> ## Documentation Index
> Fetch the complete documentation index at: https://futureagi.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Embedding Similarity

> Measures semantic similarity between the generated and reference content.

<CodeGroup>
  ```python Python theme={null}
  result = evaluator.evaluate(
      eval_templates="embedding_similarity",
      inputs={
          "expected": "The Eiffel Tower is a famous landmark in Paris, built in 1889 for the World's Fair. It stands 324 meters tall.",
          "output": "The Eiffel Tower, located in Paris, was built in 1889 and is 324 meters high."
      },
      model_name="turing_flash"
  )

  print(result.eval_results[0].output)
  print(result.eval_results[0].reason)
  ```

  ```typescript JS/TS theme={null}
  import { Evaluator, Templates } from "@future-agi/ai-evaluation";

  const evaluator = new Evaluator();

  const result = await evaluator.evaluate(
    "embedding_similarity",
    {
      expected: "The Eiffel Tower is a famous landmark in Paris, built in 1889 for the World's Fair. It stands 324 meters tall.",
      output: "The Eiffel Tower, located in Paris, was built in 1889 and is 324 meters high."
    },
    {
      modelName: "turing_flash",
    }
  );

  console.log(result);
  ```
</CodeGroup>

| **Input** |                    |                                                                     |
| --------- | ------------------ | ------------------------------------------------------------------- |
|           | **Required Input** | **Description**                                                     |
|           | `expected`         | Reference content for comparison against the model generated output |
|           | `output`           | Model-generated output to be evaluated for embedding similarity     |

| **Output** |            |                                                                        |
| ---------- | ---------- | ---------------------------------------------------------------------- |
|            | **Field**  | **Description**                                                        |
|            | **Result** | Returns score, where higher score indicates stronger similarity        |
|            | **Reason** | Provides a detailed explanation of the embedding similarity assessment |

***

### About Embedding Similarity

It evaluates how similar two texts are in meaning by comparing their vector embeddings using distance-based similarity measures. Traditional metrics like BLEU or ROUGE rely on word overlap and can fail when the generated output is a valid paraphrase with no lexical match.

### How Similarity Is Calculated?

Once both texts are encoded into a high-dimensional vector representations, the similarity between the two vectors `u` and `v` is computed using one of the following methods:

1. **Cosine Similarity:** Measures the cosine of the angle between vectors.

$$
\text{Cosine Similarity} = 1 - \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{u}\| \|\mathbf{v}\|}
$$

1. **Euclidean Distance:** Measures the **straight-line distance** between vectors (L2 Norm).

   $$
   \text{Euclidean Distance} = \sqrt{ \sum_{i=1}^{n} (u_i - v_i)^2 }
   $$

2. **Manhattan Distance:** Measures sum of absolute differences between vectors (L1 Norm).

$$
\text{Manhattan Distance} = {\sum_{i=1}^{n} |u_i - v_i|}

$$

***