Repository: deepset-ai/haystack

Issue:
Implement function to calculate Semantic Answer Similarity metric
As specified in proposal #5794 we need to implement a function to calculate the Semantic Answer Similarity metric.

Ideally the function should be part of the private interface and called only through the `calculate_metrics` function (see #6063). `_calculate_sas()` could be a nice name.

For more detailed information check out the original proposal.


Discussion:

Patch:
diff --git a/haystack/evaluation/eval.py b/haystack/evaluation/eval.py
index 7951814c18..3ce375ee24 100644
--- a/haystack/evaluation/eval.py
+++ b/haystack/evaluation/eval.py
@@ -1,5 +1,5 @@
 import collections
-from typing import Any, Callable, Dict, List, Union
+from typing import Any, Callable, Dict, List, Union, Optional
 
 import numpy as np
 
@@ -8,6 +8,13 @@
 from haystack.evaluation.eval_utils import get_answers_from_output, preprocess_text
 from haystack.evaluation.metrics import Metric, MetricsResult
 
+from haystack.lazy_imports import LazyImport
+from haystack.utils import ComponentDevice, expit
+
+with LazyImport(message="Run 'pip install scikit-learn \"sentence-transformers>=2.2.0\"'") as metrics_import:
+    from sentence_transformers import SentenceTransformer, CrossEncoder, util
+    from transformers import AutoConfig
+
 
 class EvaluationResult:
     """
@@ -89,7 +96,12 @@ def _compute_f1_single(self, label_toks: List[str], pred_toks: List[str]) -> flo
         return f1
 
     def _calculate_f1(
-        self, output_key: str, regexes_to_ignore=None, ignore_case=False, ignore_punctuation=False, ignore_numbers=False
+        self,
+        output_key: str,
+        regexes_to_ignore: Optional[List[str]] = None,
+        ignore_case: bool = False,
+        ignore_punctuation: bool = False,
+        ignore_numbers: bool = False,
     ) -> MetricsResult:
         """
         Calculates the F1 score between two lists of predictions and labels.
@@ -103,7 +115,7 @@ def _calculate_f1(
             comparison. Defaults to False.
         :param ignore_numbers (bool, optional): If True, removes numerical digits from both predictions and labels
             before comparison. Defaults to False.
-        :return: A MetricsResult object containing the calculated Exact Match (EM) score.
+        :return: A MetricsResult object containing the calculated F1 score.
         """
 
         predictions = get_answers_from_output(
@@ -136,7 +148,12 @@ def _calculate_f1(
         return MetricsResult({"f1": f1})
 
     def _calculate_em(
-        self, output_key: str, regexes_to_ignore=None, ignore_case=False, ignore_punctuation=False, ignore_numbers=False
+        self,
+        output_key: str,
+        regexes_to_ignore: Optional[List[str]] = None,
+        ignore_case: bool = False,
+        ignore_punctuation: bool = False,
+        ignore_numbers: bool = False,
     ) -> MetricsResult:
         """
         Calculates the Exact Match (EM) score between two lists of predictions and labels.
@@ -175,8 +192,106 @@ def _calculate_em(
 
         return MetricsResult({"exact_match": exact_match_score})
 
