Concept Crystals (Parallelogram/Trapezoid Structure), Linear Direction, Affine Subspace, Linear Subspace, Concept lattice (Formal Concept Analysis half-space model), Anisotropy, 1D continuum manifold, Intrinsic-dimension profile across depth, Circle, Cone, Platonic Representation Hypothesis

Translation Symmetry Hypothesis, Efficient/Capacity-Optimal Coding Hypothesis

Analogies Explained: Towards Understanding Word Embeddings (2019), A Latent Variable Model Approach to PMI-based Word Embeddings (2016), World Properties without World Models: Recovering Spatial and Temporal Structure from Co-occurrence Statistics in Static Word Embeddings (2026), Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings (2016), Towards Understanding Linear Word Analogies (2019), Analogies minus analogy test: measuring regularities in word embeddings (2020), Language Models Represent Space and Time (2024), Symmetry in Language Statistics Shapes the Geometry of Model Representations (2026), Lipstick on a Pig: Debiasing Methods Cover up Systematic Gender Biases in Word Embeddings but do not Remove Them (2019), What Does Debiasing Really Remove? A Geometric Study of PCA-Based Gender Debiasing in Word Embeddings (2026), Hierarchical Concept Geometry in Language Models Emerges from Word Co-occurrence (2026), Exploiting Similarities among Languages for Machine Translation (2013), Geometry of Polysemy (2016), All-but-the-Top: Simple and Effective Postprocessing for Word Representations (2018), Understanding Linearity of Cross-Lingual Word Embedding Mappings (2020), When Models Manipulate Manifolds: The Geometry of a Counting Task (2025), All Bark and No Bite: Rogue Dimensions in Transformer Language Models Obscure Representational Quality (2021), Measuring Intrinsic Dimension of Token Embeddings (2025), Not All Language Model Features Are One-Dimensionally Linear (2024), Shape Happens: Automatic Feature Manifold Discovery in LLMs via Supervised Multi-Dimensional Scaling (2025), Do Sparse Autoencoders Capture Concept Manifolds? (2026), Exploring the Linear Subspace Hypothesis in Gender Bias Mitigation (2020), Closed-Form Training Dynamics Reveal Learned Features and Linear Structure in Word2Vec-like Models (2025), Discovering Universal Geometry in Embeddings with ICA (2023)