A First-Principles Theory of Slow Thinking and Active Perception

2026-07-09

AI Summary

This work proposes a unified first-principles framework for slow thinking and active perception, introducing the “active lifting” theory. By lifting and projecting probability distributions between observable and latent spaces, and integrating latent sequence sampling with maximization of uncertainty reduction rate, the approach constructs an internal-time-axis reasoning mechanism. The training objective is designed following a minimum description length–like principle. This formulation reveals a dual-level structure of representation and sampling, elucidating the emergent mechanisms underlying slow-thinking formats. Furthermore, it derives a three-stage refinement pathway that not only accounts for the formation of human-like visual priors and mitigates policy collapse but also provides a unified architectural foundation for multimodal models.

Abstract

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.

Problem

• slow thinking
• active perception
• first-principles theory
• cognitive modeling
• representation learning

Innovation

• active lifting
• slow thinking
• first-principles modeling
• uncertainty reduction
• representation hierarchy