自相似先验：作为可微分形表示的神经拼贴
Self-Similarity Priors: Neural Collages as Differentiable Fractal Representations
摘要：
自然界中的许多模式都表现出自相似性：它们可以通过自指变换来描述。所述图案通常出现在自然和人造物体中，例如分子、海岸线、星系甚至图像。在这项工作中，我们研究了学习的作用，在自动发现的自相似性，并在其利用下游任务。为此，我们设计了一类新的隐式运算符，神经拼贴，它（1）将数据表示为自引用结构化变换的参数，（2）采用超网络将查找这些参数的成本分摊到单个前向传递中。我们研究如何在各种任务中利用神经拼贴产生的表示，包括数据压缩和生成。神经拼贴图像压缩器在编码过程中比其他基于自相似性的算法快几个数量级，并提供与隐式方法竞争的压缩率。最后，我们展示了神经拼贴在分形艺术和深度生成模型中的应用。
英文摘要：
Many patterns in nature exhibit self-similarity: they can be compactly described via self-referential transformations. Said patterns commonly appear in natural and artificial objects, such as molecules, shorelines, galaxies and even images. In this work, we investigate the role of learning in the automated discovery of self-similarity and in its utilization for downstream tasks. To this end, we design a novel class of implicit operators, Neural Collages, which (1) represent data as the parameters of a self-referential, structured transformation, and (2) employ hypernetworks to amortize the cost of finding these parameters to a single forward pass. We investigate how to leverage the representations produced by Neural Collages in various tasks, including data compression and generation. Neural Collages image compressors are orders of magnitude faster than other self-similarity-based algorithms during encoding and offer compression rates competitive with implicit methods. Finally, we showcase applications of Neural Collages for fractal art and as deep generative models.
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