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I think if you could somehow start computing the resultant matrix elements as soon as you read a row/column from the input ones, you could reach their "physically possible" limit.

A couch expert on computer architecture here, but a large enough systolic array could be used to achieve their "physically possible" limit? [0]

New CUDA GPUs have been coming with these tensor cores that are just systolic arrays. Google's TPU are the same.

Could someone with more knowledge on systolic arrays comment on whether a large systolic array can achieve this?

[0] https://medium.com/intuitionmachine/googles-ai-processor-is-...

For GPUs, it's actually much faster than O(n^3) because computing each entry in the result matrix is independent. Hence, the problem is embarrassingly parallel in a way.

I don't know how to use O() notation for GPUs but it should be something like O(n^2/k^2) where K is the tile size [0].

Also lower memory bandwidth becomes a bottleneck here. So there is a lot of optimizations done on how to transfer from CPU to GPU and then within GPU to efficiently query the matrices.

[0]https://docs.nvidia.com/deeplearning/performance/dl-performa...

I think what he is trying to say is that the metrics were meant be a check, a measure of knowing, for whether we are going to meet our vision/target.

Just yesterday, at our dev team at a trading firm, we went through our OKR review for the quarter. The metrics were the target yesterday. It was all about clicking those check boxes and not about delivering the bigger picture.