速度扭曲问题中临界缓慢的近乎地形学转变 (Critical Slowing Down Near Topological Transitions in Rate-Distortion Problems)

In Rate Distortion (RD) problems one seeks reduced representations of a source that meet a target distortion constraint. Such optimal representations undergo topological transitions at some critical rate values, when their cardinality or dimensionality change. We study the convergence time of the Arimoto-Blahut alternating projection algorithms, used to solve such problems, near those critical points, both for the Rate Distortion and Information Bottleneck settings. We argue that they suffer from Critical Slowing Down -- a diverging number of iterations for convergence -- near the critical points. This phenomenon can have theoretical and practical implications for both Machine Learning and Data Compression problems.

翻译：在调速器问题中,人们寻求减少达到目标扭曲限制的源的表示方式,这种最佳表示方式在主要或维度发生变化时,会以某些关键速率值进行地貌转变。我们研究了用于解决这些问题的Arimoto-Blahut交替预测算法的趋同时间,这些算法既针对调率扭曲,也针对信息瓶颈的临界点。我们争辩说,它们正经历着临界减速 -- -- 趋同的迭代数量不同 -- -- 接近临界点。这种现象可能会对机器学习和数据压缩问题产生理论和实际影响。