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README.md
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---
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license: mit
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language:
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- zh
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pipeline_tag: sentence-similarity
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tags:
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- sentence-transformers
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---
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<h1 align="center">FlagEmbedding</h1>
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<h4 align="center">
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<p>
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<a href=#model-list>Model List</a> |
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<a href=#usage>Usage</a> |
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<a href="#evaluation">Evaluation</a> |
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<a href="#train">Train</a> |
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<p>
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</h4>
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More details please refer to our Github: [FlagEmbedding](https://github.com/FlagOpen/FlagEmbedding).
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[English](README.md) | [中文](https://github.com/FlagOpen/FlagEmbedding/blob/master/README_zh.md)
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And it also can be used in vector database for LLMs.
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************* 🌟**Updates**🌟 *************
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- 08/09/2023: BGE Models are integrated into **Langchain**, you can use it like [
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- 08/05/2023: Release base-scale and small-scale models, **best performance among the models of the same size 🤗**
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- 08/02/2023: Release `bge-large-*`(short for BAAI General Embedding) Models, **rank 1st on MTEB and C-MTEB benchmark!**
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- 08/01/2023: We release the [Chinese Massive Text Embedding Benchmark](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB) (**C-MTEB**), consisting of 31 test dataset.
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| Model | Language | Description | query instruction for retrieval\* |
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|:-------------------------------|:--------:| :--------:| :--------:|
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| [BAAI/bge-large-en](https://huggingface.co/BAAI/bge-large-en) | English | rank **1st** in [MTEB](https://huggingface.co/spaces/mteb/leaderboard) leaderboard | `Represent this sentence for searching relevant passages: ` |
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| [BAAI/bge-base-en](https://huggingface.co/BAAI/bge-base-en) | English | rank **2nd** in [MTEB](https://huggingface.co/spaces/mteb/leaderboard) leaderboard | `Represent this sentence for searching relevant passages: ` |
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| [BAAI/bge-small-en](https://huggingface.co/BAAI/bge-small-en) | English | a small-scale model but with competitive performance | `Represent this sentence for searching relevant passages: ` |
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| [BAAI/bge-large-zh](https://huggingface.co/BAAI/bge-large-zh) | Chinese | rank **1st** in [C-MTEB](https://github.com/FlagOpen/FlagEmbedding/tree/master/C_MTEB) benchmark | `为这个句子生成表示以用于检索相关文章:` |
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| [BAAI/bge-large-zh-noinstruct](https://huggingface.co/BAAI/bge-large-zh-noinstruct) | Chinese | This model is trained without instruction, and rank **2nd** in [C-MTEB](https://github.com/FlagOpen/FlagEmbedding/tree/master/C_MTEB) benchmark | |
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| [BAAI/bge-base-zh](https://huggingface.co/BAAI/bge-base-zh) | Chinese | a base-scale model but has similar ability with `bge-large-zh` | `为这个句子生成表示以用于检索相关文章:` |
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| [BAAI/bge-small-zh](https://huggingface.co/BAAI/bge-small-zh) | Chinese | a small-scale model but with competitive performance | `为这个句子生成表示以用于检索相关文章:` |
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\*: If you need to search the **long** relevant passages to a **short** query (s2p retrieval task), you need to add the instruction to the query; in other cases, no instruction is needed, just use the original query directly. In all cases, **no instruction** need to be added to passages.
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## Usage
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Here are some examples to use `bge` models with
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```python
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from FlagEmbedding import FlagModel
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model = FlagModel('BAAI/bge-large-zh', query_instruction_for_retrieval="为这个句子生成表示以用于检索相关文章:")
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embeddings_1 = model.encode(
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embeddings_2 = model.encode(
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similarity = embeddings_1 @ embeddings_2.T
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print(similarity)
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The value of argument `query_instruction_for_retrieval` see [Model List](https://github.com/FlagOpen/FlagEmbedding/tree/master#model-list).
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FlagModel will use all available GPUs when encoding, please set `os.environ["CUDA_VISIBLE_DEVICES"]` to choose GPU.
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#### Using Sentence-Transformers
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```
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```python
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from sentence_transformers import SentenceTransformer
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model = SentenceTransformer('BAAI/bge-large-zh')
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embeddings_1 = model.encode(
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embeddings_2 = model.encode(
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similarity = embeddings_1 @ embeddings_2.T
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print(similarity)
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```
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model_name = "BAAI/bge-small-en"
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model_kwargs = {'device': 'cuda'}
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encode_kwargs = {'normalize_embeddings': True} # set True to compute cosine similarity
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model_name=model_name,
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model_kwargs=model_kwargs,
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encode_kwargs=encode_kwargs
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)
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```
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We employ the cross-device negatives sharing method to share negatives among different GPUs,
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which can dramatically **increase the number of negatives**.
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We trained our model on 48 A100(40G) GPUs with a large batch size of 32,
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We used the AdamW optimizer and the learning rate is 1e-5.
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The temperature for contrastive loss is 0.01.
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- For English, we collect 230M text pairs from [wikipedia](https://huggingface.co/datasets/wikipedia), [cc-net](https://github.com/facebookresearch/cc_net), and so on.
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- For chinese, we collect 120M text pairs from [wudao](https://github.com/BAAI-WuDao/Data), [simclue](https://github.com/CLUEbenchmark/SimCLUE) and so on.
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**The data collection is to be released in the future.**
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We will continually update the embedding models and training codes,
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hoping to promote the development of the embedding model community.
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## License
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FlagEmbedding is licensed under [MIT License](https://github.com/FlagOpen/FlagEmbedding/blob/master/LICENSE). The released models can be used for commercial purposes free of charge.
