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Can I run granite-4.1-3b on an RTX 5070?

Yes

Its published weights (6.81 GB) fit in the 10.8 GB an RTX 5070 can use, with room for ≈ 48K tokens of context.

Full analysis of granite-4.1-3b Everything that runs on RTX 5070 Get the weights on Hugging Face
hf download ibm-granite/granite-4.1-3b

Files and context on RTX 5070

Each file of granite-4.1-3b (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 5070 Context (16-bit)Context (8-bit)
As published6.81 GBFits48K95K
4-bit (estimate)1.91 GBFits106K128K

granite-4.1-3b on other hardware

Popular models that run on RTX 5070

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.