We propose a novel approach to learning the generative neural fields
represented by linear combinations of implicit basis networks. Our algorithm
learns basis networks in the form of implicit neural representations and their
coefficients in a latent space by either conducting meta-learning or adopting
auto-decoding paradigms. The proposed method easily enlarges the capacity of
generative neural fields by increasing the number of basis networks while
maintaining the size of a network for inference to be small through their
weighted model averaging. Consequently, sampling instances using the model is
efficient in terms of latency and memory footprint. Moreover, we customize
denoising diffusion probabilistic model for a target task to sample latent
mixture coefficients, which allows our final model to generate unseen data
effectively. Experiments show that our approach achieves competitive generation
performance on diverse benchmarks for images, voxel data, and NeRF scenes
without sophisticated designs for specific modalities and domains.

我们提出了一种学习生成神经场的新方法，它由隐式基网络的线性组合表示。我们的算法通过进行元学习或采用自动解码范式来学习隐式神经表示的基网络及其在潜在空间中的系数。该方法通过增加基网络的数量，同时保持小型推断网络的规模，从而轻松扩大生成神经场的容量，而通过加权模型平均来采样模型实例在延迟和内存占用方面高效。此外，我们还为目标任务定制了去噪扩散概率模型，以采样潜在混合系数，从而使我们的最终模型能够有效地生成看不见的数据。实验证明，我们的方法在图像、体素数据和 NeRF 场景的各种基准测试上取得了有竞争力的生成性能，而无需复杂的特定模态和领域设计。

混合神经隐式函数生成神经场

Generative Neural Fields by Mixtures of Neural Implicit Functions

In federated learning, differences in the data or objectives between the
participating nodes motivate approaches to train a personalized machine
learning model for each node. One such approach is weighted averaging between a
locally trained model and the global model. In this theoretical work, we study
weighted model averaging for arbitrary scalar mean estimation problems under
minimal assumptions on the distributions. In a variant of the bias-variance
trade-off, we find that there is always some positive amount of model averaging
that reduces the expected squared error compared to the local model, provided
only that the local model has a non-zero variance. Further, we quantify the
(possibly negative) benefit of weighted model averaging as a function of the
weight used and the optimal weight. Taken together, this work formalizes an
approach to quantify the value of personalization in collaborative learning and
provides a framework for future research to test the findings in multivariate
parameter estimation and under a range of assumptions.

本文研究了加权模型平均对任意标量均值估计问题的影响，发现加权平均模型可以减少局部模型的期望平方误差，并量化了加权模型平均的（可能为负的）益处。这项研究正式确定了一种量化协作学习个性化价值的方法，并为未来多元参数估计和基于一系列假设的检验研究提供了框架。