部分共享的组合模型中表示和推理的复杂性
Complexity of Representation and Inference in Compositional Models with Part Sharing
摘要：
本文描述了串行和并行的多个对象的组成模型与部分共享。对象是由部件-子部件组合构建的，并以对象部件的层次字典表示。这些部分表示在大小递减的网格上，从而产生执行摘要描述。我们描述了这些模型的推理和学习算法。我们从计算时间（对于串行计算机）和节点数量（例如，“神经元”）用于并行计算机。特别是，我们计算的复杂性收益的部分共享和依赖的字典规模与层次结构的水平。我们探讨了三种制度的缩放行为，其中字典大小（i）随水平呈指数级增加，（ii）由应用于真实数据的无监督组合学习算法确定，（iii）随规模呈指数级下降。这一分析表明，在某些制度中，使用共享的部分，使算法，可以执行推理的时间线性的指数数量的对象的水平。在其他制度部分共享串行计算机几乎没有优势，但可以给并行计算机上的线性处理。
英文摘要：
This paper describes serial and parallel compositional models of multiple objects with part sharing. Objects are built by part-subpart compositions and expressed in terms of a hierarchical dictionary of object parts. These parts are represented on lattices of decreasing sizes which yield an executive summary description. We describe inference and learning algorithms for these models. We analyze the complexity of this model in terms of computation time (for serial computers) and numbers of nodes (e.g., "neurons") for parallel computers. In particular, we compute the complexity gains by part sharing and its dependence on how the dictionary scales with the level of the hierarchy. We explore three regimes of scaling behavior where the dictionary size (i) increases exponentially with the level, (ii) is determined by an unsupervised compositional learning algorithm applied to real data, (iii) decreases exponentially with scale. This analysis shows that in some regimes the use of shared parts enables algorithms which can perform inference in time linear in the number of levels for an exponential number of objects. In other regimes part sharing has little advantage for serial computers but can give linear processing on parallel computers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
