Study Card: Evaluating LLM Embeddings

Direct Answer

Evaluating LLM embeddings involves assessing their ability to capture semantic relationships between text. Metrics like cosine similarity, Euclidean distance, and ranked correlation (Spearman's rho) can quantify similarity between embedding vectors. For semantic similarity tasks, benchmark datasets with human-labeled similarity scores are used to compare model performance. In information retrieval, metrics like precision, recall, and mean average precision (MAP) measure how well embeddings retrieve relevant information. Evaluating on downstream tasks and visualizing embeddings can provide further insights into their quality.

Key Terms

• Cosine Similarity: Measures the cosine of the angle between two vectors, representing their directional alignment. Higher cosine similarity indicates greater semantic relatedness.
• Euclidean Distance: Calculates the straight-line distance between two vectors. Smaller Euclidean distance suggests higher similarity.
• Spearman's Rho: A rank correlation coefficient that measures the monotonic relationship between two sets of rankings. Used to compare model-predicted similarity rankings with human judgments.
• Mean Average Precision (MAP): A metric commonly used in information retrieval to evaluate the quality of ranked search results.
• t-SNE (t-distributed Stochastic Neighbor Embedding): A dimensionality reduction technique used to visualize high-dimensional embeddings in a 2D or 3D space, revealing clusters and relationships.

Example

Consider evaluating embeddings generated by an LLM for sentence similarity. The model embeds two sentences, "The cat sat on the mat" and "The feline rested on the rug." Cosine similarity between these embeddings reflects semantic closeness. Comparing these similarity scores against human judgments on a benchmark dataset like STS Benchmark provides a quantitative measure. In information retrieval, given a query, the model retrieves documents with embeddings closest to the query embedding. MAP evaluates the ranking of retrieved documents based on relevance. Visualizing embeddings of related concepts using t-SNE can qualitatively assess if the embeddings capture semantic relationships, revealing clusters of similar concepts.

Code Implementation

import torch
from sklearn.metrics.pairwise import cosine_similarity
from scipy.stats import spearmanr
from sklearn.metrics import average_precision_score

# Example: Calculating cosine similarity
embeddings1 = torch.randn(10, 512)  # Batch of 10 embeddings, dimension 512
embeddings2 = torch.randn(10, 512)

cosine_sim = cosine_similarity(embeddings1.numpy(), embeddings2.numpy())
print("Cosine Similarity:")
print(cosine_sim)

# Example: Calculating Spearman's rho
human_similarity_scores = [4, 3, 5, 1, 2]
model_similarity_scores = [0.8, 0.7, 0.9, 0.2, 0.5] # Using cosine similarity output from before.
rho, p_value = spearmanr(human_similarity_scores, model_similarity_scores)
print(f"Spearman's rho: {rho}")

# Example: Calculating Mean Average Precision (MAP) in Information Retrieval
true_relevance = [1, 0, 1, 1, 0]  # True relevance of retrieved documents (1: relevant, 0: irrelevant)
retrieved_scores = [0.9, 0.8, 0.7, 0.6, 0.5]  # Scores assigned by the model (e.g., similarity to query)
map_score = average_precision_score(true_relevance, retrieved_scores)
print(f"Mean Average Precision (MAP): {map_score}")

# Example: Visualizing embeddings with t-SNE (using scikit-learn)
from sklearn.manifold import TSNE
import matplotlib.pyplot as plt

embeddings = torch.randn(100, 768) # Example embeddings
tsne = TSNE(n_components=2, perplexity=30, n_iter=300)
embeddings_2d = tsne.fit_transform(embeddings.numpy())

plt.scatter(embeddings_2d[:, 0], embeddings_2d[:, 1]) # Plotting in 2D
plt.show()

Related Concepts

• Semantic Similarity Datasets: Benchmark datasets like STS Benchmark, SICK, and SemEval provide human-labeled similarity scores for evaluating semantic similarity models. Interviewers might ask about specific datasets and their characteristics.
• Information Retrieval Systems: The application of embedding similarity to retrieve relevant information, such as search engines and recommender systems. Interviewers may discuss different retrieval methods and challenges.
• Bias in Embeddings: Embeddings can reflect biases present in training data, which can impact downstream tasks. You might be asked about potential biases and mitigation strategies.
• Transfer Learning with Embeddings: Using pre-trained embeddings to improve performance on downstream tasks with limited labeled data. Interviewers might ask about fine-tuning and adapting pre-trained embeddings.
• Interpretability of Embeddings: Understanding what information is captured by different dimensions of the embedding space, which can help diagnose issues and improve model performance. Could involve probing tasks or visualizing specific dimensions.