Decided to try to check how many weights in a 70b F32 model would be squashed when converted to F16 (spoiler, it's shockingly few)

The reason for this comparison is that it should represent the same percentage of squishing as bf16 to fp16

Had claude make me a script, using the new Reflection-70B, and these are the results:

Total weights: 70553706496

Fully representable: 70530215524

Squashed: 23490972

Percentage squashed: 0.03%

0.03%!!!!

A couple things to note, this uses a roundtrip of F32 -> F16 -> F32 and then torch.isclose to account for rounding errors that come up by the very nature of extremely accurate numbers, but it uses VERY small tolerances (rtol=1e-5, atol=1e-8)

This is also examining EVERY weight that was stored at F32, and for most layers I was somewhere between 0% and 0.03% of weights being squashed, no major outliers.

Overall, I feel even safer converting to F16 for llama.cpp, the extremely small number of weights that fall outside the range are likely so small that they don't actually play a role in the final output of the model at inference anyways.

The reason for this comparison is that it should represent the same percentage of squishing as bf16 to fp16

Had claude make me a script, using the new Reflection-70B, and these are the results:

Total weights: 70553706496

Fully representable: 70530215524

Squashed: 23490972

Percentage squashed: 0.03%

0.03%!!!!

A couple things to note, this uses a roundtrip of F32 -> F16 -> F32 and then torch.isclose to account for rounding errors that come up by the very nature of extremely accurate numbers, but it uses VERY small tolerances (rtol=1e-5, atol=1e-8)

This is also examining EVERY weight that was stored at F32, and for most layers I was somewhere between 0% and 0.03% of weights being squashed, no major outliers.

Overall, I feel even safer converting to F16 for llama.cpp, the extremely small number of weights that fall outside the range are likely so small that they don't actually play a role in the final output of the model at inference anyways.