Anthropic CEO Dario Amodei in May. Don Feria/AP Content Services for Anthropic Anthropic just filed a confidential S-1 draft for its highly anticipated IPO. Anthropic and OpenAI are in a race to IPO, staking claims on the lucrative AI market. Expected IPOs of Anthropic and OpenAI could value each company at over $1 trillion. The race to IPO is on: Anthropic just filed its confidential S-1 draft. On Monday morning, the AI juggernaut announced it had turned in its first IPO proposal to the U.S.