A First-Principles Theory of Slow Thinking and Active Perception
For AI researchers working on reasoning and perception, this work offers a foundational theoretical framework that unifies and potentially advances slow thinking models, though it remains largely theoretical without empirical validation.
This paper develops a mathematical theory of slow thinking and active perception, deriving a framework for designing, training, and inferring slow thinking large language models. The theory introduces 'active lifting' based on latent sequence sampling and uncertainty reduction, leading to a design space that includes existing slow thinking models and provides pathways for improvement.
As part of a series on first-principles modeling of cognitive functions, this paper attempts to provide a mathematical formulation of thinking and perception. It formally derives slow thinking or more generally, active perception, and encompasses the design, training and inference of slow thinking large language models. Our starting point is the lifting and projection of probability distributions on the observable and latent spaces, with the objective of representing complex data distributions by simple function families such as neural networks. A theory called "active lifting" is proposed, based on the sampling of latent sequences and an intrinsic drive to reduce uncertainty with maximum rate. It derives a large design space, containing the slow thinking models in a subspace that we call the static theory. These models are positioned on the representation hierarchy and sampler hierarchy induced by the static theory, and can be upgraded by climbing the two hierarchies. Active lifting further derives an inference process with an internal time axis, and a training objective that resembles minimum-length coding as well as the invention of languages. Thus, it characterizes the agency of perception, including the emergence of the slow thinking formats. Technical by-products of this theory include a three-stage pathway for improving slow thinking models, a unified approach to constructing encoders and generative models for all data modalities, a priori formation of human-like visual representations, and a possible solution to policy collapse.