Mark Zuckerberg, Meta's chief executive, recently criticized rival Anthropic in a 6,500-word essay, accusing leading A. I. labs of consolidating power while painting the future as "filled with doom." He warned that if those labs lead, "the balance of power will favor larger institutions over individuals." But privately, Meta has become one of Anthropic's largest customers. The social networking giant, which owns Facebook and Instagram, has used Anthropic's A.

I. products extensively, even projecting internal spending of up to $10 billion annually on the start-up's tools. That would represent a major chunk of Anthropic's yearly revenue, which the start-up estimated in July would pass $65 billion. Meta cut back on some Anthropic spending this summer but continues spending hundreds of millions monthly on the tools.

The company uses Anthropic's models to power and test a coming A. I. product called Hatch, which Zuckerberg described as Meta's next breakthrough agent that works "24/7 on your behalf." Meta's leaders are aware their spending could affect Anthropic ahead of a potential blockbuster initial public offering that could value the start-up at $2 trillion. Among the frenemies in Silicon Valley's A.

I. race are Google and Amazon, which have committed to investing $73 billion in Anthropic even as they develop their own models.