Sentence Pair Regression

Sentence-BERT for Sentence Pair Regression

Sentence-BERT (SBERT) is a powerful extension of BERT that can be effectively used for regression tasks, specifically for predicting the semantic similarity score between two sentences. This capability is invaluable in applications such as semantic search, paraphrase scoring, and ranking.

Understanding the Regression Task

In sentence pair regression, the objective is to train a model that can accurately predict a numerical similarity score between two given sentences. A typical dataset for this task comprises entries consisting of:

• A pair of sentences.

• A ground truth numerical similarity score, usually normalized to a range like [0, 1], reflecting their semantic closeness.

Example:

| Sentence 1 | Sentence 2 | Similarity Score | | :----------------- | :----------------- | :--------------- | | How old are you | What is your age | 0.92 | | The cat sat on the mat. | The dog barked loudly. | 0.35 |

The model learns to output a score that closely matches this ground truth score.

How Sentence-BERT Handles Sentence Pair Regression

The process leverages a Siamese network architecture, where two identical BERT models share weights, processing each sentence independently.

1. Tokenization and Special Tokens

Each sentence is first tokenized individually. Special tokens are then added to delineate the sentence structure and signal to the model the beginning and end of each input. Typically, [CLS] is prepended to the first token and [SEP] is appended to the last token of each sentence.

Consider the sentence pair:

• Sentence 1: How old are you

• Sentence 2: What is your age

After tokenization and adding special tokens:

• Tokens 1: [CLS], How, old, are, you, [SEP]

• Tokens 2: [CLS], What, is, your, age, [SEP]

2. Encoding Using Siamese BERT

The core of the SBERT approach for regression is the use of a Siamese network. This architecture consists of two identical BERT encoders that share the same weights. Each sentence from the pair is fed into one of these encoders:

• Sentence 1 → BERT Encoder 1

• Sentence 2 → BERT Encoder 2

Each encoder processes its respective sentence and outputs a sequence of contextualized token embeddings.

3. Pooling to Get Sentence Representations

To obtain a fixed-size vector representation for each sentence from the output token embeddings, a pooling strategy is applied. The most common methods are:

• Mean Pooling: The embeddings of all tokens in a sentence (excluding special tokens like [SEP]) are averaged to produce a single sentence vector.

• Max Pooling: The maximum value across each dimension of the token embeddings is taken to form the sentence vector.

This results in two dense sentence vectors:

• S₁ = Sentence embedding for Sentence 1

• S₂ = Sentence embedding for Sentence 2

These vectors effectively capture the semantic meaning of their respective sentences.

4. Calculating Similarity and Loss

The semantic similarity between the two sentences is then quantified by calculating the cosine similarity between their pooled sentence embeddings (S₁ and S₂).

Cosine Similarity Formula:

$$ \text{similarity}(S_1, S_2) = \frac{S_1 \cdot S_2}{|S_1| |S_2|} $$

Where:

• $S_1 \cdot S_2$ is the dot product of vectors $S_1$ and $S_2$.

• $|S_1|$ is the magnitude (L2 norm) of vector $S_1$.

• $|S_2|$ is the magnitude (L2 norm) of vector $S_2$.

Cosine similarity produces a scalar score typically ranging from -1 to 1, which is often rescaled to the [0, 1] range for practical similarity scoring.

The model is trained to minimize the difference between its predicted similarity score and the ground truth similarity score. The Mean Squared Error (MSE) loss is commonly used for this purpose.

Mean Squared Error (MSE) Loss Formula:

$$ \text{Loss} = \frac{1}{N} \sum_{i=1}^{N} (\text{predicted}_i - \text{actual}_i)^2 $$

Where:

• $N$ is the total number of training examples.

• $\text{predicted}_i$ is the predicted similarity score for the $i$-th sentence pair.

• $\text{actual}_i$ is the ground truth similarity score for the $i$-th sentence pair.

Visual Workflow Summary

The overall process can be visualized as follows:

1. Input: A pair of sentences along with a ground truth similarity score.

2. Siamese Encoders: Each sentence is independently processed by an identical BERT encoder (sharing weights).

3. Pooling: The output token embeddings from each encoder are pooled (e.g., mean pooling) to generate a single sentence embedding for each sentence.

4. Similarity Calculation: Cosine similarity is computed between the two sentence embeddings to produce a predicted similarity score.

5. Loss Optimization: The predicted score is compared against the ground truth score using a loss function like Mean Squared Error (MSE), and the model's weights are updated through backpropagation to minimize this loss.

Use Cases for Sentence Pair Regression

Sentence-BERT's ability to predict semantic similarity scores makes it highly effective in various NLP applications:

• Semantic Textual Similarity (STS): Directly measuring how alike two pieces of text are in meaning.

• Information Retrieval and Ranking: Ranking search results or documents based on their relevance to a query.

• Answer Relevance Scoring in QA Systems: Determining how well an answer matches a given question.

• Paraphrase Scoring and Deduplication: Identifying sentences that are semantically equivalent, useful for detecting duplicate content or finding paraphrased information.

Conclusion

Sentence-BERT, utilizing a Siamese architecture and cosine similarity for scoring, is not confined to classification tasks. It proves exceptionally capable in regression scenarios for predicting continuous similarity scores between sentence pairs. By minimizing MSE loss, SBERT models learn to assign accurate semantic similarity scores, making them a versatile tool for a wide range of real-world natural language processing applications.

Interview Questions

• How does Sentence-BERT perform sentence pair regression tasks?

• What role does the Siamese network architecture play in SBERT regression?

• How are sentences tokenized and processed for regression with SBERT?

• Explain the pooling methods used to obtain sentence embeddings in SBERT regression.

• How is cosine similarity calculated between two sentence embeddings?

• Why is cosine similarity suitable for measuring semantic similarity?

• What loss function is used to train SBERT for regression tasks, and why?

• How does Mean Squared Error (MSE) loss work in the context of SBERT regression?

• Can you name some real-world applications where SBERT regression is useful?

• What advantages does SBERT offer over vanilla BERT for regression-based similarity scoring?