UMAP

methods / Dimensionality Reduction / UMAP

Techniqueintermediate

Uniform Manifold Approximation and Projection — a nonlinear dimensionality-reduction technique that preserves local neighborhood structure, used when linear projection (PCA) doesn't reveal the shape.

Used in (9 observations)

Emotion representations trace a V-shaped open manifold with neutral at the vertexmeasured

structure: 1D continuum manifold, Linear Direction · models: Gemma-2-9B, Mistral-7B, Llama-3-70B-Instruct · paper: Latent Structure of Affective Representations in Large Language Models

In-context belief updating traces a low-dimensional manifoldmeasured

structure: Conceptual Belief Space Hypothesis, Linear Subspace · models: Llama-3.1-8B-Instruct · paper: Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space

BERT's semantic-sense subspace is largely separate from its syntactic onemeasured

structure: Linear Subspace · models: BERT-base-cased · paper: Visualizing and Measuring the Geometry of BERT

structure: Circle, Constructive Interference Hypothesis · models: BOWS Autoencoder (tied-weight, ReLU), BOWS Autoencoder (tied-weight, linear — no ReLU, baseline), BOWS Toy Transformer (1 block, 8 heads, d_model=768) · paper: From Data Statistics to Feature Geometry: How Correlations Shape Superposition

A T-maze LSTM forms place fields and switches manifold pathsmeasured

structure: Line Attractor · models: 380-unit LSTM (T-maze sensory-prediction + Q-learning) · paper: Hippocampal Representations Emerge When Training Recurrent Neural Networks on a Memory-Dependent Maze Navigation Task

A 'state of mind' spectrum is linearly decodable across five encodersmeasured

structure: Linear Direction · models: BGE-large-en-v1.5, all-mpnet-base-v2, all-MiniLM-L6-v2, Qwen3-Embedding-0.6B, Qwen2.5-3B-Instruct · paper: Probing Spectrum-Like Organization of States of Mind in Transformer Representation Spaces

Torus-cluster membership, not gridness, is causally load-bearing for path integrationmeasured

structure: Torus · models: CARNN trained on path integration across multiple (1-50) environments · paper: Coherently Remapping Toroidal Cells But Not Grid Cells are Responsible for Path Integration in Virtual Agents

A trained transformer forms separate subspaces for constants and variablesmeasured

structure: Linear Subspace · models: 12-layer, 8-head causal Transformer (d_model=512, RoPE, synthetic variable-assignment-program task) · paper: How Do Transformers Learn Variable Binding in Symbolic Programs?

Anchored projection recovers a 2D arousal-valence plane from categorical labelsmeasured

structure: Circle · models: WavLM Large · paper: Learning Arousal-Valence Representation from Categorical Emotion Labels of Speech