Language Models Represent and Transform Concepts with Shared Geometry
arXiv:2607. 04525v1 Announce Type: cross Abstract: How concepts are represented in neural networks is a fundamental question in machine learning.
The paper studies how transformer representations evolve across layers by examining the intrinsic dimensionality (ID) of token embeddings and their neighborhood structures. It finds that closed‑class tokens expand and collapse earlier than open‑class tokens, and that these changes are linked to shifts in local geometry. The authors compare encoder and decoder models, showing distinct layer‑wise behaviors, and demonstrate that geometric features alone can predict a token’s part‑of‑speech and reveal how semantic content changes across layers.
arXiv:2607. 04525v1 Announce Type: cross Abstract: How concepts are represented in neural networks is a fundamental question in machine learning.
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...
How concepts are represented in neural networks is a fundamental question in machine learning. The dominant view treats concept representations as stationary geometric objects.
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.
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.
The paper investigates the intrinsic dimension (ID) of large language model (LLM) representations as an indicator of linguistic complexity. By comparing ID across model layers for coordination vs. subordination, right‑branching vs. center‑embedding, and unambiguous vs. ambiguous attachment, the authors find consistent ID differences that align with established complexity contrasts. Experiments across six LLMs, including representational similarity and layer pruning analyses, confirm that more complex phenomena produce higher ID profiles, with peaks occurring at different layers for each contrast.
arXiv:2608. 03921v2 Announce Type: replace Abstract: This paper offers a new interpretation of the Transformer during inference.
arXiv:2609.00416v1 Announce Type: new Abstract: Probing studies have established that syntactic information is decodable in early and middle transformer layers, but what happens to that information i...
arXiv:2607. 02386v1 Announce Type: cross Abstract: While Vision Transformers have achieved remarkable success across computer vision and language applications, the geometric evolution of their internal representations throughout training remains insufficiently understood.
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:2608. 03921v1 Announce Type: new Abstract: This paper offers a new interpretation of the Transformer during inference.
The article presents a technical manual for an open toolkit designed to measure how transformer language models individuate word meanings across different contexts. It introduces the concept of a "bridge form"—a single word that appears unchanged in multiple domains but with distinct senses—and outlines a full pipeline from specifying these forms to extracting layer-wise representations, computing silhouette-based separation metrics, and visualizing results. The manual details each design choice and its intended methodological safeguards, emphasizing that it serves as a methodological reference rather than reporting empirical findings.