Learning Gradients of Homogeneous Functions
Abstract
Homogeneous gradient functions have widespread significance, including applications in maximum energy subspace selection and retrieval problems. Euler's homogeneous function theorem specifies how the potential associated with a positively k-homogeneous gradient field can be recovered directly from the field itself. We use Euler's theorem to build on GradNets and propose a homogeneous gradient network architecture that is guaranteed to correspond to the gradient of a homogeneous function. Then, we describe how monotone homogeneous GradNets universally approximate the gradients of k-homogeneous convex functions. The inductive bias of homogeneous GradNets enables them to outperform baseline ICNNs by up to 7dB in our max energy subspace projection experiment and by up to 13% higher accuracy, 98% fewer parameters, and 70% fewer FLOPS in our amortized inner product search experiment.
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BibTeX
@misc{gowda2026learning,
title = {{Learning Gradients of Homogeneous Functions}},
author = {Mayur S. Gowda and Srinivasa Pranav and Shreyas Chaudhari and José M. F. Moura},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01530},
eprint = {2611.01530},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01530},
}
RIS
TY - UNPB
TI - Learning Gradients of Homogeneous Functions
AU - Mayur S. Gowda
AU - Srinivasa Pranav
AU - Shreyas Chaudhari
AU - José M. F. Moura
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01530
UR - https://arxiv.org/abs/2611.01530
AB - Homogeneous gradient functions have widespread significance, including applications in maximum energy subspace selection and retrieval problems. Euler's homogeneous function theorem specifies how the potential associated with a positively k-homogeneous gradient field can be recovered directly from the field itself. We use Euler's theorem to build on GradNets and propose a homogeneous gradient network architecture that is guaranteed to correspond to the gradient of a homogeneous function. Then, we describe how monotone homogeneous GradNets universally approximate the gradients of k-homogeneous convex functions. The inductive bias of homogeneous GradNets enables them to outperform baseline ICNNs by up to 7dB in our max energy subspace projection experiment and by up to 13% higher accuracy, 98% fewer parameters, and 70% fewer FLOPS in our amortized inner product search experiment.
ER -