These days, large language models can handle increasingly complex tasks, writing complex code and engaging in sophisticated reasoning. But when it comes to four-digit multiplication, a task taught in elementary school, even state-of-the-art systems fail. Why?

A new paper posted to the arXiv preprint server by University of Chicago computer science Ph.D. student Xiaoyan Bai and faculty co-director of the Data Science Institute’s Novel Intelligence Research Initiative Chenhao Tan finds answers by reverse-engineering failure and success.

They worked with collaborators from MIT, Harvard University, University of Waterloo and Google DeepMind to probe AI’s “jagged frontier”—a term for its capacity to excel at complex reasoning yet stumble on seemingly simple tasks.

A biologically grounded computational model built to mimic real neural circuits, not trained on animal data, learned a visual categorization task just as actual lab animals do, matching their accuracy, variability, and underlying neural rhythms.

Like human decision-making under real-world constraints, artificial neural networks may balance free exploration in parameter space with task-relevant adaptation. In this study, we identify consistent signatures of criticality during neural network training and provide theoretical evidence that such scaling behavior arises naturally from information-driven self-organization: a dynamic balance between the maximum entropy principle that promotes unbiased exploration and mutual information constraint that relates updates with task objective. We numerically demonstrate that the power-law exponent of updates remains stable throughout training, supporting the presence of self-organized criticality.