Can I run bloomz-560m on an RTX 4090?

Yes

Its published weights (1.12 GB) fit in the 21.6 GB an RTX 4090 can use, with room for an unknown amount of context.

Full analysis of bloomz-560m Everything that runs on RTX 4090 Get the weights on Hugging Face

hf download bigscience/bloomz-560m

Files and context on RTX 4090

Each file of bloomz-560m (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.

File	Size	On RTX 4090	Context (16-bit)	Context (8-bit)
As published	1.12 GB	Fits	not known	not known
4-bit (estimate)	315 MB	Fits	not known	not known

bloomz-560m on other hardware

NVIDIA H100Yes
RTX 5090Yes
RTX 4090Yes
RTX 3090Yes
RTX 5060 Ti 16 GBYes
RTX 3060 12 GBYes
RTX 4060Yes
Mac with 32 GBYes
Mac with 64 GBYes
Mac with 128 GBYes

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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.