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<h1 align="center">FlagEmbedding</h1>
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<p align="center">
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<a href="https://github.com/FlagOpen/FlagEmbedding">
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<img alt="Build" src="https://img.shields.io/badge/Contribution-Welcome-blue">
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</a>
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<a href="https://github.com/FlagOpen/FlagEmbedding/blob/master/LICENSE">
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<img alt="License" src="https://img.shields.io/badge/LICENSE-MIT-green">
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</a>
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<a href="https://huggingface.co/C-MTEB">
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<img alt="Build" src="https://img.shields.io/badge/C_MTEB-🤗-yellow">
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</a>
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<a href="https://github.com/FlagOpen/FlagEmbedding/tree/master/FlagEmbedding/baai_general_embedding">
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<img alt="Build" src="https://img.shields.io/badge/FlagEmbedding-1.0-red">
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</a>
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</p>
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<h4 align="center">
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<p>
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<a href=#model-list>Model List</a> |
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<a href=#frequently-asked-questions>FAQ</a> |
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<a href=#usage>Usage</a> |
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<a href="#evaluation">Evaluation</a> |
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<a href="#train">Train</a> |
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<p>
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</h4>
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[English](README.md) | [中文](https://github.com/FlagOpen/FlagEmbedding/blob/master/README_zh.md)
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And it also can be used in vector database for LLMs.
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************* 🌟**Updates**🌟 *************
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+
- 08/09/2023: BGE Models are integrated into **Langchain**, you can use it like [this](#using-langchain); C-MTEB **leaderboard** is [avaliable](https://huggingface.co/spaces/mteb/leaderboard).
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- 08/05/2023: Release base-scale and small-scale models, **best performance among the models of the same size 🤗**
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+
- 08/02/2023: Release `bge-large-*`(short for BAAI General Embedding) Models, **rank 1st on MTEB and C-MTEB benchmark!** :tada: :tada:
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- 08/01/2023: We release the [Chinese Massive Text Embedding Benchmark](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB) (**C-MTEB**), consisting of 31 test dataset.
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| Model | Language | Description | query instruction for retrieval\* |
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|:-------------------------------|:--------:| :--------:| :--------:|
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+
| [BAAI/bge-large-en](https://huggingface.co/BAAI/bge-large-en) | English | :trophy: rank **1st** in [MTEB](https://huggingface.co/spaces/mteb/leaderboard) leaderboard | `Represent this sentence for searching relevant passages: ` |
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| [BAAI/bge-base-en](https://huggingface.co/BAAI/bge-base-en) | English | rank **2nd** in [MTEB](https://huggingface.co/spaces/mteb/leaderboard) leaderboard | `Represent this sentence for searching relevant passages: ` |
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| [BAAI/bge-small-en](https://huggingface.co/BAAI/bge-small-en) | English | a small-scale model but with competitive performance | `Represent this sentence for searching relevant passages: ` |
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+
| [BAAI/bge-large-zh](https://huggingface.co/BAAI/bge-large-zh) | Chinese | :trophy: rank **1st** in [C-MTEB](https://github.com/FlagOpen/FlagEmbedding/tree/master/C_MTEB) benchmark | `为这个句子生成表示以用于检索相关文章:` |
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| [BAAI/bge-large-zh-noinstruct](https://huggingface.co/BAAI/bge-large-zh-noinstruct) | Chinese | This model is trained without instruction, and rank **2nd** in [C-MTEB](https://github.com/FlagOpen/FlagEmbedding/tree/master/C_MTEB) benchmark | |
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| [BAAI/bge-base-zh](https://huggingface.co/BAAI/bge-base-zh) | Chinese | a base-scale model but has similar ability with `bge-large-zh` | `为这个句子生成表示以用于检索相关文章:` |
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| [BAAI/bge-small-zh](https://huggingface.co/BAAI/bge-small-zh) | Chinese | a small-scale model but with competitive performance | `为这个句子生成表示以用于检索相关文章:` |
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\*: If you need to search the **long** relevant passages to a **short** query (s2p retrieval task), you need to add the instruction to the query; in other cases, no instruction is needed, just use the original query directly. In all cases, **no instruction** need to be added to passages.
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## Frequently asked questions
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1. The similarity score between two dissimilar sentence is higher than 0.5
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The similarity distribution of the current BGE model is about in the interval \[0.6, 1\].
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So a similarity score greater than 0.5 does not indicate that the two sentence are similar.
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For downstream tasks, such as passage retrieval or semantic similarity,
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**what matters is the relative order of the scores, not the absolute value.**
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If you need to filter similar sentences based on a similarity threshold,
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please select an appropriate similarity threshold based on the similarity distribution on your data (such as 0.8, 0.85, or even 0.9).
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2. When do the query instruction need to be used
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For a retrieval task that uses short queries to find long related documents,
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it is recommended to add instructions for these short queries.
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For other tasks, it is recommended not to add instructions.
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For example, in Quora task, which needs to use a short question to search another related short questions,
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the instruction is not recommended to add.
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The best method to decide whether to add instructions for queries is choosing the setting which can achieve better performance in your task.
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In all cases, the documents/passages do not need to add the instruction, only need to consider whether to add the instruction for queries.
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## Usage
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Here are some examples to use `bge` models with
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```python
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from FlagEmbedding import FlagModel
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sentences_1 = ["样例数据-1", "样例数据-2"]
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sentences_2 = ["样例数据-3", "样例数据-4"]
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model = FlagModel('BAAI/bge-large-zh', query_instruction_for_retrieval="为这个句子生成表示以用于检索相关文章:")
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embeddings_1 = model.encode(sentences_1)
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embeddings_2 = model.encode(sentences_2)
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similarity = embeddings_1 @ embeddings_2.T
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print(similarity)
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The value of argument `query_instruction_for_retrieval` see [Model List](https://github.com/FlagOpen/FlagEmbedding/tree/master#model-list).
|
116 |
|
117 |
FlagModel will use all available GPUs when encoding, please set `os.environ["CUDA_VISIBLE_DEVICES"]` to choose GPU.
|
118 |
+
You also can set `os.environ["CUDA_VISIBLE_DEVICES"]=""` to make GPUs unavailable.