-    def _calculate_sas(self):
-        return MetricsResult({"exact_match": None})
+    def _calculate_sas(
+        self,
+        output_key: str,
+        regexes_to_ignore: Optional[List[str]] = None,
+        ignore_case: bool = False,
+        ignore_punctuation: bool = False,
+        ignore_numbers: bool = False,
+        model: str = "sentence-transformers/paraphrase-multilingual-mpnet-base-v2",
+        batch_size: int = 32,
+        device: Optional[ComponentDevice] = None,
+        token: Optional[Union[str, bool]] = None,
+    ) -> MetricsResult:
+        """
+        Calculates the Semantic Answer Similarity (SAS) score between two lists of predictions and labels.
+        Semantic Answer Similarity (SAS) score measures the Transformer-based similarity between the predicted text and
+        the corresponding ground truth label.
+
+        :param output_key: The key of the output to use for comparison.
+        :param regexes_to_ignore (list, optional): A list of regular expressions. If provided, it removes substrings
+            matching these regular expressions from both predictions and labels before comparison. Defaults to None.
+        :param ignore_case (bool, optional): If True, performs case-insensitive comparison. Defaults to False.
+        :param ignore_punctuation (bool, optional): If True, removes punctuation from both predictions and labels before
+            comparison. Defaults to False.
+        :param ignore_numbers (bool, optional): If True, removes numerical digits from both predictions and labels
+            before comparison. Defaults to False.
+        :param model: SentenceTransformers semantic textual similarity model, should be path or string pointing to
+            a downloadable model.
+        :param batch_size: Number of prediction-label pairs to encode at once.
+        :param device: The device on which the model is loaded. If `None`, the default device is automatically
+            selected.
+        :param token: The token to use as HTTP bearer authorization for private models from Huggingface.
+            If True, will use the token generated when running huggingface-cli login (stored in ~/.huggingface).
+            Additional information can be found here:
+            https://huggingface.co/transformers/main_classes/model.html#transformers.PreTrainedModel.from_pretrained
+        :return: A MetricsResult object containing the calculated Semantic Answer Similarity (SAS) score and the
+            list of similarity scores obtained for each prediction-label pair.
+        """
+        metrics_import.check()
+
+        predictions = get_answers_from_output(
+            outputs=self.outputs, output_key=output_key, runnable_type=self.runnable_type
+        )
+        labels = get_answers_from_output(
+            outputs=self.expected_outputs, output_key=output_key, runnable_type=self.runnable_type
+        )
+
+        if len(predictions) != len(labels):
+            raise ValueError("The number of predictions and labels must be the same.")
+        if len(predictions) == len(labels) == 0:
+            # Return SAS as 0 for no inputs
+            return MetricsResult({"sas": 0.0, "scores": [0.0]})
+
+        predictions = preprocess_text(predictions, regexes_to_ignore, ignore_case, ignore_punctuation, ignore_numbers)
+        labels = preprocess_text(labels, regexes_to_ignore, ignore_case, ignore_punctuation, ignore_numbers)
+
+        config = AutoConfig.from_pretrained(model, use_auth_token=token)
+        cross_encoder_used = False
+        if config.architectures:
+            cross_encoder_used = any(arch.endswith("ForSequenceClassification") for arch in config.architectures)
+
+        device = ComponentDevice.resolve_device(device)
+
+        # Based on the Model string we can load either Bi-Encoders or Cross Encoders.
+        # Similarity computation changes for both approaches
+
+        if cross_encoder_used:
+            # For Cross Encoders we create a list of pairs of predictions and labels
+            similarity_model = CrossEncoder(
+                model,
+                device=device.to_torch_str(),
+                tokenizer_args={"use_auth_token": token},
+                automodel_args={"use_auth_token": token},
+            )
+            sentence_pairs = [[pred, label] for pred, label in zip(predictions, labels)]
+            similarity_scores = similarity_model.predict(sentence_pairs, batch_size=batch_size, convert_to_numpy=True)
+
+            # All Cross Encoders do not return a set of logits scores that are normalized
+            # We normalize scores if they are larger than 1
+            if (similarity_scores > 1).any():
+                similarity_scores = expit(similarity_scores)
+
+            # Convert scores to list of floats from numpy array
+            similarity_scores = similarity_scores.tolist()
+
+        else:
+            # For Bi-encoders we create embeddings separately for predictions and labels
+            similarity_model = SentenceTransformer(model, device=device.to_torch_str(), use_auth_token=token)
+            pred_embeddings = similarity_model.encode(predictions, batch_size=batch_size, convert_to_tensor=True)
+            label_embeddings = similarity_model.encode(labels, batch_size=batch_size, convert_to_tensor=True)
+
+            # Compute cosine-similarities
+            scores = util.cos_sim(pred_embeddings, label_embeddings)
+
+            # cos_sim computes cosine similarity between all pairs of vectors in pred_embeddings and label_embeddings
+            # It returns a matrix with shape (len(predictions), len(labels))
+            similarity_scores = [scores[i][i].item() for i in range(len(predictions))]
+
+        sas_score = np.mean(similarity_scores)
+
+        return MetricsResult({"sas": sas_score, "scores": similarity_scores})
 
