How does noise affect similarity calculations in embeddings?

Noise in embeddings reduces the accuracy of similarity calculations by introducing random or irrelevant variations that distort the geometric relationships between vectors. Embeddings map data (like words or images) into a high-dimensional space where similarity is measured using metrics like cosine similarity or Euclidean distance. When noise is present—due to low-quality data, measurement errors, or suboptimal model training—it shifts the position of vectors in this space. For example, two semantically similar words like “happy” and “joyful” might have their embeddings pushed farther apart if noise adds unrelated features (e.g., conflating “happy” with a typo like “happly”). This leads to underestimated similarity scores, causing false negatives in tasks like search or clustering.

The impact of noise is amplified in high-dimensional spaces, which are common in embeddings. Small random perturbations across many dimensions can compound, creating larger-than-expected changes in distance metrics. For instance, in a 300-dimensional word embedding, even minor noise in 10% of the dimensions could make two related terms appear less similar. Cosine similarity, which focuses on vector direction, is slightly more robust to noise than Euclidean distance, which is sensitive to magnitude. However, both metrics suffer when noise disrupts the overall structure. Noise can also create “false neighbors,” where unrelated items appear close due to random alignment. Imagine a search system where a query for “python” (the snake) retrieves programming language articles because noisy embeddings accidentally align their vectors.

To mitigate noise, developers should prioritize data cleaning (e.g., removing typos), use robust model architectures (like BERT for text), and apply post-processing techniques. Normalizing embeddings to unit length can reduce the effect of magnitude-based noise. Dimensionality reduction (e.g., PCA) or smoothing methods (like averaging multiple embeddings) can also help. For example, in a recommendation system, averaging user interaction embeddings over time can filter out transient noise. Monitoring embedding quality through sanity checks—like verifying that known-similar items have high similarity scores—is critical. By addressing noise proactively, developers ensure embeddings reliably capture meaningful patterns, improving downstream tasks like retrieval or classification.