arXiv AI

A First-Principles Theory of Slow Thinking and Active Perception

arXiv:2607. 08196v1 Announce Type: new 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.

arXiv AI
Jun 8

The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook

arXiv:2604. 02029v2 Announce Type: replace Abstract: Latent space is rapidly emerging as a native substrate for language-based models.

By Xinlei Yu, Zhangquan Chen, Yongbo He, Tianyu Fu, Guanting Dong, Cheng Yang, Chengming Xu, Yue Ma, Xiaobin Hu, Zhe Cao, Jie Xu, Guibin Zhang, Jiale Tao, Jiayi Zhang, Siyuan Ma, Kaituo Feng, Haojie Huang, Youxing Li, Ronghao Chen, Huacan Wang, Chenglin Wu, Zikun Su, Xiaogang Xu, Kelu Yao, Kun Wang, Chen Gao, Yue Liao, Ruqi Huang, Tao Jin, Zhucun Xue, Cheng Tan, Jiangning Zhang, Wenqi Ren, Yanwei Fu, Yong Liu, Yu Wang, Xiangyu Yue, Yu-Gang Jiang, Shuicheng Yan
arXiv Machine Learning
Sep 16

Attention Mean Fields Predict Average Representation Dynamics and Reveal Context-Specific Computation

The paper presents a mean‑field analysis of attention in language models, defining an average attention kernel that propagates representations layer by layer. When conditioned on a whole corpus, the kernel predicts the average evolution of representation geometry; when conditioned on a single context, it predicts the expected geometry for that context. The difference between actual attention and the mean‑field prediction—called the mean‑field deviation—captures context‑specific computation, revealing how models diverge from average behavior during training and in few‑shot tasks.

By Micah Adler, John W. Byers, Mark Crovella
arXiv Computation and Language
Aug 27

Short Horizons and Sparse Concepts: a Mathematical View of the Readout in the J-lens

The paper presents a mathematical analysis of the Jacobian lens (J‑lens), a method for extracting verbalizable representations from language models. It treats the J‑lens as a first‑order causal transfer operator, showing that its Jacobian matrix serves as an optimal local linear approximation of downstream mappings and that its energy distribution is highly sparse, concentrating in diagonal pathways and critical positions. This sparse, short‑horizon structure explains why the J‑lens can effectively visualize concepts during a model’s reasoning process, and the authors propose a decoupling strategy that further improves its ability to read out correct intermediate concepts.

By Shi-Qi Yan, Kai-Xuan Ding, Chao-Hong Tan, Qian Chen, Wen Wang, Xiangang Li, Zhen-Hua Ling
arXiv AI
Sep 2

Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs

Latent Recurrent Thoughts (LRT) proposes a method for reasoning with frozen large language models by operating in the model’s continuous representation space. A small auxiliary network generates initial latent vectors, which a tiny recurrent reasoner refines over multiple steps, decoupling computational depth from model size. Experiments on symbolic and natural‑language reasoning tasks show that LRT outperforms prior frozen‑decoder continuous‑space methods and chain‑of‑thought prompting while using far less inference compute.

By Zhaoliang Chen, Jie Fu