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Can I run Llama-3.1-8B-Instruct-4bit on an RTX 4060?

Yes

Its published weights (4.52 GB) fit in the 7.20 GB an RTX 4060 can use, with room for ≈ 20K tokens of context.

Full analysis of Llama-3.1-8B-Instruct-4bit Everything that runs on RTX 4060 Get the weights on Hugging Face
hf download mlx-community/Llama-3.1-8B-Instruct-4bit

Files and context on RTX 4060

Each file of Llama-3.1-8B-Instruct-4bit (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 published4.52 GBFits20K40K

Llama-3.1-8B-Instruct-4bit 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.