Isomap

methods / Dimensionality Reduction / Isomap

Techniqueintermediate

Nonlinear dimensionality reduction that approximates geodesic (manifold) distance via shortest paths on a neighbor graph, then applies classical MDS to embed those geodesic distances in a low-dimensional space.

Used in (2 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

Knowledge editing shatters transformers' natural cyclic manifold geometrymeasured

structure: Circle · models: Custom Transformer (trained from scratch on a structured synthetic knowledge graph), Llama-3-8B-Instruct, Mamba-2.8B, Llama-3.1-405B-Instruct, GPT-2-small, Mistral-7B · paper: Representation Shattering in Transformers: A Synthetic Study with Knowledge Editing