There are two common use cases for which we're seeing CockroachDB being adopted by AI native companies (in addition to the expected "vector database" use cases):
- Metadata management
- Identity and Access Management (IAM)
Metadata Management
Metadata management is one of the big use cases we're seeing at some of the innovative and fast growing startups adopting CockroachDB. Sadly, these companies are very competitive and won't allow us to use their name so we can't get a case study completed.
In the absence of a customer-focused use case, I found this article that Bill has written is a fantastic explanation of the metadata management use case:

Go ahead, read the article, it's thorough (which I mean as the the highest compliment).
Gartner agrees. From their article "AI Vendor Race: Emerging Tech: Metadata Becomes the Key to Survival for Data Management Vendors" ($ Gartner subscription required):
Critical Insight: Metadata has emerged as the backbone of delivering AI-ready data, which is the top-most priority for data management leaders in the next three years.
I agree, and believe that the work we're seeing at our customers is the leading indicator proving this critical insight.
Identity and Access Management
When you can't access your systems, it's as if every application is down. Your IAM infrastructure is critical, because if you can't login, you can't do anything.
Ory, an IAM provider, uses CockroachDB on the back-end to ensure resilience and performance (the performance piece comes from placing user data near users to minimize latency for the login requests).
Here's a detailed use case from Cockroach Labs explaining how OpenAI uses CockroachDB with Ory to ensure that you can always login to their service:

Here's the same use case, written from Ory's perspective:
Both use cases are worth reading.