|
119 |
|
120 |
|
121 |
#### Using Sentence-Transformers
|
|
|
127 |
```
|
128 |
```python
|
129 |
from sentence_transformers import SentenceTransformer
|
130 |
+
sentences_1 = ["样例数据-1", "样例数据-2"]
|
131 |
+
sentences_2 = ["样例数据-3", "样例数据-4"]
|
132 |
model = SentenceTransformer('BAAI/bge-large-zh')
|
133 |
+
embeddings_1 = model.encode(sentences_1, normalize_embeddings=True)
|
134 |
+
embeddings_2 = model.encode(sentences_2, normalize_embeddings=True)
|
135 |
similarity = embeddings_1 @ embeddings_2.T
|
136 |
print(similarity)
|
137 |
```
|
|
|
158 |
model_name = "BAAI/bge-small-en"
|
159 |
model_kwargs = {'device': 'cuda'}
|
160 |
encode_kwargs = {'normalize_embeddings': True} # set True to compute cosine similarity
|
161 |
+
model = HuggingFaceBgeEmbeddings(
|
162 |
model_name=model_name,
|
163 |
model_kwargs=model_kwargs,
|
164 |
+
encode_kwargs=encode_kwargs,
|
165 |
+
query_instruction="为这个句子生成表示以用于检索相关文章:"
|
166 |
)
|
167 |
```
|
168 |
|
|
|
274 |
We employ the cross-device negatives sharing method to share negatives among different GPUs,
|
275 |
which can dramatically **increase the number of negatives**.
|
276 |
|
277 |
+
We trained our model on 48 A100(40G) GPUs with a large batch size of 32,784 (so there are **65,567** negatives for each query in a batch).
|
278 |
We used the AdamW optimizer and the learning rate is 1e-5.
|
279 |
The temperature for contrastive loss is 0.01.
|
280 |
|
|
|
291 |
|
292 |
- For English, we collect 230M text pairs from [wikipedia](https://huggingface.co/datasets/wikipedia), [cc-net](https://github.com/facebookresearch/cc_net), and so on.
|
293 |
|
294 |
+
- For chinese, we collect 120M text pairs from [wudao](https://github.com/BAAI-WuDao/Data), [simclue](https://github.com/CLUEbenchmark/SimCLUE), and so on.
|
295 |
|
296 |
**The data collection is to be released in the future.**
|
297 |
|
298 |
+
|
299 |
+
## Schedule
|
300 |
+
- [x] Chinese Massive Text Embedding Benchmark
|
301 |
+
- [x] release baai-general-embedding models
|
302 |
+
- [x] release codes for training
|
303 |
+
- [ ] Multilingual model
|
304 |
+
- [ ] Training Datasets
|
305 |
+
- [ ] ...
|
306 |
+
|
307 |
We will continually update the embedding models and training codes,
|
308 |
hoping to promote the development of the embedding model community.
|
309 |
|
310 |
|
311 |
+
## Contact
|
312 |
+
If you have any question or suggestion related to this project, feel free to open an issue or pull a request.
|
313 |
+
You also can email Shitao Xiao(stxiao@baai.ac.cn) and Zheng Liu(liuzheng@baai.ac.cn).
|
314 |
+
|
315 |
|
316 |
## License
|
317 |
FlagEmbedding is licensed under [MIT License](https://github.com/FlagOpen/FlagEmbedding/blob/master/LICENSE). The released models can be used for commercial purposes free of charge.
|
318 |
|
319 |
|
320 |
|
321 |
+
|
322 |
+
|
323 |
+
<h1 align="center">FlagEmbedding</h1>
|
324 |
+
|
325 |
+
|
326 |
+
<h4 align="center">
|
327 |
+
<p>
|
328 |
+
<a href=#model-list>Model List</a> |
|
329 |
+
<a href=#usage>Usage</a> |
|
330 |
+
<a href="#evaluation">Evaluation</a> |
|
331 |
+
<a href="#train">Train</a> |
|
332 |
+
<a href="#contact">Contact</a> |
|
333 |
+
<a href="#license">License</a>
|
334 |
+
<p>
|
335 |
+
</h4>
|
336 |
+
|
337 |
+
More details please refer to our Github: [FlagEmbedding](https://github.com/FlagOpen/FlagEmbedding).
|
338 |
+
|
339 |
+
|
340 |
+
|
341 |
+
[English](README.md) | [中文](https://github.com/FlagOpen/FlagEmbedding/blob/master/README_zh.md)
|
342 |
+
|
343 |
+
FlagEmbedding can map any text to a low-dimensional dense vector which can be used for tasks like retrieval, classification, clustering, or semantic search.
|
344 |
+
And it also can be used in vector databases for LLMs.
|
345 |
+
|
346 |
+
************* 🌟**Updates**🌟 *************
|
347 |
+
- 09/12/2023: New Release:
|
348 |
+
- **New reranker model**: release a cross-encoder model bge-reranker-base, which is more powerful than embedding model. We recommend to use/fine-tune it to re-rank top-k documents returned by embedding models.
|
349 |
+
- **update embedding model**: release bge-*-v1.5 embedding model to alleviate the issue of the similarity distribution, and enhance its retrieval ability without instruction.
|
350 |
+
- 09/07/2023: Update [fine-tune code](https://github.com/FlagOpen/FlagEmbedding/blob/master/FlagEmbedding/baai_general_embedding/README.md): Add script to mine hard negatives and support adding instruction during fine-tuning.
|
351 |
+
- 08/09/2023: BGE Models are integrated into **Langchain**, you can use it like [this](#using-langchain); C-MTEB **leaderboard** is [available](https://huggingface.co/spaces/mteb/leaderboard).
|
352 |
+
- 08/05/2023: Release base-scale and small-scale models, **best performance among the models of the same size 🤗**
|
353 |
+
- 08/02/2023: Release `bge-large-*`(short for BAAI General Embedding) Models, **rank 1st on MTEB and C-MTEB benchmark!** :tada: :tada:
|
354 |
+
- 08/01/2023: We release the [Chinese Massive Text Embedding Benchmark](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB) (**C-MTEB**), consisting of 31 test dataset.
|
355 |
+
|
356 |
+
|
357 |
+
## Model List
|
358 |
+
|
359 |
+
`bge` is short for `BAAI general embedding`.
