concept geometry

The spatial/geometric organization of conceptual structure within neural network representations; central to the paper's thesis.

Neighborhood — ranked by edge-count

concept

behavior manifold
associated_with
One-dimensional curved surface in output probability space; the paper shows this mirrors representation manifold structure.
representation manifold
associated_with
One-dimensional curved surface in internal activation space; the paper demonstrates alignment with behavior manifold.
days of the week
implements
Primary case study demonstrating circular manifold structure in both behavior and representation space of Llama-3.1-8B.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Conceptconcept0.844
Central entity of Jackson's framework: a structure invented to give coherent account of immediate consequences of actions; the building block of software design
Concept Algebraframework0.838
Probabilistic framework formalizing concept-specific subspaces for targeted steering in generative models.
Geometryconcept0.837
The actual shapes and spatial relationships of buildings, essential to living structure.
concept vectorconcept0.823
Computed directional vector in activation space representing a specific concept, used for injection experiments
concept representationconcept0.812
How a neural network encodes a semantic concept internally, argued to be better captured by manifolds than by atomic features.
concept vector computationmethod0.811
Procedure extracting concept vectors as difference of mean activations between concept-exemplifying and baseline/negative sentences
Cyclic Concept Geometryconcept0.809
The circular geometric structure that cyclically ordered concepts (days, months) exhibit in both representation and behavior space.
Concept Latticeconcept0.805
Central algebraic structure in FCA that orders formal concepts and preserves information from formal contexts.