Beyond Vector Search: The Move to Tensor-Based Retrieval

This is the second of two parts. Read also:

• Vector Search Is Reaching Its Limit. Here’s What Comes Next

In Part 1, we explored the growing limitations of vector-only search systems,  highlighting how flat embeddings fall short in scenarios requiring structured filtering, real-time updates, personalized ranking and multimodal understanding.

As AI applications evolve, it’s clear that semantic similarity alone isn’t enough. What’s needed is structure — a way to represent relationships within and across modalities in a form that’s both expressive and performant.

That’s where tensors come in.

While vectors and tensors are technically the same kind of object — both are numerical representations used in machine learning — a vector is simply a one-dimensional tensor. Tensors generalize that idea to multiple dimensions, enabling richer, more expressive representations.

Because tensors preserve critical context — sequence, position, relationships and modality-specific structure — this makes them far better suited for advanced retrieval tasks where precision and explainability matter.

Vectors vs. Tensors: A Quick Comparison

At a glance, vectors and tensors may look similar. But when it comes to expressing context and relationships, their capabilities diverge sharply:

Vectors flatten the data, representing everything as a single embedding. Tensors retain structure, enabling:

• Fine-grained retrieval, such as matching specific tokens or image regions.
• Context-aware embeddings across modalities that preserve semantic and spatial relationships.
• Precise query interaction where similarity is just one of many dimensions considered.

These capabilities make tensors the foundation for powering modern retrieval techniques like ColBERT, ColPali and temporal video search, all of which depend on comparing multiple embeddings per document, not just one.

Trying to replicate these capabilities with vectors alone leads to fragile architectures: external pipelines for reranking, disconnected model services for filtering and a patchwork of components that are costly to maintain and difficult to scale.

A Simplified Tensor Framework

In most machine learning libraries, tensors are treated as unstructured, implicitly ordered arrays with weak typing and inconsistent semantics. This can create major challenges in real-world applications:

• Large, inconsistent APIs that slow down development.
• Separate logic for handling dense vs. sparse data.
• Limited optimization potential and hard-to-read, error-prone code.

These limitations become especially painful in workloads involving hybrid data, multimodal inputs and complex ranking or inference pipelines. A more practical approach for leveraging tensors with retrieval augmented generation (RAG) pipelines should follow a more formalized framework, including:

• A minimal, composable set of tensor operations.
• Unified support for dense and sparse dimensions.
• Strong typing with named dimensions.

Let’s dig into these further.

Minimal, Composable Tensor Operations

A minimal, composable set of tensor operations keeps a framework powerful yet manageable. By replacing bloated APIs with a small, mathematically grounded set of core operations, it makes it easier to read, learn and debug code while reducing the risk of bugs. Developers can compose these building blocks to express complex logic, adapt quickly to new workloads and avoid rewriting the framework.

This lean approach also gives the system a clearer computation graph, unlocking better optimization opportunities such as vectorization, parallelization and memory reuse.

Unified Handling of Dense and Sparse Dimensions

Data often comes in both dense and sparse forms. Dense data might be a product image embedding, where every pixel or visual feature is represented, resulting in a fully populated array. Sparse data, on the other hand, could be product attributes like brand, size or material.

In many frameworks, these two types of data are handled separately, with images in one format and attributes in another, requiring different APIs and logic for each. This separation adds unnecessary complexity to development, maintenance and optimization.

By representing both dense and sparse data within the same unified tensor framework, a product’s image embeddings and its structured attributes can be combined seamlessly in a single representation, queried together and fed directly into the same ranking or inference pipeline without format conversions.

The benefits are twofold: developers only have to work with one consistent API, reducing complexity and the potential for bugs, while the system itself can optimize performance across all features at once.

In an e-commerce search or recommendation scenario, this unified handling enables richer, more precise relevance scoring by blending visual similarity with attribute-based filtering in real time, delivering faster, more accurate results to customers.

Strong Typing with Named Dimensions

Strong typing with named dimensions gives tensors a layer of semantic clarity that most generic array-based systems lack. Named dimensions act like human-readable labels for each axis in your data (such as product_id, color_channel, timestamp), so instead of juggling positions in an index, you can work directly with meaningful identifiers.

This makes computations safer by preventing dimension mismatches that could silently produce wrong results, while also making code easier to understand at a glance. The result is a framework where logic is both explicit and maintainable, reducing costly errors and accelerating iteration without sacrificing precision.

Why the Future of AI Applications Belongs to Tensors

Vector search has been a powerful enabler, but as applications grow more complex, dynamic and multimodal, vectors are no longer sufficient. Tensors provide the foundation that vector-only systems lack. If vectors help retrieve, tensors help reason.

Unlike flat vectors, tensors preserve structure, enable hybrid logic and support meaningful computation across diverse data types. With Vespa’s production-ready tensor framework, organizations can seamlessly integrate dense and sparse data, personalize experiences at scale and make real-time, context-aware decisions, all within one high-performance platform.

Making Tensors More Practical

Grounded in these core principles, Vespa developed a rigorously defined, strongly typed tensor formalism to make tensors more practical to use at scale. Unlike many machine learning frameworks that focus solely on model development, Vespa’s tensor framework is also designed for high-performance serving in real-time production environments. Learn more in this report.