|
360 |
+
|
361 |
+
| Model | Language | | Description | query instruction for retrieval\* |
|
362 |
+
|:-------------------------------|:--------:| :--------:| :--------:|:--------:|
|
363 |
+
| [BAAI/bge-reranker-large](https://huggingface.co/BAAI/bge-reranker-large) | Chinese and English | [Inference](#usage-for-reranker) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/reranker) | a cross-encoder model which is more accurate but less efficient \** | |
|
364 |
+
| [BAAI/bge-reranker-base](https://huggingface.co/BAAI/bge-reranker-base) | Chinese and English | [Inference](#usage-for-reranker) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/reranker) | a cross-encoder model which is more accurate but less efficient \** | |
|
365 |
+
| [BAAI/bge-large-en-v1.5](https://huggingface.co/BAAI/bge-large-en-v1.5) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `Represent this sentence for searching relevant passages: ` |
|
366 |
+
| [BAAI/bge-base-en-v1.5](https://huggingface.co/BAAI/bge-base-en-v1.5) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `Represent this sentence for searching relevant passages: ` |
|
367 |
+
| [BAAI/bge-small-en-v1.5](https://huggingface.co/BAAI/bge-small-en-v1.5) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `Represent this sentence for searching relevant passages: ` |
|
368 |
+
| [BAAI/bge-large-zh-v1.5](https://huggingface.co/BAAI/bge-large-zh-v1.5) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `为这个句子生成表示以用于检索相关文章:` |
|
369 |
+
| [BAAI/bge-base-zh-v1.5](https://huggingface.co/BAAI/bge-base-zh-v1.5) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `为这个句子生成表示以用于检索相关文章:` |
|
370 |
+
| [BAAI/bge-small-zh-v1.5](https://huggingface.co/BAAI/bge-small-zh-v1.5) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | version 1.5 with more reasonable similarity distribution | `为这个句子生成表示以用于检索相关文章:` |
|
371 |
+
| [BAAI/bge-large-en](https://huggingface.co/BAAI/bge-large-en) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | :trophy: rank **1st** in [MTEB](https://huggingface.co/spaces/mteb/leaderboard) leaderboard | `Represent this sentence for searching relevant passages: ` |
|
372 |
+
| [BAAI/bge-base-en](https://huggingface.co/BAAI/bge-base-en) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | a base-scale model but with similar ability to `bge-large-en` | `Represent this sentence for searching relevant passages: ` |
|
373 |
+
| [BAAI/bge-small-en](https://huggingface.co/BAAI/bge-small-en) | English | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) |a small-scale model but with competitive performance | `Represent this sentence for searching relevant passages: ` |
|
374 |
+
| [BAAI/bge-large-zh](https://huggingface.co/BAAI/bge-large-zh) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | :trophy: rank **1st** in [C-MTEB](https://github.com/FlagOpen/FlagEmbedding/tree/master/C_MTEB) benchmark | `为这个句子生成表示以用于检索相关文章:` |
|
375 |
+
| [BAAI/bge-base-zh](https://huggingface.co/BAAI/bge-base-zh) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | a base-scale model but with similar ability to `bge-large-zh` | `为这个句子生成表示以用于检索相关文章:` |
|
376 |
+
| [BAAI/bge-small-zh](https://huggingface.co/BAAI/bge-small-zh) | Chinese | [Inference](#usage-for-embedding-model) [Fine-tune](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) | a small-scale model but with competitive performance | `为这个句子生成表示以用于检索相关文章:` |
|
377 |
+
|
378 |
+
|
379 |
+
\*: If you need to search the relevant passages to a query, we suggest to add the instruction to the query; in other cases, no instruction is needed, just use the original query directly. In all cases, **no instruction** needs to be added to passages.
|
380 |
+
|
381 |
+
\**: To balance the accuracy and time cost, cross-encoder is widely used to re-rank top-k documents retrieved by other simple models.
|
382 |
+
For examples, use bge embedding model to retrieve top 100 relevant documents, and then use bge reranker to re-rank the top 100 document to get the final top-3 results.
|
383 |
+
|
384 |
+
|
385 |
+
## Frequently asked questions
|
386 |
+
|
387 |
+
<details>
|
388 |
+
<summary>1. How to fine-tune bge embedding model?</summary>
|
389 |
+
|
390 |
+
<!-- ### How to fine-tune bge embedding model? -->
|
391 |
+
Following this [example](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune) to prepare data and fine-tune your model.
|
392 |
+
Some suggestions:
|
393 |
+
- Mine hard negatives following this [example](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune#data-format), which can improve the retrieval performance.
|
394 |
+
- If you pre-train bge on your data, the pre-trained model cannot be directly used to calculate similarity, and it must be fine-tuned with contrastive learning before computing similarity.
|
395 |
+
- If the accuracy of the fine-tuned model is still not high, it is recommended to use/fine-tune the cross-encoder model (bge-reranker) to re-rank top-k results. Hard negatives also are needed to fine-tune reranker.
|
396 |
+
|
397 |
+
|
398 |
+
</details>
|
399 |
+
|
400 |
+
<details>
|
401 |
+
<summary>2. The similarity score between two dissimilar sentences is higher than 0.5</summary>
|
402 |
+
|
403 |
+
<!-- ### The similarity score between two dissimilar sentences is higher than 0.5 -->
|
404 |
+
**Suggest to use bge v1.5, which alleviates the issue of the similarity distribution.**
|
405 |
+
|
406 |
+
Since we finetune the models by contrastive learning with a temperature of 0.01,
|
407 |
+
the similarity distribution of the current BGE model is about in the interval \[0.6, 1\].
|
408 |
+
So a similarity score greater than 0.5 does not indicate that the two sentences are similar.
|
409 |
+
|
410 |
+
For downstream tasks, such as passage retrieval or semantic similarity,
|
411 |
+
**what matters is the relative order of the scores, not the absolute value.**
|
412 |
+
If you need to filter similar sentences based on a similarity threshold,
|
413 |
+
please select an appropriate similarity threshold based on the similarity distribution on your data (such as 0.8, 0.85, or even 0.9).