 
 def eval(
diff --git a/haystack/evaluation/eval_utils.py b/haystack/evaluation/eval_utils.py
index cdd6dd8463..3b7d1ca1d6 100644
--- a/haystack/evaluation/eval_utils.py
+++ b/haystack/evaluation/eval_utils.py
@@ -1,10 +1,14 @@
 import re
 import string
-from typing import Any, Dict, List
+from typing import Any, Dict, List, Optional
 
 
 def preprocess_text(
-    texts: List[str], regexes_to_ignore=None, ignore_case=False, ignore_punctuation=False, ignore_numbers=False
+    texts: List[str],
+    regexes_to_ignore: Optional[List[str]] = None,
+    ignore_case: bool = False,
+    ignore_punctuation: bool = False,
+    ignore_numbers: bool = False,
 ) -> List[str]:
     """
     Preprocess the outputs of the runnable to remove unwanted characters.
diff --git a/releasenotes/notes/add-sas-b8dbf61c0d78ba19.yaml b/releasenotes/notes/add-sas-b8dbf61c0d78ba19.yaml
new file mode 100644
index 0000000000..5078a4c93b
--- /dev/null
+++ b/releasenotes/notes/add-sas-b8dbf61c0d78ba19.yaml
@@ -0,0 +1,10 @@
+---
+features:
+  - |
+    Adds support for the Semantic Answer Similarity (SAS) metric to `EvaluationResult.calculate_metrics(...)`:
+    ```python
+    from haystack.evaluation.metrics import Metric
+    sas_metric = eval_result.calculate_metrics(
+        Metric.SAS, output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+    )
+    ```


Test patch:
diff --git a/e2e/pipelines/test_eval_extractive_qa_pipeline.py b/e2e/pipelines/test_eval_extractive_qa_pipeline.py
index f04ddd4725..989b2713b1 100644
--- a/e2e/pipelines/test_eval_extractive_qa_pipeline.py
+++ b/e2e/pipelines/test_eval_extractive_qa_pipeline.py
@@ -1,4 +1,5 @@
 import json
+import pytest
 
 from haystack import Pipeline
 from haystack.components.readers import ExtractiveReader
@@ -140,3 +141,26 @@ def test_extractive_qa_pipeline(tmp_path):
     assert f1_custom_parameters["f1"] == 1.0
     with open(tmp_path / "f1_score.json", "r") as f:
         assert f1_default == json.load(f)
+
+    # Test SAS
+    sas_default = eval_result.calculate_metrics(
+        Metric.SAS, output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+    )
+    sas_custom_parameters = eval_result.calculate_metrics(
+        Metric.SAS,
+        output_key="answers",
+        ignore_case=True,
+        ignore_punctuation=True,
+        ignore_numbers=True,
+        model="cross-encoder/ms-marco-MiniLM-L-6-v2",
+    )
+    # Save SAS metric results to json
+    sas_default.save(tmp_path / "sas_score.json")
+
+    assert sas_default["sas"] == pytest.approx(1.0)
+    assert sas_default["scores"] == pytest.approx([1.0, 1.0, 1.0])
+    assert sas_custom_parameters["sas"] == pytest.approx(0.9996823, abs=1e-5)
+    assert sas_custom_parameters["scores"] == pytest.approx([0.999672, 0.999608, 0.999767])
+
+    with open(tmp_path / "sas_score.json", "r") as f:
+        assert sas_default == json.load(f)
diff --git a/e2e/pipelines/test_eval_rag_pipelines.py b/e2e/pipelines/test_eval_rag_pipelines.py
index 23e674d22a..7dc5129772 100644
--- a/e2e/pipelines/test_eval_rag_pipelines.py
+++ b/e2e/pipelines/test_eval_rag_pipelines.py
@@ -1,4 +1,5 @@
 import json
+import pytest
 
