> ## Documentation Index
> Fetch the complete documentation index at: https://www.getmaxim.ai/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Hamming Embedding Distance

> Counts the number of positions at which two embedding vectors differ, making it suitable for comparing binary or categorical data.

### Input

* **`output`** (str): The generated text to be evaluated.
* **`expectedOutput`** (str): The reference or ground truth text.

### Output

* **`Result`** (int): An integer distance score, from 0 to the dimension of the vectors.

## Interpretation

* **`0`**: The vectors are identical.
* **Higher scores**: The vectors have more differing positions.
  > The result is a discrete integer, not a continuous value.

## Formula

$$
\mathrm{Hamming}(x, y) = \sum_i \mathbb{1}[x_i \ne y_i]
$$

The sum counts the number of positions `i` where the elements differ.

<Note>This is a **distance metric**. Lower scores indicate greater similarity. The score is an integer representing the count of differing dimensions.</Note>

## How It Works

The evaluator computes embeddings for both texts, compares them dimension by dimension, and counts the number of differing positions. For non-binary vectors, this can involve binarization (e.g., thresholding).

## Use Cases

* Comparing binary hashes or fingerprints of data
* Error detection in telecommunications
* Genetics (comparing DNA sequences)
* Evaluating binary or categorical embeddings