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Incompressible Knowledge Probes: Estimating Black-Box LLM Parameter Counts via Factual Capacity

arxiv.org

Figure 1: IKP calibration curve — knowledge scales log-linearly with model size across 89 open-weight models (R² = 0.917), enabling parameter estimation of proprietary models via horizontal dashed lines.

  • Calibrating what the authors call “Incompressible Knowledge Probes” on open source models with known parameter counts, they found that knowledge scales log-linearly with model size
  • Using this trend, they were able to estimate the parameter count of proprietary frontier models
  • For instance, at the frontier level, GPT-5.5 is estimated to be 9.7T params, Claude Opus 4.6 is estimated to be 5.3T params, and Gemini 3.1 Pro is excluded as the largest landmark.
  • At the sub-frontier level, Sonnet 4.6 is est. 1.7T params while GPT-5 mini is est. 410B params.
  • For me, this is a reminder that scaling laws still hold and we are still scaling compute and data as much as we are scaling architectural refinements

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