Geometry Evolution

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How to Read: Concept Space

Each dot represents a concept (like "gravity" or "justice") positioned by how the model represents it internally. Concepts that the model treats as similar appear close together.

Colors show domain: physical (teal), institutional (yellow), moral (red).

Clusters mean the model distinguishes domains. If physical concepts group together and moral concepts group separately, the model has learned meaningful categories.

Collapse means all dots converge to one point — the model treats every concept identically regardless of meaning.

Silhouette score (top right) measures cluster quality. Higher = better domain separation. Near zero = no meaningful structure.

Click a dot to tag it and track its movement across training steps.

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How to Read: Concept Space

Each dot represents a concept positioned by how the model represents it internally. Concepts the model treats as similar appear close together.

Colors show domain: physical (teal), institutional (yellow), moral (red).

Watch for collapse: as the shuffled model trains, dots converge. When everything is in one tight cluster, the model has lost the ability to distinguish concepts from different domains.

Compare with the left panel — do the two models organize concepts differently?

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How to Read: Concept Similarity

This grid shows how similar every pair of concepts is inside the model. Each row and column is a concept, grouped by domain. Brighter = more similar.

Blue blocks on the diagonal = within-domain similarity. Bright blue blocks mean the model groups concepts within the same domain together.

Amber off-diagonal = cross-domain similarity. Bright amber means the model treats concepts from different domains as similar — it can't distinguish them.

Block structure is healthy: bright diagonal blocks (same-domain similarity) with dark off-diagonal (cross-domain distinction). A uniformly bright grid means the model has collapsed all concepts together.

Scale bar (bottom right) shows the value range. Note: each panel scales independently to maximize contrast.

White lines separate the domains.

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How to Read: Concept Similarity

Same as the left panel. Watch for uniform brightness — when the entire grid goes bright, including the amber cross-domain cells, every concept has collapsed to the same representation.

A model with cosine similarity of 0.999 between "gravity" and "compassion" literally cannot distinguish physics from morality.