Topographic feature maps are low dimensional representations of data, that
preserve spatial dependencies. Current methods of training such maps (e.g. self
organizing maps - SOM, generative topographic maps) require centralized control
and synchronous execution, which restricts scalability. We present an algorithm
that uses $N$ autonomous units to generate a feature map by distributed
asynchronous training. Unit autonomy is achieved by sparse interaction in time
\& space through the combination of a distributed heuristic search, and a
cascade-driven weight updating scheme governed by two rules: a unit i) adapts
when it receives either a sample, or the weight vector of a neighbor, and ii)
broadcasts its weight vector to its neighbors after adapting for a predefined
number of times. Thus, a vector update can trigger an avalanche of adaptation.
We map avalanching to a statistical mechanics model, which allows us to
parametrize the statistical properties of cascading. Using MNIST, we
empirically investigate the effect of the heuristic search accuracy and the
cascade parameters on map quality. We also provide empirical evidence that
algorithm complexity scales at most linearly with system size $N$. The proposed
approach is found to perform comparably with similar methods in classification
tasks across multiple datasets.

提出一种基于自主单元、分布式异步训练、电路驱动的权重更新方案以及启发式搜索的算法，使得拓扑特征图的训练在无需中央控制和同步执行的条件下实现，可进行可扩展的大规模数据集处理，同时实验结果表明算法在多个数据集上的分类任务中性能表现稳定。