How Do Simple Components With Only Local Rewards

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• The transformer likely uses a local code for token-in-context features rather than purely compositional representations, because local codes enable sharper predictionsclaim0.699
  Authors argue the prevalence of token-in-context features reflects genuine model computation rather than dictionary learning artifact
• Local symmetries act as a kind of glue which holds space together; the more glue there is, the more the space is one, solid, unified, coherent—and the symmetrical segments must overlap for the glue to be effectiveclaim0.699
  Interpretation of the experimental finding: overlapping local symmetries are the hidden structural feature that creates perceived wholeness
• DiffLogic CA can directly learn the local rules needed to achieve desired macroscopic computation, addressing the fundamental challenge identified by Toffoli and Margolusclaim0.690
  Core thesis of the paper framed against the historical challenge of hand-crafting CA rules
• The life of a center—even in a simple door—depends on the configuration of component centers and the wider system of centers around it.claim0.688
  Generalization from the door examples.
• To what extent can physical systems learn by exploiting typically local natural processes without any explicit cost function?question0.687
  Central research question defining the scope of physical learning; asks about achievable learning under locality constraints
• At each step, doing the simplest thing that can be done to intensify existing centers will produce living structure.hypothesis0.684
  Operational hypothesis equating simplicity of step with emergence of life.
• Local vs Compositional Representationsframework0.684
  Theoretical distinction between representing token-context pairs as individual features (local) vs combining independent features (compositional)
• The shortest statement of what one is trying to do in architecture is to obtain the field of centers by introducing one center at a time into the whole, so as to extend the whole and preserve structure.claim0.680