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Can I run bloomz-560m on a Mac with 32 GB?

Yes

Its published weights (1.12 GB) fit in the 21.3 GB a Mac with 32 GB can use, with room for an unknown amount of context.

Full analysis of bloomz-560m Everything that runs on Mac with 32 GB Get the weights on Hugging Face
hf download bigscience/bloomz-560m

Files and context on Mac with 32 GB

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.

FileSizeOn Mac with 32 GB Context (16-bit)Context (8-bit)
As published1.12 GBFitsnot knownnot known
4-bit (estimate)315 MBFitsnot knownnot known

bloomz-560m on other hardware

Popular models that run on Mac with 32 GB

Assumes 67% of the Mac's memory is usable (macOS's default limit for the GPU; it can be raised) 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.