“Sat Chatterjee has waged a campaign of misinformation against me and Azalia for over two years now,” Ms. Goldie said in a written statement.

She said the work had been peer-reviewed by Nature, one of the most prestigious scientific publications. And she added that Google had used their methods to build new chips and that these chips were currently used in Google’s computer data centers.

Laurie M. Burgess, Dr. Chatterjee’s lawyer, said it was disappointing that “certain authors of the Nature paper are trying to shut down scientific discussion by defaming and attacking Dr. Chatterjee for simply seeking scientific transparency.” Ms. Burgess also questioned the leadership of Dr. Dean, who was one of 20 co-authors of the Nature paper.

“Jeff Dean’s actions to repress the release of all relevant experimental data, not just data that supports his favored hypothesis, should be deeply troubling both to the scientific community and the broader community that consumes Google services and products,” Ms. Burgess said.

Dr. Dean did not respond to a request for comment.

After the rebuttal paper was shared with academics and other experts outside Google, the controversy spread throughout the global community of researchers who specialize in chip design.

The chip maker Nvidia says it has used methods for chip design that are similar to Google’s, but some experts are unsure what Google’s research means for the larger tech industry.

“If this is really working well, it would be a really great thing,” said Jens Lienig, a professor at the Dresden University of Technology in Germany, referring to the A.I. technology described in Google’s paper. “But it is not clear if it is working.”

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