A First-Principles Theory of Slow Thinking and Active Perception
Authors: Hongkang Yang, Zhi-Qin John Xu, Feiyu Xiong, Weinan E
Organizations: 1MemTensor (Shanghai) Technology Co., Ltd. · Institute for Advanced Algorithms Research, Shanghai · 3Shanghai JiaoTong University · 4Peking University
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.
Current large language models are extraordinary statistical engines. They compress vast amounts of text into useful patterns and can explain science, write code, imitate reasoning, and participate in philosophical conversation. Yet pattern mastery is not the same as general intelligence. A human infant begins with little explicit knowledge, but gradually discovers object permanence, cause and effect, other minds, bodily agency, and the persistence of the physical world. We make an argument that the path to artificial superintelligence (ASI) depends on a missing capacity we call \emph{situation perception}: the ability to construct, revise, and act within internal simulations of possible worlds across latent time. \emph{ perception} requires at least three core components: abstract prediction, long-term compressed memory, and active learning guided by objectives. In this work, we analyse why modern large language models remain incomplete, and propose the appropriate tests for measuring progress and consequences of machines that can simulate futures, pursue self-directed goals, and possibly judge their own creators.
Vision-Language Models (VLMs) deployed as situated agents in high-resolution visual environments require active perception -- the ability to dynamically decide where to look through operations like zooming, cropping, and panning. However, current training paradigms produce models that mimic the surface form of such operations without functionally depending on their outputs, a phenomenon we term lazy perception. We trace this to a fundamental learning asymmetry: when coarse global views combined with language priors suffice for moderate accuracy, the model has no incentive to learn harder multi-step visual search. If a model can succeed without actively looking, it will never learn to look. This motivates Starve to Perceive, a training paradigm that constrains visual bandwidth -- restricting each observation to a tight token budget so that no single view suffices for task completion, making active perception the only viable strategy. Despite requiring no auxiliary losses, reward shaping, or architectural changes -- serving as a minimal, plug-in modification to standard post-training pipelines -- models trained under perceptual starvation achieve substantial gains of 5% average relative improvement across diverse benchmarks.
While Large Language Models (LLMs) employing Chain-of-Thought (CoT) exhibit superior reasoning capabilities, the neural mechanisms distinguishing this explicit Thinking mode from direct answer generation (NoThinking mode) remain poorly understood. To deconstruct this cognitive process, we apply Top-K Sparse Autoencoders (SAEs) to the intermediate representations of DeepSeek-R1-Distill-Qwen-7B and examine the model's divergent behaviors across math-solving tasks of three distinct difficulty levels. Observationally, we identify a clear distinction in how the model functions under two reasoning modes: Thinking mode relies on sparse and high-intensity feature activations driving verbal deduction independent of problem complexity, whereas NoThinking mode exhibits an adaptive and diffuse pattern prioritizing symbolic manipulation. Causally, suppressing the three most active sparse features by Total Activation Volume reveals three principles: (i) reasoning and syntactic structure are tightly coupled, as interventions consistently degrade \LaTeX{} and boxed-solution formatting; (ii) Thinking responds to disruption with compensatory over-generation marked by increased metacognitive cues and repetitive, low-information continuations; and (iii) coherent CoT behavior depends on a fragile coordination among specialized features, yielding distinct failure modes under perturbation but a consistently impaired output structure.