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：在扭曲率(RD)问题中,我们寻求减少一个达到目标扭曲限制的来源的表述,这种最佳表述在改变其基本或维度时,会发生一些关键率值的地形转变。我们研究了用于解决这些问题的Arimoto-Blahut交替投影算法的趋同时间,这些算法既用于计算率扭曲,也用于计算信息瓶颈设置的临界点。我们争辩说,它们受到临界减速 -- -- 趋同的迭代数不同 -- -- 的困扰,接近临界点。这一现象可能对机器学习和数据压缩问题产生理论和实践影响。