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Can I run gpt2 on an RTX 4060?

Yes

Its published weights (548 MB) fit in the 7.20 GB an RTX 4060 can use, with room for ≈ 1K tokens of context.

Full analysis of gpt2 Everything that runs on RTX 4060 Get the weights on Hugging Face
hf download openai-community/gpt2

Files and context on RTX 4060

Each file of gpt2 (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

FileSizeOn RTX 4060 Context (16-bit)Context (8-bit)
As published548 MBFits1K1K
4-bit (estimate)77.1 MBFits1K1K

gpt2 on other hardware

Popular models that run on RTX 4060

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.