Some AI problems stay unsolvable, even with infinite data

A team from the University of Cambridge and the University of California, Santa Barbara says there are hard limits to what AI can learn — and in some cases, more data does not help. In work published in Nature Communications, the researchers built “adversarial” mathematical systems designed to fool any AI algorithm, with the goal of showing exactly where prediction methods fail.

The target is a common problem in science and engineering: systems such as the oceans, the human brain, or robots are often too messy to capture with neat equations, so researchers turn to machine learning instead. But according to the study, some of these problems are not just difficult. They are fundamentally impossible to solve reliably, even with infinite data.

What breaks AI prediction

Lead author Dr. Matthew Colbrook of Cambridge’s Department of Applied Mathematics and Theoretical Physics said the work is about identifying the boundary between solvable and unsolvable tasks.

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“We’re probing the boundaries of what you can and can’t do with AI.”

The team used Koopman operator learning, a method that recasts complex nonlinear behavior into a linear form that is easier to analyze. From there, they found two main reasons machine learning breaks down in complex systems:

• the algorithm cannot tell when it has seen enough data to produce a reliable answer
• key patterns are hidden or too difficult to distinguish

Colbrook said a widespread assumption in AI research is that enough data will eventually make learning work, but the team’s results show that is “often wrong.” In some cases, learning must happen in multiple steps and in the right order.

The paper also links these limits to chaotic systems, where tiny differences in starting conditions can lead to very different outcomes. In those cases, short-term prediction can still work, but long-term prediction becomes unreliable as errors compound. The researchers say the same kind of instability may help explain why chatbots such as ChatGPT or Claude can sound accurate at first, then drift or hallucinate over longer responses.

Arctic sea ice test and a lower-cost reliability check

The researchers also developed what they describe as a provably reliable and highly efficient algorithm with built-in error bounds, aimed at helping users judge when an AI model’s output can actually be trusted. They say it can do that at a fraction of the cost of most supercomputers.

To test it, the team applied the method to more than 40 years of Arctic sea ice data. According to the study, the algorithm uncovered hidden patterns in the decline of sea ice and outperformed current leading AI models while running on a standard laptop.

“We’re at the stage now where there have been a lot of flashy examples and success stories in AI, but it’s vital that we also ask how certain the models are, and how we know whether they’re certain.”

The paper is titled “Adversarial dynamical systems characterize when data-driven learning succeeds or fails” and carries the DOI 10.1038/s41467-026-74220-8.