Inspired by the versatility of sinusoidal representation networks (SIRENs),
we present a modified Guidance & Control Networks (G&CNETs) variant using
periodic activation functions in the hidden layers. We demonstrate that the
resulting G&CNETs train faster and achieve a lower overall training error on
three different control scenarios on which G&CNETs have been tested previously.
A preliminary analysis is presented in an attempt to explain the superior
performance of the SIREN architecture for the particular types of tasks that
G&CNETs excel on.

通过修改隐藏层中的周期性激活函数，我们演示了使用正弦表示网络（SIRENs）多功能性的指导与控制网络（G&CNETs）变种。我们展示了结果 G&CNETs 在三种不同的控制场景上训练更快并实现更低的整体训练误差，通过初步分析试图解释 SIREN 架构在 G&CNETs 擅长的特定任务类型上表现出色。

带周期激活函数的指导与控制网络

Guidance and Control Networks with Periodic Activation Functions

Implicitly defined, continuous, differentiable signal representations
parameterized by neural networks have emerged as a powerful paradigm, offering
many possible benefits over conventional representations. However, current
network architectures for such implicit neural representations are incapable of
modeling signals with fine detail, and fail to represent a signal's spatial and
temporal derivatives, despite the fact that these are essential to many
physical signals defined implicitly as the solution to partial differential
equations. We propose to leverage periodic activation functions for implicit
neural representations and demonstrate that these networks, dubbed sinusoidal
representation networks or Sirens, are ideally suited for representing complex
natural signals and their derivatives. We analyze Siren activation statistics
to propose a principled initialization scheme and demonstrate the
representation of images, wavefields, video, sound, and their derivatives.
Further, we show how Sirens can be leveraged to solve challenging boundary
value problems, such as particular Eikonal equations (yielding signed distance
functions), the Poisson equation, and the Helmholtz and wave equations. Lastly,
we combine Sirens with hypernetworks to learn priors over the space of Siren
functions.

提出了一种新的神经网络模型 —— 正弦表示网络，可以用于处理带有细节特征的复杂信号及其导数，可以解决泊松方程、赫姆霍兹方程、波动方程等各种边界值问题，并且可以通过超网络学习 Siren 函数的先验知识。