 from haystack import Pipeline
 from haystack.components.builders.answer_builder import AnswerBuilder
@@ -142,6 +143,29 @@ def test_bm25_rag_pipeline(tmp_path):
     with open(tmp_path / "f1_score.json", "r") as f:
         assert f1_default == json.load(f)
 
+    # Test SAS
+    sas_default = eval_result.calculate_metrics(
+        Metric.SAS, output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+    )
+    sas_custom_parameters = eval_result.calculate_metrics(
+        Metric.SAS,
+        output_key="answers",
+        ignore_case=True,
+        ignore_punctuation=True,
+        ignore_numbers=True,
+        model="cross-encoder/ms-marco-MiniLM-L-6-v2",
+    )
+    # Save SAS metric results to json
+    sas_default.save(tmp_path / "sas_score.json")
+
+    assert sas_default["sas"] == pytest.approx(1.0)
+    assert sas_default["scores"] == pytest.approx([1.0, 1.0, 1.0])
+    assert sas_custom_parameters["sas"] == pytest.approx(0.9769593, abs=1e-5)
+    assert sas_custom_parameters["scores"] == pytest.approx([0.975823, 0.957218, 0.997837], abs=1e-5)
+
+    with open(tmp_path / "sas_score.json", "r") as f:
+        assert sas_default == json.load(f)
+
 
