Off-manifold divergences can activate hidden pathways that produce misleadingly confirmatory behavior while the true mechanism is never exercised

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

• Patching h[1] with a divergent representation can activate distinct, hidden pathways that result in misleadingly confirmatory behavior and/or undetected behavior.quote0.842
  Load-bearing description of the core pernicious divergence mechanism illustrated in Figure 1
• Minimizing divergence magnitude does not guarantee elimination of hidden pathways; it only reduces the risk surfaceclaim0.824
  Important caveat to the CL loss solution, noting it is a step not a complete fix
• manifold steering produces clean probability shifts along natural behavior structure; linear steering cuts across manifold and produces off-target noisy effectsfinding0.787
  Empirical demonstration on Llama-3.1-8B that steering along representation manifold aligns outputs with behavior manifold, whereas linear steering does not.
• Linear steering produces noisy off-target effects; manifold steering cleanly shifts probability mass between sequential concepts.finding0.769
  Core empirical claim comparing steering approaches on cyclic concepts.
• Interventions along activation manifold M_h yield behavioral trajectories following behavior manifold M_y, and vice versa — bidirectional relationship demonstrated across language models and video world models.finding0.752
  Central empirical result showing causal coupling between representation and behavior geometry across multiple substrates and modalities.
• Divergence within the behavioral null-space is harmless to functional claims about a function's computation when the claim ignores internal sub-computationsclaim0.748
  Key theoretical claim distinguishing harmless from pernicious divergence
• Independently trained model families converge on a common semantic manifold under self-referential processing, suggesting an attractor dynamic that transcends training variancehypothesis0.747
  Hypothesis tested in Experiment 3; independently trained GPT, Claude, Gemini architectures converge on similar descriptive vocabulary
• Larger hidden representations create more random structure that DAS can search through, allowing manipulation of counterfactual behavior even in randomly initialized networkshypothesis0.747
  Tested in Section 4.4 calibration experiment; confirmed by findings.