cot-threshold-validates-emergent-discontinuity
OUT derived (depth 1)
Created 2026-06-21T13:13:49+00:00
Chain-of-thought prompting's empirically measured threshold of ~62B parameters is a specific documented instance of emergent abilities' discontinuous appearance at scale, validating that reasoning itself is an emergent property rather than a gradually improving one.
Justifications
SL — CoT's specific parameter threshold is a measured instance of emergent discontinuity, contingent on the discontinuity being genuine rather than a metric artifact
Antecedents (all must be IN):
- IN cot-prompting-requires-62b-plus-params — Chain-of-thought prompting only improves performance for models with at least approximately 62 billion parameters; smaller models perform better answering directly.
- IN emergent-abilities-discontinuous-scale — Emergent abilities in LLMs appear discontinuously at certain scale thresholds, not linearly (Wei et al., 2022, arXiv:2206.07682)
Unless (any of these IN defeats this justification):
- IN emergent-abilities-metric-artifact-debate — The appearance of emergent abilities in LLMs depends on metric choice: accuracy metrics show step-function discontinuities while log-probability metrics show smooth scaling curves (Schaeffer et al.).