# Why is BCELoss used for multi-label classification?
**URL:**
**Author:**  [@acmc](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Fu%2Facmc)%5C
**Post date:** [October 4, 2024, 2:08pm UTC](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Ft%2Fwhy-is-bceloss-used-for-multi-label-classification%2F110131%2F1 "2024-10-04T14:08:13Z")
I was looking into the code for some models (e.g. [transformers/src/transformers/models/bert/modeling\_bert.py at de4112e4d20795b27bad0050e30f324a1a3a26f2 ¡ huggingface/transformers ¡ GitHub](https://github.com/huggingface/transformers/blob/de4112e4d20795b27bad0050e30f324a1a3a26f2/src/transformers/models/bert/modeling_bert.py#L1729)), and noticed this:
```py
elif self.config.problem_type == "single_label_classification":
loss_fct = CrossEntropyLoss()
loss = loss_fct(logits.view(-1, self.num_labels), labels.view(-1))
elif self.config.problem_type == "multi_label_classification":
loss_fct = BCEWithLogitsLoss()
loss = loss_fct(logits, labels)
```
I donât get why the code looks like this. If we have a binary classification problem, Iâd expect to use BCE there. Is this a bug or have I missed something?
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**Author:**  [@swtb](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Fu%2Fswtb)%5C
**Post date:** [October 7, 2024, 9:31am UTC](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Ft%2Fwhy-is-bceloss-used-for-multi-label-classification%2F110131%2F2 "2024-10-07T09:31:56Z")
[machine learning - Should I use a categorical cross-entropy or binary cross-entropy loss for binary predictions? - Cross Validated (stackexchange.com)](https://stats.stackexchange.com/questions/260505/should-i-use-a-categorical-cross-entropy-or-binary-cross-entropy-loss-for-binary#:~:text=Binary%20Cross%20Entropy%20is%20a%20special%20case)
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**Author:**  [@acmc](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Fu%2Facmc)%5C
**Post date:** [October 7, 2024, 12:06pm UTC](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Ft%2Fwhy-is-bceloss-used-for-multi-label-classification%2F110131%2F3 "2024-10-07T12:06:03Z")
Yes, exactly. Which just adds to my point. Why is BCE used when we have **2+ labels** , _i.e._, `"multi_label_classification"`?
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**Author:**  [@swtb](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Fu%2Fswtb)%5C
**Post date:** [October 12, 2024, 2:17pm UTC](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Ft%2Fwhy-is-bceloss-used-for-multi-label-classification%2F110131%2F4 "2024-10-12T14:17:32Z")
âFor multi-label classification, the idea is the same. But instead of say 3 labels to indicate 3 classes, we have 6 labels to indicate presence or absence of each class (class1=1, class1=0, class2=1, class2=0, class3=1, and class3=0). The loss then is the sum of cross-entropy loss for each of these 6 classes.â
According to this comment its still binary within each class.
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**Author:**  [@acmc](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Fu%2Facmc)%5C
**Post date:** [October 12, 2024, 7:37pm UTC](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Ft%2Fwhy-is-bceloss-used-for-multi-label-classification%2F110131%2F5 "2024-10-12T19:37:33Z")
Thanks for your answer. I appreciate you looking into this.
So â this is what I understand, feel free to correct my thinking:
My question is about why BCELoss is used for problems of type `multi-label-classification` (my assumption is that there may be 1+ true classes for a given data point).
A multi-label classifier would output O=(c\_1,c\_2,\dots,c\_n), c \in [0,1].
My intuition would be to apply CELoss as:
loss = - \sum\_{i}^{n} y\_i \* \log{c\_i}
I really canât see why this wouldnât work. Itâs the most standard formula ever.
Despite all, the implementation in HF Transformers uses a binary cross-entropy loss formula, which is a variation of the above for 2-label cases.
Then, you quote an answer in Cross Validated that says that you can reformulate a binary classification problem (e.g.):
> Is Schrodingerâs cat dead or alive?
BCEloss=reality \* \log{p(dead)} + (1 - reality) \* \log{p(alive)}
As:
CEloss=reality\_{dead} \* \log{p(dead)} + (1 - reality\_{dead}) \* \log{(1 - p(dead))} + reality\_{alive} \* \log{p(alive)} + (1 - reality\_{alive}) \* \log{(1 - p(alive))}
Ok. All good with this. I absolutely agree that you can do this and it works with multi-label classification, also expanded to 2+ classes. But my question, the one in the first message, is still **why canât you use the usual CE loss?**
I feel that youâre quoting that answer in Cross Validated as if it were obvious, but even if it may be obvious to you, it may not be obvious to everyone. I would really appreciate it if there was a bit more explanation, rather than copy-pasting as if somehow Iâd be able to read the mind of others đ˘
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**Author:**  [@DhineshR](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Fu%2FDhineshR)%5C
**Post date:** [August 8, 2026, 11:48pm UTC](/static-proxy?url=https%3A%2F%2Fdiscuss.huggingface.co%2Ft%2Fwhy-is-bceloss-used-for-multi-label-classification%2F110131%2F6 "2026-08-08T23:48:59Z")
This is a bit late, but Iâd still share my answer. There is a difference between multi-label and multi-class classification. In multi-label classification, the output is not probability distribution of one random variable that cross-entropy consumes as input to compare against target distribution. Sum of predicted probabilities of output classes need not sum up to one in multi-label classification. Each output is positive class probability, hence BCEloss is applied to each output independently.