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