The translation of written language has been known since the 3rd century BC; however, its necessity has become increasingly common in the information age. Today, many translators exist, based on encoder-decoder deep architectures, nevertheless, no quantitative objective methods are available to assess their performance, likely because the entropy of even a single language remains unknown. This study presents a quantitative method for estimating translation entropy, with the following key finding. Given a translator, several sentences that differ by only one selected token of a given pivot sentence yield identical translations. Analyzing the statistics of this phenomenon across an ensemble of such sentences, consisting each of a pivot selected token, yields the probabilities of replacing this specific token with others while preserving the translation. These probabilities constitute the entropy of the selected token, and the average across all selected pivot tokens provides an estimate of the translator's overall translation entropy, which is enhanced along the decoder blocks. This entropic measure allows for the quantitative ranking of several publicly available translators and reveals whether mutual translation entropy is symmetric. Extending the proposed method to include the replacement of two tokens in a given pivot sentence demonstrates a multiplicative effect, where translation degeneracy is proportional to the product of the degeneracies of the two tokens. These findings establish translation entropy as a measurable property and objective benchmarking of artificial translators. Results are based on MarianMT, T5-Base and NLLB-200 translators.

翻译：书面语言的翻译自公元前3世纪以来便已存在；然而，在信息时代，其必要性日益凸显。如今，许多基于编码器-解码器深度架构的翻译系统已经问世，但尚无定量的客观方法来评估其性能，这可能是因为即使是单一语言的熵值也尚未被探明。本研究提出了一种估计翻译熵的定量方法，并得出以下关键发现。给定一个翻译系统，对于一个给定的枢轴句子，仅改变其中一个选定标记的若干句子会产生相同的翻译结果。通过分析由每个枢轴选定标记构成的此类句子集合中的统计现象，可以获得在保持翻译不变的情况下，将该特定标记替换为其他标记的概率。这些概率构成了选定标记的熵，而所有选定枢轴标记的平均值则提供了翻译系统整体翻译熵的估计值，该熵值沿解码器模块增强。这一熵度量允许对多个公开可用的翻译系统进行定量排序，并揭示互译熵是否具有对称性。将所提方法扩展至替换给定枢轴句子中的两个标记时，显示出一种乘性效应，即翻译简并度与两个标记简并度的乘积成正比。这些发现确立了翻译熵作为一种可测量的属性，并为人工翻译系统提供了客观的基准测试依据。研究结果基于MarianMT、T5-Base和NLLB-200翻译系统得出。