Expressive Sign Equivariant Networks for Spectral Geometric Learning
This work addresses a theoretical bottleneck in spectral geometric learning for researchers and practitioners in machine learning, offering a novel architectural solution with provable expressiveness.
The paper tackles the limitation of sign invariance in machine learning models for eigenvectors by proposing sign equivariant neural networks, which achieve improved performance in tasks like building orthogonally equivariant models and learning node positional encodings for link prediction in graphs.
Recent work has shown the utility of developing machine learning models that respect the structure and symmetries of eigenvectors. These works promote sign invariance, since for any eigenvector v the negation -v is also an eigenvector. However, we show that sign invariance is theoretically limited for tasks such as building orthogonally equivariant models and learning node positional encodings for link prediction in graphs. In this work, we demonstrate the benefits of sign equivariance for these tasks. To obtain these benefits, we develop novel sign equivariant neural network architectures. Our models are based on a new analytic characterization of sign equivariant polynomials and thus inherit provable expressiveness properties. Controlled synthetic experiments show that our networks can achieve the theoretically predicted benefits of sign equivariant models. Code is available at https://github.com/cptq/Sign-Equivariant-Nets.