What does a text embedding encode, and what does it fail to encode?

What the vector is

An embedding model maps a span of text to a fixed-length vector, trained so that texts people treat as related end up close together under a distance measure — usually cosine similarity. What "related" means is not a mathematical property; it is whatever the training objective and training pairs taught the model. A model trained on question-and-passage pairs learns that a question and the passage answering it should be close. A model trained on paraphrase pairs learns that two sentences meaning the same thing should be close. Those are different spaces and they behave differently on the same corpus.

The practical consequence is that an embedding compresses meaning into a few hundred or a few thousand numbers, and compression is lossy in a specific direction: it keeps what varies across the training distribution and discards what does not. Broad topical content survives. Fine distinctions that rarely mattered during training do not.

Similarity is not relevance

The gap that matters most is conceptual rather than technical. Nearest-neighbour search returns the passages closest to the query, and closeness correlates with usefulness without being it. A question and its own restatement are extremely close, and the restatement answers nothing. The FAQ entry asking exactly your question and replying "contact your administrator" is closer to the query than the buried paragraph that contains the answer, because the query's vocabulary is in the question, not in the answer.

This is also why a query and a document are not symmetric objects. A five-word question and a 300-word passage have different lengths, different registers and different information content, and treating them as the same kind of thing is a modelling choice that some models make deliberately and others do not. Models trained for asymmetric retrieval, sometimes with distinct instructions or prefixes for the query and the document side, exist precisely because the naive symmetric treatment underperforms. Using a model outside the regime it was trained for is a common and invisible mistake, because the results are plausible rather than broken.

The three failure classes worth naming

Exact identifiers. Part numbers, error codes, ticket references, invoice numbers, unusual proper nouns. A tokeniser splits EM-4471-B into fragments that carry almost no learned meaning, so its vector is dominated by whatever context surrounded it. Two different part numbers in similar sentences therefore sit close together, and a search for one will happily return the other. This is the single most reported complaint about a dense-only system in an enterprise, because internal corpora are full of identifiers and users type them expecting exact matching.

Negation. "The warranty covers water damage" and "the warranty does not cover water damage" share almost every token and almost all their topic. Their embeddings are close, and a retriever asked which products lack a feature will return passages about products that have it. Nothing in the standard training objective forces a model to separate a claim from its denial, so it largely does not.

Numeric and temporal constraints. "Orders above £500" and "orders above £50" differ by one character and by the entire meaning of a policy. Embeddings do not encode magnitude comparison, so a query about a threshold retrieves passages about thresholds. The same applies to dates: a question about the 2025 rate card retrieves rate cards, and which year it belongs to is a fact you must have stored as metadata and filtered on.

There is a fourth, less discussed: domain drift. A model trained on general web text has thin representations of the vocabulary of your specialised corpus — clinical abbreviations, a trading desk's jargon, a company's internal product names — so distances in that region of the space are noisier than the benchmark numbers suggest. Retrieval benchmarks that span heterogeneous domains exist because in-domain results do not transfer.

What follows from the limits

None of this is an argument against embeddings. It is an argument that dense retrieval is one signal, and the queries where it fails are predictable enough to be routed. A lexical index handles the identifier case directly, because BM25 rewards the literal token that an embedding dissolves. Structured metadata and a filter handle dates and thresholds properly rather than approximately, since a numeric constraint is a WHERE clause pretending to be a search. And a reranker that reads the query and passage together can separate a claim from its negation in a way that two independently computed vectors cannot, because it sees both texts at once.

The signal an interviewer is looking for is whether you know which class a failing query belongs to before you start tuning. Reaching for a larger embedding model when the failing queries are all part numbers is the most expensive way to make no progress.

A high similarity score means the retrieved text resembles the query. It does not mean the text answers it, and for identifiers, negations and numeric limits the resemblance is close enough to be actively misleading.