[emacs28]

For everyone discussing the reduced accuracy/numerical stability of the algorithms in floating-point, this is true. But note that the application of the algorithms in the work is explored for fixed-point MM/quantized integer NN inference, not floating-point MM/inference. Hence, there is no reduction in accuracy for that application of it compared to using conventional fixed-point MM.

[pclmulqdq]

"Conventional fixed-point MM" is a large suite of algorithms. It is correct that this is a 2x reduction in MULs compared to naive fixed-point matrix multiply, but there is a large body of literature out there with other circuits. This is a cool trick to add to the group.

[p1esk]

Inference world is gradually switching from INT formats to FP formats. FP8 is already supported in modern hardware, and FP4 support is coming. In my experiments I get better perplexity in language models with FP4 than with INT4.

[SJC_Hacker]

How is FP fundamentally different than integers? I've done FPGA programming and it just seems like the programmer has to decide where/when to do the shifting based on the expected range of the data. I'm not sure how this is "natively supported" in hardware.

[p1esk]

If you have designed FPUs you should know that FP computation involves a lot more additional operations than just shifting (e.g. rounding, subnormals, and special value handling). That’s why, for example, CPUs use different hardware blocks for INT vs FP computation.

But that’s not the point. The point is, this particular method to speed up matmul is not suitable for FP.

[abetusk]

I'm no expert but I suspect this is wrong. To me, this is like saying you don't need to worry about integer overflow because your operations are only working on fixed integers. Really? You don't care if you multiply or add two large numbers and they spill over?

The more appropriate answer, I suspect, is that the numerical precision and stability sacrifices are more than adequate for normal usage.

If I'm wrong about this, I would certainly like to know.

[pclmulqdq]

In hardware, you control your integer widths completely, so if you add two 32-bit ints to a 33-bit int, there is no chance of overflow. The same goes for multiplications, etc.

[SJC_Hacker]

Yeah with shifts you can guarantee no overflow, but you have to decide under what circumstances is avoiding overflow/clipping worth the loss of precision.

Fixed point typically requires alot more programming, but sometimes its worth it if you know what the data ranges are.