Equivariant Architectures for Learning in Deep Weight Spaces

TL;DR

This paper introduces a novel neural network architecture designed to process deep weight spaces by leveraging permutation equivariance, enabling tasks like domain adaptation and object editing in function representations.

Contribution

It presents the first architecture for learning in deep weight spaces that is equivariant to permutation symmetries, with a full characterization of invariant and equivariant layers.

Findings

Outperforms baseline models in various learning tasks

Effectively encodes permutation symmetries in weight spaces

Demonstrates versatility in adapting pre-trained networks

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.