|
414 |
+
|
415 |
+
</details>
|
416 |
+
|
417 |
+
<details>
|
418 |
+
<summary>3. When does the query instruction need to be used</summary>
|
419 |
+
|
420 |
+
<!-- ### When does the query instruction need to be used -->
|
421 |
+
|
422 |
+
For a retrieval task that uses short queries to find long related documents,
|
423 |
+
it is recommended to add instructions for these short queries.
|
424 |
+
**The best method to decide whether to add instructions for queries is choosing the setting that achieves better performance on your task.**
|
425 |
+
In all cases, the documents/passages do not need to add the instruction.
|
426 |
+
|
427 |
+
</details>
|
428 |
+
|
429 |
+
|
430 |
+
## Usage
|
431 |
+
|
432 |
+
### Usage for Embedding Model
|
433 |
+
|
434 |
+
Here are some examples for using `bge` models with
|
435 |
+
[FlagEmbedding](#using-flagembedding), [Sentence-Transformers](#using-sentence-transformers), [Langchain](#using-langchain), or [Huggingface Transformers](#using-huggingface-transformers).
|
436 |
+
|
437 |
+
#### Using FlagEmbedding
|
438 |
+
```
|
439 |
+
pip install -U FlagEmbedding
|
440 |
+
```
|
441 |
+
If it doesn't work for you, you can see [FlagEmbedding](https://github.com/FlagOpen/FlagEmbedding/blob/master/FlagEmbedding/baai_general_embedding/README.md) for more methods to install FlagEmbedding.
|
442 |
+
|
443 |
+
```python
|
444 |
+
from FlagEmbedding import FlagModel
|
445 |
+
sentences_1 = ["样例数据-1", "样例数据-2"]
|
446 |
+
sentences_2 = ["样例数据-3", "样例数据-4"]
|
447 |
+
model = FlagModel('BAAI/bge-large-zh', query_instruction_for_retrieval="为这个句子生成表示以用于检索相关文章:")
|
448 |
+
embeddings_1 = model.encode(sentences_1)
|
449 |
+
embeddings_2 = model.encode(sentences_2)
|
450 |
+
similarity = embeddings_1 @ embeddings_2.T
|
451 |
+
print(similarity)
|
452 |
+
|
453 |
+
# for s2p(short query to long passage) retrieval task, suggest to use encode_queries() which will automatically add the instruction to each query
|
454 |
+
# corpus in retrieval task can still use encode() or encode_corpus(), since they don't need instruction
|
455 |
+
queries = ['query_1', 'query_2']
|
456 |
+
passages = ["样例文档-1", "样例文档-2"]
|
457 |
+
q_embeddings = model.encode_queries(queries)
|
458 |
+
p_embeddings = model.encode(passages)
|
459 |
+
scores = q_embeddings @ p_embeddings.T
|
460 |
+
```
|
461 |
+
For the value of the argument `query_instruction_for_retrieval`, see [Model List](https://github.com/FlagOpen/FlagEmbedding/tree/master#model-list).
|
462 |
+
|
463 |
+
By default, FlagModel will use all available GPUs when encoding. Please set `os.environ["CUDA_VISIBLE_DEVICES"]` to select specific GPUs.
|
464 |
+
You also can set `os.environ["CUDA_VISIBLE_DEVICES"]=""` to make all GPUs unavailable.
|
465 |
+
|
466 |
+
|
467 |
+
#### Using Sentence-Transformers
|
468 |
+
|
469 |
+
You can also use the `bge` models with [sentence-transformers](https://www.SBERT.net):
|
470 |
+
|
471 |
+
```
|
472 |
+
pip install -U sentence-transformers
|
473 |
+
```
|
474 |
+
```python
|
475 |
+
from sentence_transformers import SentenceTransformer
|
476 |
+
sentences_1 = ["样例数据-1", "样例数据-2"]
|
477 |
+
sentences_2 = ["样例数据-3", "样例数据-4"]
|
478 |
+
model = SentenceTransformer('BAAI/bge-large-zh')
|
479 |
+
embeddings_1 = model.encode(sentences_1, normalize_embeddings=True)
|
480 |
+
embeddings_2 = model.encode(sentences_2, normalize_embeddings=True)
|
481 |
+
similarity = embeddings_1 @ embeddings_2.T
|
482 |
+
print(similarity)
|
483 |
+
```
|
484 |
+
For s2p(short query to long passage) retrieval task,
|
485 |
+
each short query should start with an instruction (instructions see [Model List](https://github.com/FlagOpen/FlagEmbedding/tree/master#model-list)).
|
486 |
+
But the instruction is not needed for passages.
|
487 |
+
```python
|
488 |
+
from sentence_transformers import SentenceTransformer
|
489 |
+
queries = ['query_1', 'query_2']
|
490 |
+
passages = ["样例文档-1", "样例文档-2"]
|
491 |
+
instruction = "为这个句子生成表示以用于检索相关文章:"
|
492 |
+
|
493 |
+
model = SentenceTransformer('BAAI/bge-large-zh')
|
494 |
+
q_embeddings = model.encode([instruction+q for q in queries], normalize_embeddings=True)
|
495 |
+
p_embeddings = model.encode(passages, normalize_embeddings=True)
|
496 |
+
scores = q_embeddings @ p_embeddings.T
|
497 |
+
```
|
498 |
+
|
499 |
+
#### Using Langchain
|
500 |
+
|
501 |
+
You can use `bge` in langchain like this:
|
502 |
+
```python
|
503 |
+
from langchain.embeddings import HuggingFaceBgeEmbeddings
|
504 |
+
model_name = "BAAI/bge-small-en"
|
505 |
+
model_kwargs = {'device': 'cuda'}
|
506 |
+
encode_kwargs = {'normalize_embeddings': True} # set True to compute cosine similarity
|
507 |
+
model = HuggingFaceBgeEmbeddings(
|
508 |
+
model_name=model_name,
|
509 |
+
model_kwargs=model_kwargs,
|
510 |
+
encode_kwargs=encode_kwargs,
|
511 |
+
query_instruction="为这个句子生成表示以用于检索相关文章:"
|
512 |
+
)
|
513 |
+
model.query_instruction = "为这个句子生成表示以用于检索相关文章:"
|
514 |
+
```
|
515 |
+
|
516 |
+
|
517 |
+
#### Using HuggingFace Transformers
|
518 |
+
|
519 |
+
With the transformers package, you can use the model like this: First, you pass your input through the transformer model, then you select the last hidden state of the first token (i.e., [CLS]) as the sentence embedding.
