Vespa Tensor Formalism
Advanced Retrieval, Ranking, and Personalization Beyond Vector Similarity
Vespa is vector- and tensor-native by design. By preserving structure across scalars, dense and sparse vectors, and higher-order tensors, Vespa enables precise retrieval, transparent ranking logic, and real-time personalization that vectors alone can’t support.
AI Systems Need Structure, Not Just Similarity
Think of vectors as 1-dimensional tensors. Collapsing signals into a single dimension may work for global semantic similarity, but it discards the structure needed to explain why something is relevant.
Vespa’s tensor framework keeps that structure intact.
With tensors, you can:
- Score at token/patch-level (late interaction models)
- Combine dense + sparse + lexical relevance in one pipeline
- Express sophisticated ranking logic with transparent math
- Represent personalization signals without external joins
- Run tensor computations where the data lives, with predictable latency
The result is hybrid relevance that goes beyond what vector-only systems can express.
Tensor Capabilities Across the Vespa Platform
Vespa moves beyond “how similar is this document?” by evaluating structure, interaction, and context throughout retrieval and ranking. Tensor-based relevance scoring and real-time personalization work together in one pipeline, delivering precise, explainable results that adapt as data, models, and business needs evolve.
Tensor-Based Retrieval
From Candidate Selection to Fine-Grained Matching
Documents are represented as multiple embeddings (tokens, passages, or regions), allowing queries to match the most relevant parts of each document for precise late-interaction scoring.
Hybrid Retrieval with Preserved Structure
Sparse and dense embeddings, along with structured filters, all participate in the same retrieval phase, without flattening signals or stitching systems together.
Scale without Losing Precision
All tensor-based retrieval operations execute where the data lives, on Vespa content nodes. Tensors are indexed, updated in real time, and evaluated efficiently at query time.
Tensor-Based Ranking and Scoring
Expressive Ranking with Tensor Math
Vespa ranking expressions operate on scalars and tensors, enabling similarity, aggregation, normalization, and weighting across tokens, features, modalities, and user attributes, so ranking reflects how relevance is actually determined, not just vector distance.
Combine Multiple Relevance Signals
Dense embeddings, sparse lexical features, structured metadata, business rules, and personalization signals are combined in a single scoring function. Each signal keeps its structure, allowing explicit weighting and normalization instead of collapsing everything into one embedding.
Increase Precision with Multi-Phase Ranking
Vespa applies fast vector scoring to large candidate sets, then progressively more detailed tensor-based scoring to smaller result sets, delivering high relevance with predictable performance at scale.
Tensor-Based Personalization
Model Signals as Tensors
Vespa represents user preferences, interaction history, and contextual signals as structured tensors. These signals update continuously and independently of content, keeping personalization aligned with the most recent user behavior.
Personalization as Tensor Computation
At query time, Vespa compares user and context tensors directly with content tensors using ranking expressions, balancing long-term preferences with short-term intent through explicit, inspectable tensor math.
Blend Personalization with Global Relevance
Personalization participates in the same ranking framework as semantic, lexical, freshness, and business signals, delivering real-time relevance that is personalized without becoming brittle, narrow, or opaque.
Build with Tensors in Vespa
From sparse lexical features to token-level late interaction and multimodal embeddings, Vespa’s tensor framework gives you one engine for advanced retrieval, ranking, and personalization built for production.
Start building enterprise-grade RAG, Search, and Recommendation systems on Vespa Cloud.
Other Resources
Building Scalable RAG for Market Intelligence & Data Providers
Learn how Vespa delivers accurate, high-performance retrieval for GenAI agents at web scale.
The RAG Blueprint
Accelerate your path to production with a best-practice template that prioritizes retrieval quality, inference speed, and operational scale.