 def test_embedding_retrieval_rag_pipeline(tmp_path):
     # Create the RAG pipeline
@@ -287,3 +311,26 @@ def test_embedding_retrieval_rag_pipeline(tmp_path):
     assert f1_custom_parameters["f1"] == 1.0
     with open(tmp_path / "f1_score.json", "r") as f:
         assert f1_default == json.load(f)
+
+    # Test SAS
+    sas_default = eval_result.calculate_metrics(
+        Metric.SAS, output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+    )
+    sas_custom_parameters = eval_result.calculate_metrics(
+        Metric.SAS,
+        output_key="answers",
+        ignore_case=True,
+        ignore_punctuation=True,
+        ignore_numbers=True,
+        model="cross-encoder/ms-marco-MiniLM-L-6-v2",
+    )
+    # Save SAS metric results to json
+    sas_default.save(tmp_path / "sas_score.json")
+
+    assert sas_default["sas"] == pytest.approx(1.0)
+    assert sas_default["scores"] == pytest.approx([1.0, 1.0, 1.0])
+    assert sas_custom_parameters["sas"] == pytest.approx(0.9769593, abs=1e-5)
+    assert sas_custom_parameters["scores"] == pytest.approx([0.975823, 0.957218, 0.997837], abs=1e-5)
+
+    with open(tmp_path / "sas_score.json", "r") as f:
+        assert sas_default == json.load(f)
diff --git a/test/evaluation/test_eval_sas.py b/test/evaluation/test_eval_sas.py
new file mode 100644
index 0000000000..5b1fb70a8a
--- /dev/null
+++ b/test/evaluation/test_eval_sas.py
@@ -0,0 +1,347 @@
+import pytest
+
+from haystack import Pipeline
+from haystack.dataclasses import GeneratedAnswer
+from haystack.evaluation.eval import EvaluationResult
+
+
+class TestSAS:
+    def create_evaluation_result(self, predictions, labels):
+        """
+        Creates an evaluation result of a RAG pipeline using the list of predictions and labels for testing the
+         Semantic Answer Similarity (SAS) Metric.
+        """
+        runnable = Pipeline()
+        inputs = []
+        outputs = [
+            {"answer_builder": {"answers": [GeneratedAnswer(data=pred, query="", documents=[], meta={})]}}
+            for pred in predictions
+        ]
+        expected_outputs = [
+            {"answer_builder": {"answers": [GeneratedAnswer(data=label, query="", documents=[], meta={})]}}
+            for label in labels
+        ]
+        evaluation_result = EvaluationResult(runnable, inputs, outputs, expected_outputs)
+        return evaluation_result
+
+    def test_sas_empty_inputs(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with empty inputs.
+        """
+        runnable = Pipeline()
+        inputs = []
+        outputs = [
+            {"answer_builder": {"answers": []}},
+            {"answer_builder": {"answers": []}},
+            {"answer_builder": {"answers": []}},
+        ]
+        expected_outputs = [
+            {"answer_builder": {"answers": []}},
+            {"answer_builder": {"answers": []}},
+            {"answer_builder": {"answers": []}},
+        ]
+        evaluation_result = EvaluationResult(runnable, inputs, outputs, expected_outputs)
+        # Expecting 0% SAS for empty inputs
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+        )
+
+        assert sas_result["sas"] == 0.0
+        assert sas_result["scores"] == [0.0]
+
+    def test_calculate_sas_with_different_lengths(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with default parameters.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+        ]
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+
+        with pytest.raises(ValueError, match="The number of predictions and labels must be the same."):
+            evaluation_result._calculate_sas(
+                output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+            )
+
+    @pytest.mark.integration
+    def test_sas_same_inputs(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with default parameters.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+        )
+
+        assert sas_result["sas"] == pytest.approx(1.0)
+        assert sas_result["scores"] == pytest.approx([1.0, 1.0, 1.0])
+
+    @pytest.mark.integration
+    def test_sas_single_word(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with single-word inputs.
+        """
+        predictions = ["A construction budget of US $2.3 billion"]
+        labels = ["US $2.3 billion"]
+
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+        )
+
+        assert sas_result["sas"] == pytest.approx(0.689089, abs=1e-5)
+        assert sas_result["scores"] == pytest.approx([0.689089], abs=1e-5)
+
+    @pytest.mark.integration
+    def test_sas_negative_case(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with deliberately mismatched predictions and labels.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "US $2.3 billion",
+            "Paris's cultural magnificence is symbolized by the Eiffel Tower",
+            "Japan was transformed into a modernized world power after the Meiji Restoration.",
+        ]
+
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2"
+        )
+
+        assert sas_result["sas"] == pytest.approx(0.8227189)
+        assert sas_result["scores"] == pytest.approx([0.689089, 0.870389, 0.908679], abs=1e-5)
+
+    @pytest.mark.integration
+    def test_sas_ignore_case(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with ignoring case sensitivity.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US $2.3 BILLION",
+            "The EIFFEL TOWER, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The MEIJI RESTORATION in 1868 transformed Japan into a modernized world power.",
+        ]
+
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        # SAS after case ignoring
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers", model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2", ignore_case=True
+        )
+
+        assert sas_result["sas"] == pytest.approx(1.0)
+        assert sas_result["scores"] == pytest.approx([1.0, 1.0, 1.0])
+
+    @pytest.mark.integration
