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NOTE: "binary cross-entropy" is a terminology used in Machine Learning field.


交叉熵 seems to mean "cross-entropy" in Mandarin Chinese. According to this page however, it expresses the "binary cross-entropy loss" as 交叉熵损失.

Also, according to Keras documentation on Chinese (Keras is a popular deep learning library on Python):

下面我们训练自编码器,来重构MNIST中的数字,这里使用逐像素的交叉熵作为损失函数,优化器为adam

However, it uses "binary cross-entropy" as a loss function.

Now, 交叉 means cross and 熵 means entropy. So there is no word for binary to be fit into. This page written in Chinese also shows it as "cross-entropy":

交叉熵(Cross-Entropy)

So I wonder if it is no problem to just use 交叉熵 to mean "binary cross-entropy". Or is there any other word to specifically mean "binary cross-entropy"? How about other jargons, such as "categorical cross-entropy"? If I use 交叉熵, does it always mean "binary cross-entropy"?

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    Not sure in your area. However, I have dealt with lots of binary files in my work. We translate the word binary to 二进制 in Chinese. So, binary file ==二进制文件, where you can only see 010101110000.... These files can be read/interpreted by specific machines or some decoding software. – dan Aug 17 '17 at 12:34
  • @dan Right, there should be something specifically related to it. That's why I wondered and asked it. Thank you for the insight. – Blaszard Aug 17 '17 at 12:50
  • What is the difference between "cross entropy" and "binary cross-entropy"? – fefe Sep 1 '17 at 6:53
  • I can no longer access the link to the Keras document – fefe Oct 2 '17 at 0:43
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I cannot find the Keras page you linked now. But I can still find the Keras document through search.

Binary cross entropy in the document is just a special case when the output can take only one of two classes. Make the context clear, there is no need to distinguish them in normal text. The mathematical formula of cross entropy just can deal with any number of classes (2 and above). So whether it is "binary" is implied in the problem you want to solve. There is no need to make it explicit.

So why the Keras documents explicitly distinguish them? This is because when the output can take only two classes, the input can take a different format than when there are multiple classes, and may save some space. So they have "binary_crossentropy" and "categorical_crossentropy", which deals with different input. Note that even you have only two classes, you can still use "categorical_crossentropy" by manipulating your input format to fit the requirements of "categorical_crossentropy".

As the translation, you may use "二类的交叉熵" and "多类的交叉熵". But these are only words that I coined up. There is no specific term for this, as this is only a software thing.

  • Very sorry, I overlooked this answer... It is actually a really good one. – Blaszard Mar 1 '18 at 14:00
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I happen to be a computer science guy and Chinese, so I think I may answer your question. Yes, your doubt is correct. These suppose to be an adjective for "binary". Using "交叉熵" as the translation for "binary cross-entropy" is not precise. "交叉熵" should be the translation for "cross-entropy".

I did some quick search, and it seems that there's no formal Chinese translation for the term "binary cross-entropy", may be because the term "binary cross-entropy" is not used as frequently as "cross-entropy". Also, I did not see a formal translation for the term "categorical cross-entropy". So, I guess you can use direct translation, such as "0-1交叉熵" or “二元交叉熵” for "binary cross entropy".

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"Binary" means 二元的 in Chinese. Such terminology appears at "binary tree"(二叉树, literally "two-forked tree"), "binary distribution"(二项分布, literally "two-item distribution").
Please provide the explanation of "binary" in the context of "binary cross-entropy loss function" and I'll update my answer.
P.S. I know a little about ML and DL, so don't be afraid of using ML-specific terminologies.

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