The spark for this idea comes from the functional role of biological sleep. Far from being a passive pause, dreaming is a state where the brain actively consolidates memories and creatively recombines distant ideas. This may explain why mathematical breakthroughs often feel less like linear deduction and more like the sudden alignment of distant concepts—arriving after the mind has wandered and reorganized its internal knowledge.

Machine Reverie asks a simple question: Can we give large language models a similar "subconscious" loop? While modern models excel at reproducing known proofs, they remain brittle when the path isn’t clearly laid out. They lack the intuitive flexibility to reorganize their internal knowledge, spot deep analogies, or form the "hunches" that drive discovery.

To bridge this gap, the project introduces a training rhythm inspired by this biological cycle. The model alternates between two modes. In the "wake" mode, it pursues rigorous, goal-directed problem solving. In the "dream" mode, it relaxes constraints to explore—generating new proof sketches and unexpected connections based on its own recent activity. This structure aims to transform the model from a passive reciter into an active thinker capable of genuine mathematical growth.