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Can I run Ornith-1.0-35B on an RTX 4060?

No

Even its smallest file (4-bit (estimate), 19.7 GB) is more than an RTX 4060 can hold (7.20 GB usable): it needs 3 of them.

Full analysis of Ornith-1.0-35B Everything that runs on RTX 4060

Files and context on RTX 4060

Each file of Ornith-1.0-35B (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 published70.2 GBDoesn't fit——
BF16ornith-ai/Ornith-1.0-35B-GGUF69.4 GBDoesn't fit——
Q8_0ornith-ai/Ornith-1.0-35B-GGUF36.9 GBDoesn't fit——
Q6_Kornith-ai/Ornith-1.0-35B-GGUF28.5 GBDoesn't fit——
Q5_K_Mornith-ai/Ornith-1.0-35B-GGUF24.7 GBDoesn't fit——
Q4_K_Mornith-ai/Ornith-1.0-35B-GGUF21.2 GBDoesn't fit——

Ornith-1.0-35B 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.