The paper investigates why token prediction, a common pre‑training objective for language models, yields useful representations. It introduces a statistical framework linking token prediction accuracy to the geometry of token embeddings, showing that accurate predictions organize embeddings according to Hellinger distances between context distributions. The authors also propose a self‑consistency principle that refines contextual representations through repeated application of a shared block, and provide downstream guarantees for token generation, community recovery, and linear classification.
By Shulei Wang
arXiv:2609.10305v1 Announce Type: new
Abstract: Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transfor...
By Fang Li
arXiv:2602. 15029v3 Announce Type: replace Abstract: The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes can be decoded using a linear probe.
By Dhruva Karkada, Daniel J. Korchinski, Andres Nava, Matthieu Wyart, Yasaman Bahri
Neural Collapse predicts that balanced one-hot classification pushes model representations to be equally far from each other; a symmetric configuration that depends only on the output label and ignores any semantic similarity in the inputs. This creates a puzzle: next-token prediction language models are trained predominantly (as context length increases) with one-hot labels: the same context is very unlikely to appear twice in training with different labels.
The paper investigates how large language models (LLMs) share a common Fisher‑Rao geometry in their next‑token probability distributions, revealing that behaviour largely determines this geometry while activation geometry depends on coordinate choices. Across transformer, state‑space, and recurrent architectures, output geometries align more closely than activation geometries, and this shared structure facilitates semantic‑category transfer and improves agreement with human word choices as models scale and train. The study further demonstrates that geometry can guide minimum‑disturbance interventions, enabling reusable control that preserves behaviour better than Euclidean methods and enhances steering, editing, attribution, dictionary learning, and fine‑tuning.
By Dario Picozzi
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.
By Narmeen Oozeer, Shivam Raval, Philip Quirke, Manikandan Ravikiran, Jeff Phillips, Shriyash Upadhyay, Amirali Abdullah
The paper shows that language models trained on natural text develop number representations that exhibit periodic features with dominant periods at T = 2, 5, 10. It identifies a two‑tiered hierarchy: all models learn Fourier‑domain spikes at these periods, but only some acquire geometrically separable features that allow linear classification of numbers modulo T. The study demonstrates that data, architecture, optimizer, and tokenizer influence whether these separable features emerge, and that models can learn them either from co‑occurrence signals in language or from multi‑token addition tasks, illustrating convergent evolution across diverse models.
By Deqing Fu, Tianyi Zhou, Mikhail Belkin, Vatsal Sharan, Robin Jia
arXiv:2606. 26749v1 Announce Type: new Abstract: Neural Collapse predicts that balanced one-hot classification pushes model representations to be equally far from each other; a symmetric configuration that depends only on the output label and ignores any semantic similarity in the inputs.
By Yize Zhao, Isabel Papadimitriou, Christos Thrampoulidis
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:2606. 05173v1 Announce Type: cross Abstract: Masked language modelling (MLM) has been the dominant pre-training objective for text encoders since BERT, yet it encourages representations that are strongly anchored to surface-form token identity rather than deeper semantic structure.
By Aimen Boukhari
arXiv:2608.30315v1 Announce Type: new
Abstract: Token embeddings are the basic representational units that connect discrete tokens with continuous computation in language models. Although modern lang...
By Junjie Yao, Liangkai Hang, Zhi-Qin John Xu
arXiv:2607. 13660v1 Announce Type: new Abstract: Contrastive Language-Image Pretraining (CLIP) representations form a semantic embedding space governed by cosine similarity, reflecting an intrinsic hyperspherical geometry.
By Zijie Yu, Gaowen Liu, Ramana Rao Kompella, Philip S. Yu, Yue Song