Neural Cellular Automata (NCA) have shown a remarkable ability to learn the
required rules to "grow" images, classify morphologies, segment images, as well
as to do general computation such as path-finding. We believe the inductive
prior they introduce lends itself to the generation of textures. Textures in
the natural world are often generated by variants of locally interacting
reaction-diffusion systems. Human-made textures are likewise often generated in
a local manner (textile weaving, for instance) or using rules with local
dependencies (regular grids or geometric patterns). We demonstrate learning a
texture generator from a single template image, with the generation method
being embarrassingly parallel, exhibiting quick convergence and high fidelity
of output, and requiring only some minimal assumptions around the underlying
state manifold. Furthermore, we investigate properties of the learned models
that are both useful and interesting, such as non-stationary dynamics and an
inherent robustness to damage. Finally, we make qualitative claims that the
behaviour exhibited by the NCA model is a learned, distributed, local algorithm
to generate a texture, setting our method apart from existing work on texture
generation. We discuss the advantages of such a paradigm.

本文利用神经元细胞自动机（NCA）算法实现了基于单个模板图像的纹理生成器，其中神经元细胞自动机算法提供了一种学习分布式本地算法生成纹理的范例，并具有高保真度和鲁棒性。

神经元细胞自动机纹理生成

Texture Generation with Neural Cellular Automata

Local Hebbian learning is believed to be inferior in performance to
end-to-end training using a backpropagation algorithm. We question this popular
belief by designing a local algorithm that can learn convolutional filters at
scale on large image datasets. These filters combined with patch normalization
and very steep non-linearities result in a good classification accuracy for
shallow networks trained locally, as opposed to end-to-end. The filters learned
by our algorithm contain both orientation selective units and unoriented color
units, resembling the responses of pyramidal neurons located in the cytochrome
oxidase 'interblob' and 'blob' regions in the primary visual cortex of
primates. It is shown that convolutional networks with patch normalization
significantly outperform standard convolutional networks on the task of
recovering the original classes when shadows are superimposed on top of
standard CIFAR-10 images. Patch normalization approximates the retinal
adaptation to the mean light intensity, important for human vision. We also
demonstrate a successful transfer of learned representations between CIFAR-10
and ImageNet 32x32 datasets. All these results taken together hint at the
possibility that local unsupervised training might be a powerful tool for
learning general representations (without specifying the task) directly from
unlabeled data.

本文提出了一种局部学习算法，结合图像数据和卷积滤波器、块归一化和非线性方法，可以成功地对 CIFAR-10 和 ImageNet 32x32 数据集进行分类，并展示了有关如何使用无标签数据从中学习通用表示的成功转移学习案例。

图像分析的本地无监督学习

Local Unsupervised Learning for Image Analysis

We present a local algorithm for finding dense subgraphs of bipartite graphs,
according to the definition of density proposed by Kannan and Vinay. Our
algorithm takes as input a bipartite graph with a specified starting vertex,
and attempts to find a dense subgraph near that vertex. We prove that for any
subgraph S with k vertices and density theta, there are a significant number of
starting vertices within S for which our algorithm produces a subgraph S' with
density theta / O(log n) on at most O(D k^2) vertices, where D is the maximum
degree. The running time of the algorithm is O(D k^2), independent of the
number of vertices in the graph.

本文提出一种用于寻找二分图中密集子图的本地算法，通过 Kannan 和 Vinay 提出的密度定义来衡量，在最多 O (Dk^2) 个顶点上，在密度 theta / O (log n) 的情况下找到最接近指定起始点的密集子图，算法的时间复杂度为 O (Dk^2)，与图中的顶点数无关。