concept
active
concept:euclidean-geometry-assumptionEuclidean Geometry Assumption
The implicit assumption of linear steering methods, which the paper argues is inappropriate for neural activation spaces
Neighborhood — ranked by edge-count
Claims (1)
claim
- Attribution of failure to Euclidean assumption.
Methods (1)
method
- linear steeringimplementsTypical approach that adds a scaled steering vector to representations; the paper argues this is mismatched with actual representation geometry.
Concepts (1)
concept
- Linear steering implicitly assumes a flat, Euclidean activation space, leading to off-manifold excursions.
Related by similarity (8)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- Ancient algorithm from Euclid's Elements (circa 300 B.C.) that computes greatest common divisor; shown to structurally parallel Bjorklund's rhythm generation algorithm.
- The actual shapes and spatial relationships of buildings, essential to living structure.
- The spatial/geometric organization of conceptual structure within neural network representations; central to the paper's thesis.
- The structured geometry present in the external world (e.g., circles, spatial manifolds) that networks learn to mirror.
- Family of musical rhythms generated via Bjorklund's algorithm, where k onsets are distributed evenly across n time units; denoted E(k,n).
- Research thread within About Blank concerning the structure and relational properties of neural network feature representations; covariance pooling tangentially supports this thread.
- General principle supported tangentially by covariance pooling work; relates to feature co-occurrence structure.
- The process through which form is created by successive differentiating operations, not by adding parts.