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Equivariant Architectures for Learning in Deep Weight Spaces
Aviv Navon · Aviv Shamsian · Idan Achituve · Ethan Fetaya · Gal Chechik · Haggai Maron

Wed Jul 26 08:04 PM -- 08:12 PM (PDT) @ Meeting Room 313

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

Author Information

Aviv Navon (Bar-Ilan University)
Aviv Shamsian (Bar Ilan University)
Idan Achituve (Bar-Ilan)
Ethan Fetaya (Bar-Ilan University)
Gal Chechik (NVIDIA / Bar-Ilan University)
Haggai Maron (NVIDIA Research)

I am a Research Scientist at NVIDIA Research. My main fields of interest are machine learning, optimization, and shape analysis. More specifically, I am working on applying deep learning to irregular domains (e.g., graphs, point clouds, and surfaces) and graph/shape matching problems. I completed my Ph.D. in 2019 at the Department of Computer Science and Applied Mathematics at the Weizmann Institute of Science under the supervision of Prof. Yaron Lipman.

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