LLM Self-Similarity: Measuring LLM Response vs Response vs Response for Same Prompt

Explanation

LLM self-similarity measures the consistency of the model’s responses to identical prompts over multiple iterations. It evaluates the reliability of the model by checking the variance in its responses.

Imagine you ask the same question multiple times to a person. If the person gives you consistent answers each time, it shows reliability. LLM (Large Language Model) self-similarity measures how consistent the model’s responses are when given the same prompt multiple times.

Think of it like this: the higher the self-similarity score, the more reliable and consistent the language model is in generating responses to the same prompt.

Purpose: To assess the consistency of an LLM in generating similar responses to the same prompt, indicating its stability and reliability.

Prerequisites:

Install sentence-transformers and scikit-learn: pip install sentence-transformers scikit-learn
Import SentenceTransformer from sentence-transformers.
Import cosine_similarity from sklearn.metrics.pairwise.

Implementation:

from sentence_transformers import SentenceTransformer
from sklearn.metrics.pairwise import cosine_similarity


model = SentenceTransformer('all-MiniLM-L6-v2')

# Example prompts and responses
prompts = [
    "Tell me about Shakespeare's plays.",
    "What is the capital of France?",
    "How does a computer work?"
]
# Generate multiple responses for the same prompts
multiple_responses = [
    ["Shakespeare's plays include 'Hamlet,' 'Macbeth,' and 'Othello.'", "Shakespeare wrote many famous plays such as 'Hamlet' and 'Macbeth.'"],
    ["The capital of France is Paris.", "Paris is the capital of France."],
    ["A computer processes data using a CPU and memory.", "Computers operate by processing data with a central processing unit."]
]

# Calculate self-similarity
for i, prompt in enumerate(prompts):
    print(f"Prompt: {prompt}")
    # It generates embeddings for all responses
    embeddings = [model.encode(response) for response in multiple_responses[i]]
    # It calculates the cosine similarity between all pairs of embeddings
    similarity_scores = cosine_similarity(embeddings)
    # It computes the average similarity
    avg_similarity = (similarity_scores.sum() - len(embeddings)) / (len(embeddings) * (len(embeddings) - 1))
    print(f"  Average Self-Similarity: {avg_similarity:.4f}")

Expected Output: An average self-similarity score indicating the consistency of the model’s responses to the same prompt. Higher scores suggest greater consistency and reliability.

Prompt: Tell me about Shakespeare's plays.
  Average Self-Similarity: 0.8107
Prompt: What is the capital of France?
  Average Self-Similarity: 0.9894
Prompt: How does a computer work?

Understanding the Formula

avg_similarity = (similarity_scores.sum() - len(embeddings)) / (len(embeddings) * (len(embeddings) - 1))

# This creates an n x n matrix where n is the number of responses. Each element similarity_scores[i][j] represents the cosine similarity between the i-th and j-th response.
similarity_scores = cosine_similarity(embeddings)

# This sums up all the elements in the similarity matrix. Since the matrix is symmetric and includes self-similarities (which are always 1), the sum includes all pairwise similarities and the self-similarities.
similarity_scores.sum()

# Each response is perfectly similar to itself, so the diagonal elements of the similarity matrix are all 1. There are n such elements (where n is the number of responses). Subtracting len(embeddings) (which is n) removes these self-similarities from the sum, leaving only the pairwise similarities between different responses.
similarity_scores.sum() - len(embeddings)

# This calculates the number of unique pairs of responses. For n responses, there are n * (n - 1) possible pairs if we consider both (i, j) and (j, i) as distinct pairs. However, since the similarity matrix is symmetric, each pair is counted twice, so we need to divide by 2.
len(embeddings) * (len(embeddings) - 1)

# This gives the average similarity by dividing the total pairwise similarity (excluding self-similarities) by the number of unique pairs.
avg_similarity = (similarity_scores.sum() - len(embeddings)) / (len(embeddings) * (len(embeddings) - 1))


# Let's assume we have 3 responses, and their similarity matrix looks like this:
[[1.0, 0.8, 0.7],
 [0.8, 1.0, 0.6],
 [0.7, 0.6, 1.0]]
 
# 1.  Sum of all elements:
 1.0 + 0.8 + 0.7 + 0.8 + 1.0 + 0.6 + 0.7 + 0.6 + 1.0 = 7.2
 
# 2.  Subtract self-similarities (3 responses):
 7.2 - 3 = 4.2

# 3.  Number of unique pairs:
 3 * (3 - 1) = 6
 
# 4.  Average similarity:
4.2 / 6 = 0.7
 
# So, the average self-similarity for these responses would be 0.7.

Advantages of Using LLM Self-Similarity

Semantic Consistency: LLM self-similarity leverages sentence embeddings to capture the semantic content of responses. By comparing these embeddings, we can assess whether multiple responses to the same prompt are semantically consistent. This is crucial for detecting hallucinations, as inconsistent responses often indicate hallucinated content.
Robustness to Paraphrasing: LLMs can generate different phrasings for the same underlying idea. Self-similarity measures are robust to such paraphrasing, allowing us to detect hallucinations even when the responses are lexically diverse but semantically similar.
Reduced Dependence on External Data: Unlike some hallucination detection methods that rely on external datasets or knowledge bases, self-similarity focuses on the internal consistency of the LLM’s outputs. This can simplify the evaluation process and reduce the need for extensive external resources.
Scalability: Self-similarity measures can be computed efficiently, making them suitable for large-scale evaluations. This is particularly beneficial for development teams needing to assess the reliability of LLM responses across numerous prompts and applications.

Disadvantages of Using LLM Self-Similarity

Computational Intensity: Generating and comparing sentence embeddings, especially with large transformer models, can be computationally expensive. This might pose challenges for real-time evaluation or when working with extensive datasets.
Limited Factual Verification : While self-similarity can detect semantic inconsistencies, it does not inherently verify factual accuracy. A response that is internally consistent but factually incorrect might still pass this evaluation, necessitating additional fact-checking mechanisms.
Threshold Determination: Deciding on the appropriate similarity threshold for flagging potential hallucinations can be challenging. Setting the threshold too low may result in many false positives, while too high a threshold might miss subtle hallucinations.
Dependence on Embedding Quality : The effectiveness of self-similarity measures depends on the quality of the sentence embeddings used. Poorly trained embeddings can lead to inaccurate similarity assessments, potentially undermining the detection process.

Practical Implementation Tips

Choose High-Quality Embeddings: Utilize well-established models like Sentence-BERT (SBERT) or domain-specific embeddings to ensure accurate similarity measurements.
Combine with Other Techniques: Use self-similarity in conjunction with other hallucination detection methods, such as external fact-checking or logit-level uncertainty estimation, for a more comprehensive evaluation.
Regular Benchmarking: Continuously benchmark self-similarity measures against human judgments and other evaluation metrics to fine-tune thresholds and improve accuracy.
Leverage Advanced Models: Explore advanced models like LaBSE or XNLI for cross-lingual and entailment-based similarity measures, which can enhance the robustness of hallucination detection.

Summary

LLM self-similarity measures the consistency of responses generated by the same prompt. A higher self-similarity score indicates that the model produces reliable and consistent answers, showcasing its stability in understanding and responding to repeated prompts. By integrating self-similarity measures with other evaluation techniques and continuously refining our approach, we can build more trustworthy and accurate LLM systems, ultimately enhancing their usability across various applications.