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Weight memory is parameters multiplied by bytes per parameter, so precision is the only lever that matters at rest: 7 billion parameters occupy 28 GB in fp32, 14 GB in fp16, 7 GB in int8 and about 3.5 GB in int4. Loader buffers, alignment padding and allocator fragmentation add a single-digit percentage on top.
Weight footprint
bytes = parameters x bytes per parameter x (1 + overhead); GiB = bytes / 1024^3
Yes, both are 2 bytes. bf16 trades mantissa bits for exponent range, which makes training more numerically stable without changing the footprint.
Quantisation stores scales and zero points per group, and some layers such as embeddings and norms are often kept at higher precision.