MAP 1 · ENDPOINTS vs SCOPE
What do representations converge to — and how many winners are there?
MAP 2 · GRANULARITY vs STRENGTH
Is it observed, exploited, or proven — and at what level of description?
READING THE AXES
An endpoint is a representational destination at the limit of training and scale — one attractor means all good systems end up in the same representation space; plurality means several stable spaces persist.
Map 1 · Endpoints vs Scope
- Y — Number of endpoints
- How many final representation spaces the hypothesis allows. Bottom: one global attractor (PRH, Strong PRH). Top: durable plurality (URH's ecological clusters, Superposition's per-model interference; CKA sits high because as a metric it registers dissimilarity as real structure).
- X — Scope of claim
- Who the hypothesis is about. Left: inside one network (Manifold, Superposition, LRH). Middle: across trained models (Convergent, Anna Karenina, Perfect PRH). Right: all representation-learners including brains (PRH, Universality, URH).
- The corners
- PRH bottom-right: everything converges to one. URH top-right: everything is constrained but splits into clusters.
Map 2 · Claim strength × Granularity
- Y — Granularity
- Level of description. Bottom: global geometry — distances, subspaces, linear maps (PRH, Manifold). Top: identifiable mechanisms — curve detectors, induction heads (Circuits; Superposition and Linear bridge partway up).
- X — Strength of claim
- Epistemic status. Left: empirical observation (Convergent 2015, CKA). Middle: constructive demonstration (vec2vec built a translator) or falsifiable test (Universality's fMRI predictions). Right: mathematical proof (Perfect PRH) or calibrated formal claim (Aristotelian).
- The tension
- The strongest claims (right edge) are all geometric. The 2026 critiques sit between the rows, arguing geometry-level agreement may only be the linear part.