The Uncertainty Principle of Information Retrieval

Vector search has become the backbone of modern information retrieval systems, powering everything from recommendation engines to RAG (Retrieval-Augmented Generation) applications. While the technology is undeniably powerful, I’ve encountered several fundamental issues that keep me up at night as someone building these systems. Let me share the three core problems that make me question whether we’re truly solving information retrieval or just creating a more sophisticated form of ignorance.

The Completeness Problem: Did I Miss Something Critical?

The most haunting aspect of vector search is that you never know if you’ve found all the relevant information. Unlike traditional keyword search where you can at least verify that certain terms appear or don’t appear in your corpus, vector search operates in a high-dimensional space that’s fundamentally opaque to human intuition.

Consider this scenario: You’re building a medical diagnosis assistant and someone queries about “chest pain.” Your vector search might return documents about heart attacks, angina, and muscle strain. But what if there’s a crucial document about a rare condition that manifests similarly but uses completely different terminology? The embedding model might have learned to associate those terms differently, or the document might use medical jargon that doesn’t align with your query’s semantic space.

The terrifying reality is that absence of results doesn’t mean absence of relevant information. In traditional databases, a null result tells you something definitive. In vector search, it might just mean your query vector happened to land in a sparse region of the embedding space, while perfectly relevant documents exist just beyond your similarity threshold.

The Multi-Semantic Query Paradox

Here’s where things get mathematically interesting and practically frustrating. What happens when your query contains multiple distinct semantic concepts? How does the embedding model decide which semantic dimension to prioritize when computing the query vector?

Let’s say someone searches for “sustainable energy investment opportunities in developing countries.” This query contains at least four distinct semantic domains:

• Sustainability and environmental concepts
• Energy and technology terminology
• Financial and investment language
• Geopolitical and development economics

When the embedding model processes this query, it creates a single vector that somehow represents all these concepts. But which semantic aspect dominates the vector representation? The model might weight the “investment” semantics more heavily, leading you to financial documents that mention energy in passing. Or it might prioritize “sustainable energy,” missing critical documents about investment strategies in developing markets.

The fundamental issue is that we’re compressing multi-dimensional semantic meaning into a single point in vector space. It’s like trying to represent the full complexity of a symphony with a single musical note – some information is inevitably lost in translation.

The HYDE Multiplication Problem: How Many Hypothetical Documents is Enough?

HyDE (Hypothetical Document Embeddings) was supposed to solve some of these problems by generating hypothetical answers and using their embeddings for search. But this approach introduces a new question that borders on the philosophical: How many HyDEs do you need to generate to ensure you’ve captured all possible semantic interpretations?

If I generate one hypothetical document for “chest pain,” I might get something focused on cardiac issues. Generate another, and it might emphasize respiratory problems. A third might discuss musculoskeletal causes. Each hypothetical document represents a different semantic pathway through the information space.

But here’s the catch: You don’t know how many different semantic pathways exist until you’ve already found them. It’s a classic chicken-and-egg problem. You need to know what you’re looking for to know if you’ve looked hard enough.

This becomes exponentially worse with complex queries. For our “sustainable energy investment” example, you’d need hypothetical documents covering:

• Technical energy analyses
• Investment prospectuses
• Sustainability reports
• Development economics papers
• Policy documents
• Case studies
• Market analyses

Where do you stop? How do you know you’ve generated enough HyDEs to cover the semantic space?

The High-Stakes Inference Problem

All of these uncertainties compound into what I consider the most serious issue: We’re making confident assertions based on fundamentally uncertain information retrieval.

RAG systems don’t just return search results – they generate authoritative-sounding responses based on whatever documents the vector search happened to find. If your search missed a critical piece of information due to any of the problems above, your generated response might be confidently wrong rather than appropriately uncertain.

This is particularly dangerous in high-stakes applications like medical advice, legal research, or financial recommendations. Traditional search systems at least made their limitations obvious – you could see the queries that returned no results, understand which keywords weren’t found. With vector search, the system always returns something, creating an illusion of completeness that might be entirely false.

What This Means for Practitioners

I’m not arguing that we should abandon vector search – it’s still incredibly powerful for many applications. But we need to acknowledge these limitations and build systems accordingly:

1. Implement multiple retrieval strategies – Don’t rely solely on vector search. Combine it with keyword search, knowledge graphs, and other retrieval methods.

2. Make uncertainty visible – Design interfaces that communicate the inherent uncertainty in vector search results rather than presenting them as complete and authoritative.

3. Test for edge cases – Systematically test whether your system finds known relevant documents, especially those that use different terminology than your typical queries.

4. Consider semantic diversity – When generating HyDEs or query variations, explicitly try to cover different semantic interpretations rather than just paraphrasing the same concept.

The future of information retrieval isn’t about perfecting vector search – it’s about building systems that acknowledge and work with uncertainty rather than hiding it behind a veneer of mathematical sophistication.

Until we solve these fundamental problems, every vector search system carries with it a hidden asterisk: “Based on the information we happened to find.” The question is whether we’re comfortable with that uncertainty, and more importantly, whether our users know it exists.