|
520 |
+
|
521 |
+
```python
|
522 |
+
from transformers import AutoTokenizer, AutoModel
|
523 |
+
import torch
|
524 |
+
# Sentences we want sentence embeddings for
|
525 |
+
sentences = ["样例数据-1", "样例数据-2"]
|
526 |
+
|
527 |
+
# Load model from HuggingFace Hub
|
528 |
+
tokenizer = AutoTokenizer.from_pretrained('BAAI/bge-large-zh')
|
529 |
+
model = AutoModel.from_pretrained('BAAI/bge-large-zh')
|
530 |
+
model.eval()
|
531 |
+
|
532 |
+
# Tokenize sentences
|
533 |
+
encoded_input = tokenizer(sentences, padding=True, truncation=True, return_tensors='pt')
|
534 |
+
# for s2p(short query to long passage) retrieval task, add an instruction to query (not add instruction for passages)
|
535 |
+
# encoded_input = tokenizer([instruction + q for q in queries], padding=True, truncation=True, return_tensors='pt')
|
536 |
+
|
537 |
+
# Compute token embeddings
|
538 |
+
with torch.no_grad():
|
539 |
+
model_output = model(**encoded_input)
|
540 |
+
# Perform pooling. In this case, cls pooling.
|
541 |
+
sentence_embeddings = model_output[0][:, 0]
|
542 |
+
# normalize embeddings
|
543 |
+
sentence_embeddings = torch.nn.functional.normalize(sentence_embeddings, p=2, dim=1)
|
544 |
+
print("Sentence embeddings:", sentence_embeddings)
|
545 |
+
```
|
546 |
+
|
547 |
+
### Usage for Reranker
|
548 |
+
|
549 |
+
You can get a relevance score by inputting query and passage to the reranker.
|
550 |
+
The reranker is optimized based cross-entropy loss, so the relevance score is not bounded to a specific range.
|
551 |
+
|
552 |
+
|
553 |
+
#### Using FlagEmbedding
|
554 |
+
```
|
555 |
+
pip install -U FlagEmbedding
|
556 |
+
```
|
557 |
+
|
558 |
+
Get relevance score:
|
559 |
+
```python
|
560 |
+
from FlagEmbedding import FlagReranker
|
561 |
+
reranker = FlagReranker('BAAI/bge-reranker-base', use_fp16=True) #use fp16 can speed up computing
|
562 |
+
|
563 |
+
score = reranker.compute_score(['query', 'passage'])
|
564 |
+
print(score)
|
565 |
+
|
566 |
+
scores = reranker.compute_score([['what is panda?', 'hi'], ['what is panda?', 'The giant panda (Ailuropoda melanoleuca), sometimes called a panda bear or simply panda, is a bear species endemic to China.']])
|
567 |
+
print(scores)
|
568 |
+
```
|
569 |
+
|
570 |
+
|
571 |
+
#### Using Huggingface transformers
|
572 |
+
|
573 |
+
```python
|
574 |
+
import torch
|
575 |
+
from transformers import AutoModelForSequenceClassification, AutoTokenizer, BatchEncoding, PreTrainedTokenizerFast
|
576 |
+
|
577 |
+
tokenizer = AutoTokenizer.from_pretrained('BAAI/bge-reranker-base')
|
578 |
+
model = AutoModelForSequenceClassification.from_pretrained('BAAI/bge-reranker-base')
|
579 |
+
model.eval()
|
580 |
+
|
581 |
+
pairs = [['what is panda?', 'hi'], ['what is panda?', 'The giant panda (Ailuropoda melanoleuca), sometimes called a panda bear or simply panda, is a bear species endemic to China.']]
|
582 |
+
with torch.no_grad():
|
583 |
+
inputs = tokenizer(pairs, padding=True, truncation=True, return_tensors='pt', max_length=512)
|
584 |
+
scores = model(**inputs, return_dict=True).logits.view(-1, ).float()
|
585 |
+
print(scores)
|
586 |
+
```
|
587 |
+
|
588 |
+
## Evaluation
|
589 |
+
|
590 |
+
`baai-general-embedding` models achieve **state-of-the-art performance on both MTEB and C-MTEB leaderboard!**
|
591 |
+
For more details and evaluation tools see our [scripts](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB/README.md).
