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Can I run K2-Horizon-3.7B on an RTX 5070?

Yes, just

Its published weights (10.1 GB) fit in the 10.8 GB an RTX 5070 can use, with room for ≈ 5K tokens of context.

Full analysis of K2-Horizon-3.7B Everything that runs on RTX 5070 Get the weights on Hugging Face
hf download IFM/K2-Horizon-3.7B

Files and context on RTX 5070

Each file of K2-Horizon-3.7B (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 published10.1 GBTight5K9K
4-bit (estimate)2.85 GBFits53K105K

K2-Horizon-3.7B 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.