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.
arXiv:2601. 16407v3 Announce Type: replace-cross Abstract: Large language models (LLMs) make next-token predictions based on clues present in their context, such as semantic descriptions and in-context examples.
arXiv:2607. 15495v1 Announce Type: cross Abstract: Out of everything the human brain processes, only a small fraction is consciously accessible, in the sense of being available for verbal report, deliberate control, and flexible reasoning.
arXiv:2608.31084v1 Announce Type: new Abstract: The Jacobian Lens (J-lens) is a recent tool for interpreting LLMs. It reads a hidden state as a ranked list of vocabulary tokens, leaving multi-token c...
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.
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.
Lens methods interpret large language models (LLMs) by mapping intermediate activations to the output vocabulary, revealing how next-token predictions develop through the network. Trained lenses remain expensive: affine-translator parameters grow quadratically with model width, while exact, full-vocabulary Kullback--Leibler (KL) training dominates memory.
arXiv:2608. 15022v1 Announce Type: new Abstract: Language models hold latent quantities in a form they can report on, and more of a quantity is present in that form when the task requires reusing it flexibly.
arXiv:2607. 08843v1 Announce Type: new Abstract: In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space.
arXiv:2604. 06374v2 Announce Type: replace-cross Abstract: Latent reasoning via continuous chain-of-thoughts (Latent CoT) has emerged as a promising alternative to discrete CoT reasoning.
arXiv:2607. 10578v1 Announce Type: new Abstract: Existing hypotheses represent a concept in an LLM as a single point, a linear direction, or a Gaussian cluster, yet it remains unclear how and why such structures emerge.
arXiv:2607. 07128v1 Announce Type: new Abstract: Language models perform a wide range of tasks at varying levels of abstraction with the capacity to flexibly infer tasks from context, execute multiple tasks simultaneously, and select among competing tasks.
arXiv:2608. 10260v1 Announce Type: new Abstract: Lens methods interpret large language models (LLMs) by mapping intermediate activations to the output vocabulary, revealing how next-token predictions develop through the network.