A minority of artificial-intelligence systems used by federal government agencies can be classified as highly sophisticated, a new study shows, pointing to the technology gap between the public and private sectors.

The report, published last week by Stanford Law School and New York University School of Law, examined 157 use cases of AI spread across 64 nonmilitary agencies. The researchers were able to analyze only 61 of the 157 systems; for the majority, not enough technical documentation was publicly available to do so, the study said.

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The data set, while limited, shows that the use of highly sophisticated AI in the public sector lags behind the private sector, said David Engstrom, associate dean at Stanford Law School and a co-author of the report. That’s a concern because less-sophisticated AI makes it harder for the government to use the technology to achieve operational gains, he said.

“If you want an effective, efficient government, you want it to be able to leverage cutting-edge technology,” Mr. Engstrom said. “Especially for an enforcement agency, you don’t want the government operating with one hand tied behind its back.”

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The Stanford report comes as the U.S. is seeking to ramp up investments in AI, fueled in part by fierce global competition from China and amid regulatory pressures emanating from the European Union. The White House this month proposed roughly doubling nondefense research-and-development spending on AI to $2 billion over the next two years. The Navy is pressing ahead with plans to update its aging tech infrastructure.

Here is how Mr. Engstrom defined the levels of sophistication described in the report:

• Many highly sophisticated AI systems utilize neural networks, a machine-learning approach that has gained steam in recent years and is known for powering object-recognition and natural-language-understanding systems. The Bureau of Labor Statistics has a tool that uses a neural network to categorize worker injuries by reading those workers’ written accounts.
• Medium-level tools include chatbots and prediction engines. For instance, The U.S. Postal Service has a tool that provides customers with time-window predictions for deliveries.
• Low-sophistication tools include a Department of Veterans Affairs system that identifies veterans who are at elevated risk for suicide, based on factors including hospital admissions and prescription history.

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Mr. Engstrom said some agencies are introducing advanced AI systems. The Social Security Administration has developed a natural-language-processing tool that helps determine if a judge erred in deciding whether someone qualifies for disability benefits, he said. The system does that by analyzing a draft decision and flagging roughly 30 types of issues that are suggestive of policy noncompliance or internal inconsistencies.