Coordinate networks are widely used in computer vision due to their ability
to represent signals as compressed, continuous entities. However, training
these networks with first-order optimizers can be slow, hindering their use in
real-time applications. Recent works have opted for shallow voxel-based
representations to achieve faster training, but this sacrifices memory
efficiency. This work proposes a solution that leverages second-order
optimization methods to significantly reduce training times for coordinate
networks while maintaining their compressibility. Experiments demonstrate the
effectiveness of this approach on various signal modalities, such as audio,
images, videos, shape reconstruction, and neural radiance fields.

本文提出了一种利用二阶优化方法显著减少坐标网络训练时间并维护其可压缩性的解决方案，并在各种信号模态（如音频、图像、视频、形状重构和神经辐射场）上证明了其有效性。

曲率感知坐标网络的训练

Curvature-Aware Training for Coordinate Networks

Coordinate networks like Multiplicative Filter Networks (MFNs) and BACON
offer some control over the frequency spectrum used to represent continuous
signals such as images or 3D volumes. Yet, they are not readily applicable to
problems for which coarse-to-fine estimation is required, including various
inverse problems in which coarse-to-fine optimization plays a key role in
avoiding poor local minima. We introduce a new coordinate network architecture
and training scheme that enables coarse-to-fine optimization with fine-grained
control over the frequency support of learned reconstructions. This is achieved
with two key innovations. First, we incorporate skip connections so that
structure at one scale is preserved when fitting finer-scale structure. Second,
we propose a novel initialization scheme to provide control over the model
frequency spectrum at each stage of optimization. We demonstrate how these
modifications enable multiscale optimization for coarse-to-fine fitting to
natural images. We then evaluate our model on synthetically generated datasets
for the the problem of single-particle cryo-EM reconstruction. We learn high
resolution multiscale structures, on par with the state-of-the art.

通过引入跳连接和新的初始化方案，我们提出了一种新的坐标网络架构和训练方案，实现了对学习重建的频率支持的细粒度控制，并在多尺度优化的背景下解决了粗到中等估计的问题，该方法在单粒子冷冻电镜重建的实验中，取得了与最先进技术相媲美的高分辨率多尺度结构。