Task-Dependent Critical Threshold (Sc)

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• Hypothesis 1 (Threshold Behavior): There exists a task-dependent threshold Sc such that performance exhibits sharp changes as S crosses Sc, with value and transition width depending on model, layer, and poolinghypothesis0.805
  Core testable hypothesis of UCCT about the nature of performance transitions under anchoring
• Threshold Scconcept0.804
  Value of S above which performance sharply increases; varies by model, layer, and task.
• Threshold-like performance flips occur when anchoring strength S crosses a task-dependent critical value Sc.claim0.772
  Interpretation of abrupt behavior changes.
• Small prompt changes can yield threshold-like shifts because S crosses the critical value Scclaim0.725
  Authors' explanation for abrupt behavioral changes
• Task-specific parameterconcept0.717
  Parameter specific to each task, e.g., task head.
• GWT-4: State-dependent attention enabling sequential querying of modules for complex tasksconcept0.710
  Indicator: state-dependent attention and sequential module recruitment for System 2 thought.
• Task difficulty operationalized as the number of discrete operations required to verify correctness of the input.concept0.705
  The paper's specific operationalization of task difficulty enabling controlled experiments.
• Energy Thresholdconcept0.697