Estimating Parameter Counts of Private LLMs via IKP: Claude Sonnet ~766B, GPT-5.5 Pro ~5.3T

A New Approach to Estimating Private LLM Sizes

With the parameter counts of frontier models like GPT and Claude kept private, it has been difficult to accurately estimate their size based solely on API pricing or hardware information. Consequently, the Incompressible Knowledge Probes (IKP) technique, which back-calculates size based on the amount of knowledge the model actually remembers, is gaining attention. Unlike reasoning capabilities, this technique is based on the premise that rare factual knowledge requires storage space proportional to model size.

Principles and Validation of IKP

IKP measures accuracy by posing rare factual questions to the model that cannot be answered through reasoning. Validation on 93 open-weight models revealed a consistent relationship (R²=0.910) where accuracy increases by approximately 15.9 percentage points for every tenfold increase in parameters. Additionally, no trend was found where newer models remember more facts at the same parameter count, proving that knowledge storage capacity is a stable indicator of model size.

Estimates for Major Frontier Models

The knowledge capacity (estimated parameter count), calculated by substituting the accuracy of private models into the IKP baseline, is as follows:

• GPT-5.5 Pro: ~5.3T
• GPT-5.5: ~4.7T
• Claude Fable 5: ~3.5T
• Gemini 2.5 Pro: ~3.0T
• Claude Sonnet 4.6: ~766B

These figures are not identical to the actual parameter counts of the models and should be interpreted as the effective knowledge capacity based on open-weight models required to store that knowledge. In particular, the uncertainty is high in the range above 1T due to a lack of comparable models, but it can serve as a useful indicator for gauging model scale.