|
592 |
+
|
593 |
+
- **MTEB**:
|
594 |
+
|
595 |
+
| Model Name | Dimension | Sequence Length | Average (56) | Retrieval (15) |Clustering (11) | Pair Classification (3) | Reranking (4) | STS (10) | Summarization (1) | Classification (12) |
|
596 |
+
|:----:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
|
597 |
+
| [BAAI/bge-large-en-v1.5](https://huggingface.co/BAAI/bge-large-en-v1.5) | 1024 | 512 | **64.23** | **54.29** | 46.08 | 87.12 | 60.03 | 83.11 | 31.61 | 75.97 |
|
598 |
+
| [BAAI/bge-base-en-v1.5](https://huggingface.co/BAAI/bge-base-en-v1.5) | 768 | 512 | 63.55 | 53.25 | 45.77 | 86.55 | 58.86 | 82.4 | 31.07 | 75.53 |
|
599 |
+
| [BAAI/bge-small-en-v1.5](https://huggingface.co/BAAI/bge-small-en-v1.5) | 384 | 512 | 62.17 |51.68 | 43.82 | 84.92 | 58.36 | 81.59 | 30.12 | 74.14 |
|
600 |
+
| [bge-large-en](https://huggingface.co/BAAI/bge-large-en) | 1024 | 512 | 63.98 | 53.9 | 46.98 | 85.8 | 59.48 | 81.56 | 32.06 | 76.21 |
|
601 |
+
| [bge-base-en](https://huggingface.co/BAAI/bge-base-en) | 768 | 512 | 63.36 | 53.0 | 46.32 | 85.86 | 58.7 | 81.84 | 29.27 | 75.27 |
|
602 |
+
| [gte-large](https://huggingface.co/thenlper/gte-large) | 1024 | 512 | 63.13 | 52.22 | 46.84 | 85.00 | 59.13 | 83.35 | 31.66 | 73.33 |
|
603 |
+
| [gte-base](https://huggingface.co/thenlper/gte-base) | 768 | 512 | 62.39 | 51.14 | 46.2 | 84.57 | 58.61 | 82.3 | 31.17 | 73.01 |
|
604 |
+
| [e5-large-v2](https://huggingface.co/intfloat/e5-large-v2) | 1024| 512 | 62.25 | 50.56 | 44.49 | 86.03 | 56.61 | 82.05 | 30.19 | 75.24 |
|
605 |
+
| [bge-small-en](https://huggingface.co/BAAI/bge-small-en) | 384 | 512 | 62.11 | 51.82 | 44.31 | 83.78 | 57.97 | 80.72 | 30.53 | 74.37 |
|
606 |
+
| [instructor-xl](https://huggingface.co/hkunlp/instructor-xl) | 768 | 512 | 61.79 | 49.26 | 44.74 | 86.62 | 57.29 | 83.06 | 32.32 | 61.79 |
|
607 |
+
| [e5-base-v2](https://huggingface.co/intfloat/e5-base-v2) | 768 | 512 | 61.5 | 50.29 | 43.80 | 85.73 | 55.91 | 81.05 | 30.28 | 73.84 |
|
608 |
+
| [gte-small](https://huggingface.co/thenlper/gte-small) | 384 | 512 | 61.36 | 49.46 | 44.89 | 83.54 | 57.7 | 82.07 | 30.42 | 72.31 |
|
609 |
+
| [text-embedding-ada-002](https://platform.openai.com/docs/guides/embeddings) | 1536 | 8192 | 60.99 | 49.25 | 45.9 | 84.89 | 56.32 | 80.97 | 30.8 | 70.93 |
|
610 |
+
| [e5-small-v2](https://huggingface.co/intfloat/e5-base-v2) | 384 | 512 | 59.93 | 49.04 | 39.92 | 84.67 | 54.32 | 80.39 | 31.16 | 72.94 |
|
611 |
+
| [sentence-t5-xxl](https://huggingface.co/sentence-transformers/sentence-t5-xxl) | 768 | 512 | 59.51 | 42.24 | 43.72 | 85.06 | 56.42 | 82.63 | 30.08 | 73.42 |
|
612 |
+
| [all-mpnet-base-v2](https://huggingface.co/sentence-transformers/all-mpnet-base-v2) | 768 | 514 | 57.78 | 43.81 | 43.69 | 83.04 | 59.36 | 80.28 | 27.49 | 65.07 |
|
613 |
+
| [sgpt-bloom-7b1-msmarco](https://huggingface.co/bigscience/sgpt-bloom-7b1-msmarco) | 4096 | 2048 | 57.59 | 48.22 | 38.93 | 81.9 | 55.65 | 77.74 | 33.6 | 66.19 |
|
614 |
+
|
615 |
+
|
616 |
+
|
617 |
+
- **C-MTEB**:
|
618 |
+
We create the benchmark C-MTEB for Chinese text embedding which consists of 31 datasets from 6 tasks.
|
619 |
+
Please refer to [C_MTEB](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB/README.md) for a detailed introduction.
|
620 |
+
|
621 |
+
| Model | Embedding dimension | Avg | Retrieval | STS | PairClassification | Classification | Reranking | Clustering |
|
622 |
+
|:-------------------------------|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:|
|
623 |
+
| [**BAAI/bge-large-zh-v1.5**](https://huggingface.co/BAAI/bge-large-zh-v1.5) | 1024 | **64.53** | 70.46 | 56.25 | 81.6 | 69.13 | 65.84 | 48.99 |
|
624 |
+
| [BAAI/bge-base-zh-v1.5](https://huggingface.co/BAAI/bge-base-zh-v1.5) | 768 | 63.13 | 69.49 | 53.72 | 79.75 | 68.07 | 65.39 | 47.53 |
|
625 |
+
| [BAAI/bge-small-zh-v1.5](https://huggingface.co/BAAI/bge-small-zh-v1.5) | 512 | 57.82 | 61.77 | 49.11 | 70.41 | 63.96 | 60.92 | 44.18 |
|
626 |
+
| [BAAI/bge-large-zh](https://huggingface.co/BAAI/bge-large-zh) | 1024 | 64.20 | 71.53 | 54.98 | 78.94 | 68.32 | 65.11 | 48.39 |
|
627 |
+
| [bge-large-zh-noinstruct](https://huggingface.co/BAAI/bge-large-zh-noinstruct) | 1024 | 63.53 | 70.55 | 53 | 76.77 | 68.58 | 64.91 | 50.01 |
|
628 |
+
| [BAAI/bge-base-zh](https://huggingface.co/BAAI/bge-base-zh) | 768 | 62.96 | 69.53 | 54.12 | 77.5 | 67.07 | 64.91 | 47.63 |
|
629 |
+
| [multilingual-e5-large](https://huggingface.co/intfloat/multilingual-e5-large) | 1024 | 58.79 | 63.66 | 48.44 | 69.89 | 67.34 | 56.00 | 48.23 |
|
630 |
+
| [BAAI/bge-small-zh](https://huggingface.co/BAAI/bge-small-zh) | 512 | 58.27 | 63.07 | 49.45 | 70.35 | 63.64 | 61.48 | 45.09 |
|
631 |
+
| [m3e-base](https://huggingface.co/moka-ai/m3e-base) | 768 | 57.10 | 56.91 | 50.47 | 63.99 | 67.52 | 59.34 | 47.68 |
|
632 |
+
| [m3e-large](https://huggingface.co/moka-ai/m3e-large) | 1024 | 57.05 | 54.75 | 50.42 | 64.3 | 68.2 | 59.66 | 48.88 |
|
633 |
+
| [multilingual-e5-base](https://huggingface.co/intfloat/multilingual-e5-base) | 768 | 55.48 | 61.63 | 46.49 | 67.07 | 65.35 | 54.35 | 40.68 |
|
634 |
+
| [multilingual-e5-small](https://huggingface.co/intfloat/multilingual-e5-small) | 384 | 55.38 | 59.95 | 45.27 | 66.45 | 65.85 | 53.86 | 45.26 |
|
635 |
+
| [text-embedding-ada-002(OpenAI)](https://platform.openai.com/docs/guides/embeddings/what-are-embeddings) | 1536 | 53.02 | 52.0 | 43.35 | 69.56 | 64.31 | 54.28 | 45.68 |
|
636 |
+
| [luotuo](https://huggingface.co/silk-road/luotuo-bert-medium) | 1024 | 49.37 | 44.4 | 42.78 | 66.62 | 61 | 49.25 | 44.39 |
|
637 |
+
| [text2vec-base](https://huggingface.co/shibing624/text2vec-base-chinese) | 768 | 47.63 | 38.79 | 43.41 | 67.41 | 62.19 | 49.45 | 37.66 |
|
638 |
+
| [text2vec-large](https://huggingface.co/GanymedeNil/text2vec-large-chinese) | 1024 | 47.36 | 41.94 | 44.97 | 70.86 | 60.66 | 49.16 | 30.02 |
|
639 |
+
|
640 |
+
|
641 |
+
- **Reranking**:
|
642 |
+
See [C_MTEB](https://github.com/FlagOpen/FlagEmbedding/blob/master/C_MTEB/) for evaluation script.
