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: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.
By Chunwei Ma, Russell Wolfinger
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.
By Wes Gurnee, Nicholas Sofroniew, Adam Pearce, Mateusz Piotrowski, Isaac Kauvar, Runjin Chen, Anna Soligo, Paul Bogdan, Euan Ong, Rowan Wang, Ben Thompson, David Abrahams, Subhash Kantamneni, Emmanuel Ameisen, Joshua Batson, Jack Lindsey
The paper compares latent representations in Selective State Space Models (SSMs) like Mamba and Transformers such as Pythia using Sparse Autoencoders. Across a 10‑million token corpus, 99.98% of Mamba features align closely with Pythia’s, supporting the Universality Hypothesis that core semantic representations are similar across architectures. A tiny 0.02% of features diverge, with Mamba’s recurrent bottleneck causing it to compress syntactic anomalies into polysemantic neurons, whereas Pythia’s attention can isolate distinct formatting edge‑cases.
By Rithin Nagaraj, Rupa Laalasa Oruganti, Prerna Subhashchandra Kunder, Ashwini M Joshi
The paper introduces a method to embed a controllable latent variable into natural-looking text by steering a teacher LLM along eight sparse autoencoder directions that follow a ring-shaped Markov chain. A small transformer trained on this data successfully tracks the Bayesian posterior of the planted variable and arranges the eight states in the same ring order, linking belief states to concept geometry. This demonstrates that LLMs can model latent variables and that concept geometry may arise from the statistical dynamics of these variables.
By Alexandru-Iulius Jerpelea
The paper investigates whether a global workspace—a set of verbalisable, causally potent representations—emerges in transformer models that use recurrence instead of a stack of distinct layers. Using a Jacobian lens extended with a virtual‑unrolling adapter, the authors analyze two recurrent transformer architectures, Ouro‑2.6B and Huginn‑0125, and compare them to a standard Qwen3.6‑27B baseline. They find that a workspace does form in the iterated parts of both models, but recurrence alters how it can be accessed: Ouro reconstructs workspace content in every loop and requires writes and ablations across all loops, whereas Huginn forwards content across all recurrences but limits reads, writes, and ablations to a sliding window of about two recurrences.
By Wenlong Wang, Fergal Reid
arXiv:2609.35599v2 Announce Type: replace
Abstract: When recalling lists of concepts (e.g., animals) during the semantic fluency task (SFT), both humans and large language models (LLMs) organise thei...
By Luke Leckie, Peter M. Todd, Jacob G. Foster
The paper identifies a single direction in the unembedding matrix of large language models that encodes the unigram distribution of the training corpus, acting as a Bayesian prior when the model is uncertain. By projecting the final prediction state onto this direction, the authors derive a per‑token prior loading factor, λ, which decreases as context becomes more informative and decomposes predictions into a tempered prior and a context‑driven likelihood. Experiments across four model families (Llama, Qwen, Gemma, Pythia) show that larger models rely less on the prior in high‑context settings and that manipulating λ can steer predictions toward or away from the unigram prior in KL divergence.
By Toni J. B. Liu, Jiajun Bao, Yizhou Liu, Gurbir Arora, Nicolas Boull\'e, Rapha\"el Sarfati, Christopher J. Earls
The paper investigates whether large language models (LLMs) maintain belief states—probability distributions over latent variables—by embedding a controllable latent variable into natural text. An LLM teacher generates ordinary text while subtly steering it along one of eight sparse autoencoder directions, which follow a ring-shaped Markov chain. A small transformer trained on this data successfully tracks the Bayesian posterior of the planted variable and arranges the eight states on a ring in the same order as the Markov chain, suggesting a link between concept geometry and latent variable dynamics.
arXiv:2609.17376v1 Announce Type: new
Abstract: Large language models (LLMs) trained on next-token prediction exhibit remarkable in-context learning (ICL) abilities, yet the representations that supp...
By Daniel Balcells, Andrew Jun Lee, Chirag Rastogi, Paul M. Riechers, Adam Shai, Xavier Poncini
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...
By Xijie Gong, Tonghan Wang
The paper introduces Jacobian Scopes, a set of gradient‑based, token‑level causal attribution techniques for large language models (LLMs). These methods, grounded in perturbation theory and information geometry, measure how individual input tokens affect specific logits, the overall predictive distribution, and model uncertainty. Experiments on instruction understanding, translation, and in‑context learning tasks show that Jacobian Scopes uncover political biases, translation strategies, and mechanisms in time‑series forecasting, and outperform existing attribution methods on token‑ablation benchmarks across six LLMs.
By Toni J. B. Liu, Baran Zadeo\u{g}lu, Gurbir Arora, Rapha\"el Sarfati, Nicolas Boull\'e, Christopher J. Earls