A new attempt to infer the scale of proprietary AI models
A recent study led by Li Bojie, chief scientist at Pine AI, set out to estimate the parameter counts of several proprietary large language models using an indirect measurement method. Published under the title Incompressible Knowledge Probes, the research did not rely on company disclosures. Instead, it attempted to reverse-engineer model size from performance on carefully selected knowledge tests.
The study used 1,400 obscure factual questions as probes to test how well models retained rare information. Researchers then mapped the performance of proprietary systems onto a scaling curve derived from 89 open-source models with known parameter counts. Based on that calibration, the paper produced parameter estimates for several major closed-source models. The authors noted that the approach may still involve variation, but argued that it can generate meaningful approximations.
GPT-5.5 tops the list at an estimated 9.7 trillion
According to the study, GPT-5.5 is estimated to have roughly 9.7 trillion parameters, making it the largest model in the comparison by a wide margin. The next model cited was Claude Opus 4.6 at around 5.3 trillion parameters. The paper also estimated Grok-4 at about 3.2 trillion parameters, while GPT-5 and Claude Opus 4.7 were described as following closely behind.
The findings highlight the continued expansion in parameter counts among newer frontier models. In the study’s framing, GPT-5.5 represents a particularly notable step up in capacity, suggesting that competition at the top end of the AI model market is still pushing scale higher.
Important caveat: these are estimates, not official disclosures
The figures presented in the paper are estimates derived from methodology rather than numbers confirmed by the companies behind the models. Because proprietary systems often keep their architectures, sparsity designs, and deployment details private, outside analysis typically depends on indirect signals. Even so, the research offers a useful lens for tracking the pace of change in advanced AI systems.