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Thanks for writing this post. I have a handful of quick questions: (a) What was the reference MIPS (or the corresponding CPU) you used for the c. 2019-2020 data point? (b) What was the constant amount of RAM you used to run Stockfish? (c) Do I correctly understand that the Stockfish-to-MIPS comparison is based on the equation [edit: not sure how to best format this LaTeX...]:

So, your post piqued my interest to investigate the Intel 80486 a bit more with the question in mind: how comparable are old vs. new CPUs according not just to MIPS but also to other metrics?

  • Instructions per second (MIPS): Using the Wikipedia MIPS source, the 80486 has 70 MIPS at 100 MHz, whereas a recent Skylake 8-core CPU (i9-9900K) has around 50,000 MIPS/core at a clock of 4.7 GHz, and closer to 40,000 MIPS/core at a sustained clock of 3.6 GHz.
  • Memory bandwidth: From Wikipedia, the 80486 has a 33 MHz bus and a data rate of up to 32 bits, so roughly 130 MB/s, whereas the 9900K is closer to 40 GB/s (from Intel).
  • Memory latency: The 80486 takes 5 bus cycles at 33 MHz, or 15 CPU cycles at 100 MHz, to access memory (16 byte cache line size, from comp.arch). From Anandtech, Skylake can take 100 cycles to access memory (64 byte cache line size, typical for x86_64).
  • Memory capacity: The 80486 is a 32-bit CPU and can address up to 4 GB of RAM. Again from Wikipedia, the 80486 accepts SIMM form factor RAM, with up to 2 GB capacity (but tens of MB may have been more commonly available). On the other hand, the 9900K supports a maximum memory capacity of 128 GB.

It would seem that improvements in MIPS have outpaced improvements in memory-related metrics, e.g. memory latency in units of cycles has gotten worse. What I don't know is how sensitive Stockfish is to variations in memory performance. However I would conclude that I'd update the estimated SF8 ELO on older hardware upwards when additionally accounting for the effect of memory-related metrics in addition to MIPS. In other words, it seems more likely to me that the SF8 ELO curve is underestimated when you include both MIPS and memory-related effects.

(There is another direction one could follow: get Stockfish to compile on an 80486 or other old hardware that one has lying around, and report back with results.)

nostalgebraist's blog is a must-read regarding GPT-x, including GPT-3. Perhaps, start here ("the transformer... 'explained'?"), which helps to contextualize GPT-x within the history of machine learning.

(Though, I should note that nostalgebraist holds a contrarian "bearish" position on GPT-3 in particular; for the "bullish" case instead, read Gwern.)