Scientists have uncovered new insights into how artificial intelligence agents internally represent the world, showing that their learning isn’t confined to simple smooth structures but instead involves complex, layered geometric patterns. In a study led by mathematicians at the University at Albany, researchers analyzed how a transformer-based agent navigates a game environment and discovered that its internal representations jump between different geometric “strata” rather than lying on a straightforward surface. This suggests AI systems organize information in much richer and more varied ways than previously assumed.
The team tracked how the agent processed visual frames — treating each frame like a “token” in a language model — and measured the dimensional complexity of those internal representations. They found clear differences in geometric structure depending on task difficulty: lower-dimensional states appeared when the environment was simpler or when the agent was confident in its actions, while higher-dimensional states corresponded to moments of uncertainty, such as evaluating multiple possible moves or interpreting complex scenes. This pattern suggests the AI’s internal “thinking space” expands when decisions are harder.
To reveal these patterns, the researchers used a mathematical tool called the Volume Growth Transform, which maps how the volume of internal representation changes over time. Their findings challenge previous assumptions (such as manifold and fiber-bundle hypotheses) that AI representations lie on smooth mathematical surfaces. Instead, the results point to a stratified geometry with abrupt transitions between layers, each reflecting different reasoning contexts or levels of uncertainty the model encounters during tasks.
The discovery not only improves our fundamental understanding of how AI systems think internally but could also have practical implications. By linking specific geometric changes to particular moments of decision-making difficulty, researchers believe this framework could guide new training methods or diagnostic tools that pinpoint where an AI model struggles most. Such insights may ultimately help developers tailor learning and evaluation processes, making future AI agents more reliable and adaptable.
