← 研踪 PaperTrailarXiv:2611.01530 · v1
Learning Gradients of Homogeneous Functions
首次提交 2026-11-01 12:01
版本更新 2026-11-01 12:01
雷达观测 2026-11-04 23:43
摘要
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.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-01 12:01 · 最新观测版本
Learning Gradients of Homogeneous Functions
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.
查看此版本解读 →查看此版本原文 ↗