Existing popular search engines (Google, Bing) are sort of bad. Almost nobody is trying to fix this. Exa is, but appears to have pivoted toward LLM agent systems, where they do not have an obvious comparative advantage, and make odd technical decisions such as using IVF/PQ (see Vector Indexing), apparently hosting things on AWS, and running off disk rather than out of RAM (limiting query throughput: see https://x.com/exaailabs/status/1859690195463045630).
What should a search engine do?
The job of a search engine is to retrieve useful information for users. This is usually mostly inferred from/determined by the query, but most modern engines make some use of user history and data. How can a search engine work better?
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Better user intent modelling.
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Better information sources to retrieve from.
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Better search, search indexing and understanding of information sources.