Maximum inner-product search

Maximum inner-product search (MIPS) is a search problem, with a corresponding class of search algorithms which attempt to maximise the inner product between a query and the data items to be retrieved. MIPS algorithms are used in a wide variety of big data applications, including recommendation algorithms and machine learning. ^[1]

Formally, for a database of vectors ${\displaystyle x_{i}}$ defined over a set of labels ${\displaystyle S}$ in an inner product space with an inner product ${\displaystyle \langle \cdot ,\cdot \rangle }$ defined on it, MIPS search can be defined as the problem of determining

${\displaystyle {\underset {i\in S}{\operatorname {arg\,max} }}\ \langle x_{i},q\rangle }$

for a given query ${\displaystyle q}$.

Although there is an obvious linear-time implementation, it is generally too slow to be used on practical problems. However, efficient algorithms exist to speed up MIPS search. ^{[1] [2]}

Under the assumption of all vectors in the set having constant norm, MIPS can be viewed as equivalent to a nearest neighbor search (NNS) problem in which maximizing the inner product is equivalent to minimizing the corresponding distance metric in the NNS problem. ^[3] Like other forms of NNS, MIPS algorithms may be approximate or exact. ^[4]

MIPS search is used as part of DeepMind's RETRO algorithm. ^[5]

References

1. Abuzaid, Firas; Sethi, Geet; Bailis, Peter; Zaharia, Matei (2019-03-14). "To Index or Not to Index: Optimizing Exact Maximum Inner Product Search". arXiv: 1706.01449 [cs.IR].
2. Steve Mussmann, Stefano Ermon. Learning and Inference via Maximum Inner Product Search. In Proc. 33rd International Conference on Machine Learning (ICML), 2016.
3. Shrivastava, Anshumali; Li, Ping (2015-07-12). "Improved asymmetric locality sensitive hashing (ALSH) for Maximum Inner Product Search (MIPS)". Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence. UAI'15. Arlington, Virginia, USA: AUAI Press: 812–821. arXiv: 1410.5410 . ISBN   978-0-9966431-0-8.
4. Keivani, Omid; Sinha, Kaushik; Ram, Parikshit (May 2017). "Improved maximum inner product search with better theoretical guarantees". 2017 International Joint Conference on Neural Networks (IJCNN). pp. 2927–2934. doi:10.1109/IJCNN.2017.7966218. ISBN   978-1-5090-6182-2. S2CID   8352165.
5. "RETRO Is Blazingly Fast". Mitchell A. Gordon. 2022-07-01. Retrieved 2022-07-04.

See also

• Nearest neighbor search