optimization of interventions to follow behavior manifold M_y

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• behavior manifold M_yconcept0.831
  Manifold fitted to output probability distributions (behavior).
• 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.finding0.831
  Central empirical result showing causal coupling between representation and behavior geometry across multiple substrates and modalities.
• Optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h.finding0.814
  Demonstrates bidirectional causal link: behavior manifold geometry can be recovered by optimizing in representation space.
• behavior manifold fitting (M_y)method0.812
  Method to fit a manifold M_y to output probability distributions.
• behavior manifoldconcept0.800
  One-dimensional curved surface in output probability space; the paper shows this mirrors representation manifold structure.
• We hypothesize that interventions that respect the geometry of activation space will yield behaviors close to those the model exhibits naturallyhypothesis0.786
  The core testable hypothesis driving the experimental design
• Manifold geometry provides a practical blueprint for steering model behavior across diverse tasks and modalities.hypothesis0.765
  The generalizing predictive claim that manifold steering is a broadly applicable framework beyond the days-of-week case study.
• Manifold steering demonstrates bidirectional geometry-behavior link in a video world model on tasks with geometry corresponding to physical dynamicsfinding0.755
  Extension of manifold steering validation to video world models and physical dynamics tasks, demonstrating cross-modal generality