超表达网络在信号表示与科学计算中表现更优。
Unveiling the Potential of Superexpressive Networks in Implicit Neural Representations
- 采用宽、深、高三维度结构的超表达网络
- 在图像与偏微分方程求解任务上超越现有隐式神经表示
- 适合从事视觉与科学机器学习的研究者参考
本研究考察了超表达网络在学习神经函数以表示复杂信号及执行下游机器学习任务中的潜力。重点评估其在计算机视觉和科学机器学习任务（包括信号表示/反问题及偏微分方程求解）中的表现。通过在多个基准任务上的实证分析，我们证明了由[Zhang et al., NeurIPS, 2022]提出的超表达网络——一种具有额外维度（即宽度、深度和‘高度’）的特殊网络结构——可超越使用高度专业化非线性激活函数的最新隐式神经表示方法。
原文摘要 · Abstract (English)
In this study, we examine the potential of one of the ``superexpressive'' networks in the context of learning neural functions for representing complex signals and performing machine learning downstream tasks. Our focus is on evaluating their performance on computer vision and scientific machine learning tasks including signal representation/inverse problems and solutions of partial differential equations. Through an empirical investigation in various benchmark tasks, we demonstrate that superexpressive networks, as proposed by [Zhang et al. NeurIPS, 2022], which employ a specialized network structure characterized by having an additional dimension, namely width, depth, and ``height'', can surpass recent implicit neural representations that use highly-specialized nonlinear activation functions.
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