Faster-converging trajectories take direct PCA-space paths to the true solution; slower trajectories take indirect routes visiting saddle points

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

• Optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h.finding0.765
  Demonstrates bidirectional causal link: behavior manifold geometry can be recovered by optimizing in representation space.
• Manifold-respecting steering produces smooth natural behavioral trajectories while linear steering teleports between non-adjacent concepts.claim0.746
• Progress on the contemplative path is using these (vascular system motifs) less and needing them less.claim0.745
  Mapping contemplative development to reduction in vasocomputation.
• Steering along manifolds provides better control than linear steering when the concept geometry is non-linear.claim0.736
  The central thesis of the paper, motivating the shift from linear to geometry-aware manifold steering.
• Saddle points in reasoning latent space correspond to nearly-correct attempted solutions of the underlying problemclaim0.735
  Interprets the decoded latent states near saddles (Fig.3D) as near-miss answers.
• In LLaMA-2-13B, larger_than and smaller_than separate along antipodal directions in PCA; in LLaMA-2-70B they align along a common directionfinding0.735
  Scale-dependent alignment result demonstrating how more abstract truth representations emerge with scale
• Turner et al. 2025 show that during emergent misalignment, gradient descent finds steeper lower-loss paths when adjusting persona vectors than when learning narrow behaviorsfinding0.728
  Mechanistic explanation of why fine-tuning shifts persona vectors rather than directly learning narrow behaviors
• There is a clear bidirectional relationship between the geometry of behavior and representation: steering along representation manifolds follows behavior manifolds, and vice versa.claim0.724
  The paper's finding that the alignment holds in both directions — from representation to behavior and from behavior back to representation space.