|
643 |
+
|
644 |
+
| Model | T2Reranking | T2RerankingZh2En\* | T2RerankingEn2Zh\* | MmarcoReranking | CMedQAv1 | CMedQAv2 | Avg |
|
645 |
+
|:-------------------------------|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:|:--------:|
|
646 |
+
| text2vec-base-multilingual | 64.66 | 62.94 | 62.51 | 14.37 | 48.46 | 48.6 | 50.26 |
|
647 |
+
| multilingual-e5-small | 65.62 | 60.94 | 56.41 | 29.91 | 67.26 | 66.54 | 57.78 |
|
648 |
+
| multilingual-e5-large | 64.55 | 61.61 | 54.28 | 28.6 | 67.42 | 67.92 | 57.4 |
|
649 |
+
| multilingual-e5-base | 64.21 | 62.13 | 54.68 | 29.5 | 66.23 | 66.98 | 57.29 |
|
650 |
+
| m3e-base | 66.03 | 62.74 | 56.07 | 17.51 | 77.05 | 76.76 | 59.36 |
|
651 |
+
| m3e-large | 66.13 | 62.72 | 56.1 | 16.46 | 77.76 | 78.27 | 59.57 |
|
652 |
+
| bge-base-zh-v1.5 | 66.49 | 63.25 | 57.02 | 29.74 | 80.47 | 84.88 | 63.64 |
|
653 |
+
| bge-large-zh-v1.5 | 65.74 | 63.39 | 57.03 | 28.74 | 83.45 | 85.44 | 63.97 |
|
654 |
+
| [BAAI/bge-reranker-base](https://huggingface.co/BAAI/bge-reranker-base) | 67.28 | 63.95 | 60.45 | 35.46 | 81.26 | 84.1 | 65.42 |
|
655 |
+
| [BAAI/bge-reranker-large](https://huggingface.co/BAAI/bge-reranker-large) | 67.6 | 64.03 | 61.44 | 37.16 | 82.15 | 84.18 | 66.09 |
|
656 |
+
|
657 |
+
\* : T2RerankingZh2En and T2RerankingEn2Zh are cross-language retrieval task
|
658 |
+
|
659 |
+
## Train
|
660 |
+
|
661 |
+
### BAAI Embedding
|
662 |
+
|
663 |
+
We pre-train the models using retromae and train them on large-scale pairs data using contrastive learning.
|
664 |
+
**You can fine-tune the embedding model on your data following our [examples](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/finetune).**
|
665 |
+
We also provide a [pre-train example](https://github.com/FlagOpen/FlagEmbedding/tree/master/examples/pretrain).
|
666 |
+
Note that the goal of pre-training is to reconstruct the text, and the pre-trained model cannot be used for similarity calculation directly, it needs to be fine-tuned.
|
667 |
+
More training details for bge see [baai_general_embedding](https://github.com/FlagOpen/FlagEmbedding/blob/master/FlagEmbedding/baai_general_embedding/README.md).
|
668 |
+
|
669 |
+
|
670 |
+
|
671 |
+
### BGE Reranker
|
672 |
+
|
673 |
+
Cross-encoder will perform full-attention over the input pair,
|
674 |
+
which is more accurate than embedding model (i.e., bi-encoder) but more time-consuming than embedding model.
|
675 |
+
Therefore, it can be used to re-rank the top-k documents returned by embedding model.
|
676 |
+
We train the cross-encoder on a multilingual pair data,
|
677 |
+
The data format is the same as embedding model, so you can fine-tune it easily following our example.
|
678 |
+
More details pelease refer to [./FlagEmbedding/reranker/README.md](./FlagEmbedding/reranker/README.md)
|
679 |
+
|
680 |
+
|
681 |
+
## Contact
|
682 |
+
If you have any question or suggestion related to this project, feel free to open an issue or pull request.
|
683 |
+
You also can email Shitao Xiao(stxiao@baai.ac.cn) and Zheng Liu(liuzheng@baai.ac.cn).
|
684 |
+
|
685 |
+
|
686 |
+
## License
|
687 |
+
FlagEmbedding is licensed under the [MIT License](https://github.com/FlagOpen/FlagEmbedding/blob/master/LICENSE). The released models can be used for commercial purposes free of charge.
|
688 |
+
|
689 |
+
|
690 |
+
|