Equivariant Architectures for Learning in Deep Weight Spaces
This work addresses the problem of learning in deep weight spaces, which could enable tasks like adapting pre-trained networks or editing neural representations, but it is an incremental step as it focuses on a specific architecture for MLPs.
The paper tackles the challenge of designing machine learning architectures that process neural networks in their raw weight matrix form by introducing a novel network architecture that is equivariant to the permutation symmetries of MLP weights, demonstrating its effectiveness in various learning tasks.
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.