+    def test_sas_ignore_punctuation(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with ignoring punctuation.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration, in 1868, transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower completed in 1889 symbolizes Paris's cultural magnificence",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power",
+        ]
+
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        # SAS after ignoring punctuation
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers",
+            model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2",
+            ignore_punctuation=True,
+        )
+
+        assert sas_result["sas"] == pytest.approx(1.0)
+        assert sas_result["scores"] == pytest.approx([1.0, 1.0, 1.0])
+
+    @pytest.mark.integration
+    def test_sas_ignore_numbers(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with ignoring numbers.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration, in 1868, transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US $10.3 billion",
+            "The Eiffel Tower, completed in 2005, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration, in 1989, transformed Japan into a modernized world power.",
+        ]
+
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        # SAS after ignoring numbers
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers",
+            model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2",
+            ignore_numbers=True,
+        )
+
+        assert sas_result["sas"] == pytest.approx(1.0)
+        assert sas_result["scores"] == pytest.approx([1.0, 1.0, 1.0])
+
+    @pytest.mark.integration
+    def test_sas_regex_ignore(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with ignoring specific regex patterns.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration, in 1868, transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US $10.3 billion",
+            "The Eiffel Tower, completed in 2005, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration, in 1989, transformed Japan into a modernized world power.",
+        ]
+
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        # Ignore numeric patterns
+        regex_to_ignore = [r"\d+"]
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers",
+            model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2",
+            regexes_to_ignore=regex_to_ignore,
+        )
+
+        assert sas_result["sas"] == pytest.approx(1.0)
+        assert sas_result["scores"] == pytest.approx([1.0, 1.0, 1.0])
+
+    @pytest.mark.integration
+    def test_sas_multiple_ignore_regex(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with multiple ignoring parameters.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration, in 1868, transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US #10.3 billion",
+            "The Eiffel Tower!!, completed in 2005, symbolizes Paris's cultural magnificence.",
+            "The **Meiji Restoration**, in 1989, transformed Japan into a modernized world power.",
+        ]
+
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        # Ignore numeric patterns and punctuation excluding whitespaces
+        regex_to_ignore = [r"\d+", r"[^\w\s]"]
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers",
+            model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2",
+            regexes_to_ignore=regex_to_ignore,
+        )
+
+        assert sas_result["sas"] == pytest.approx(1.0)
+        assert sas_result["scores"] == pytest.approx([1.0, 1.0, 1.0])
+
+    @pytest.mark.integration
+    def test_sas_multiple_ignore_combination(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score with multiple ignoring parameters combined.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration, in 1868, transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US #10.3 BILLION",
+            "The EIFFEL TOWER!!, completed in 2005, symbolizes Paris's cultural magnificence.",
+            "The **MEIJI RESTORATION**, in 1989, transformed Japan into a modernized world power.",
+        ]
+
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        # Ignore only special characters using regex
+        regex_to_ignore = [r"[^\w\s\d]+"]
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers",
+            model="sentence-transformers/paraphrase-multilingual-mpnet-base-v2",
+            ignore_numbers=True,
+            ignore_punctuation=True,
+            ignore_case=True,
+            regexes_to_ignore=regex_to_ignore,
+        )
+
+        assert sas_result["sas"] == pytest.approx(1.0)
+        assert sas_result["scores"] == pytest.approx([1.0, 1.0, 1.0])
+
+    @pytest.mark.integration
+    def test_sas_bi_encoder(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score using a Bi-Encoder model.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers", model="sentence-transformers/all-mpnet-base-v2"
+        )
+
+        assert sas_result["sas"] == pytest.approx(1.0)
+        assert sas_result["scores"] == pytest.approx([1.0, 1.0, 1.0])
+
+    @pytest.mark.integration
+    def test_sas_cross_encoder(self):
+        """
+        Test calculation of Semantic Answer Similarity (SAS) Score using a Cross Encoder model.
+        """
+        predictions = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        labels = [
+            "A construction budget of US $2.3 billion",
+            "The Eiffel Tower, completed in 1889, symbolizes Paris's cultural magnificence.",
+            "The Meiji Restoration in 1868 transformed Japan into a modernized world power.",
+        ]
+        evaluation_result = self.create_evaluation_result(predictions, labels)
+        sas_result = evaluation_result._calculate_sas(
+            output_key="answers", model="cross-encoder/ms-marco-MiniLM-L-6-v2"
+        )
+
+        assert sas_result["sas"] == pytest.approx(0.999967, abs=1e-5)
+        assert sas_result["scores"] == pytest.approx(
+            [0.9999765157699585, 0.999968409538269, 0.9999572038650513], abs=1e-5
+        )