Faster Maximum Inner Product Search in High Dimensions
A 2022 research paper presenting algorithms for faster MIPS (Maximum Inner Product Search) in high-dimensional spaces. MIPS is crucial for recommendation systems, neural networks, and various machine learning applications.
About this tool
Overview
Published as arXiv:2212.07551, this paper addresses Maximum Inner Product Search (MIPS) in high-dimensional spaces—a problem closely related to but distinct from nearest neighbor search.
What is MIPS?
Maximum Inner Product Search finds vectors with the highest inner product (dot product) with a query vector:
- Different from nearest neighbor (uses distance, not inner product)
- Important for recommendation systems
- Fundamental to neural network operations
- Common in machine learning applications
Why MIPS Matters
Recommendation Systems
User-item scores often computed as inner products of embedding vectors
Neural Networks
Attention mechanisms rely on inner product computations
Information Retrieval
Some relevance models use inner product for scoring
Matrix Factorization
Finding top components in factorized representations
High-Dimensional Challenge
As dimensionality increases:
- Naive algorithms become computationally expensive
- Traditional ANN techniques don't directly apply
- Inner product structure differs from distance-based search
- Need specialized algorithms
Key Contributions
The paper likely presents:
- Faster algorithms specifically designed for MIPS
- Theoretical analysis of complexity
- Practical heuristics for high dimensions
- Experimental validation on real-world datasets
Relationship to ANN
MIPS can be transformed to nearest neighbor search, but:
- Transformation increases dimensionality
- Direct MIPS algorithms can be more efficient
- Different index structures may be optimal
Use Cases
- Large-scale recommendation engines (millions of items)
- Neural network inference optimization
- Collaborative filtering systems
- Embedding-based retrieval
- Top-K selection in high-dimensional spaces
Practical Impact
Many real-world systems use MIPS:
- Product recommendations in e-commerce
- Content recommendations in streaming services
- Ad targeting systems
- Search ranking
Faster MIPS algorithms directly improve user experience and reduce infrastructure costs.
Availability
ArXiv preprint arXiv:2212.07551 with algorithmic details and performance analysis.
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