Equivariant Architectures for Learning in Deep Weight Spaces

• URL: http://arxiv.org/abs/2301.12780v2
• Date: Wed, 31 May 2023 19:24:08 GMT
• Title: Equivariant Architectures for Learning in Deep Weight Spaces
• Authors: Aviv Navon, Aviv Shamsian, Idan Achituve, Ethan Fetaya, Gal Chechik, Haggai Maron
• Abstract summary: We present a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trainedvariant. We show how these layers can be implemented using three basic operations.
• Score: 54.61765488960555
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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