guandao Yang · Tianyi Zhang · Polina Kirichenko · Junwen Bai · Andrew Wilson · Christopher De Sa -
2019 Oral: Improving Neural Network Quantization without Retraining using Outlier Channel Splitting »
Ritchie Zhao · Yuwei Hu · Jordan Dotzel · Christopher De Sa · Zhiru Zhang -
2019 Oral: A Kernel Theory of Modern Data Augmentation »
Tri Dao · Albert Gu · Alexander J Ratner · Virginia Smith · Christopher De Sa · Christopher Re -
2018 Poster: Minibatch Gibbs Sampling on Large Graphical Models »
Christopher De Sa · Vincent Chen · Wong -
2018 Oral: Minibatch Gibbs Sampling on Large Graphical Models »
Christopher De Sa · Vincent Chen · Wong -
2018 Poster: Representation Tradeoffs for Hyperbolic Embeddings »
Frederic Sala · Christopher De Sa · Albert Gu · Christopher Re -
2018 Oral: Representation Tradeoffs for Hyperbolic Embeddings »
Frederic Sala · Christopher De Sa · Albert Gu · Christopher Re