On the growth rate of Leela Zero compared to AlphaGoZero

There are not many sources online, but one reference from January says of Leela Zero (LZ) that:

The strength depends on the hardware and on thinking time, but from the thread “LeelaZero adventures on Fox”, and from petgo3’s rank on KGS, I guess that on medium hardware, and with relatively fast time settings, LZ is about professional strength but not top pro

At the time this was published LZ’s best network had had ~11.75 million training games.

In contrast, AlphaGo Zero (AGZ) had a total of ~29 million training games. Assuming that the number of training games were spaced out evenly, the number of LZ’s training games by January would correspond to about day 14 of AGZ training.

But by day 14 of training AGZ was very close to AlphaGo Master’s level, which is way above top pro level.

This doesn’t add up, LZ was made mimicking AGZ so the growth rate should be similar, but this makes it seem like it is considerably slower.

What factors could be causing this? Is it the hardware (like the Tensor units?) used for the runs or the depth with which the games are analyzed? Is it something having to do with the implementation of the neural network itself? Or… maybe… is it just that LZ has very bad luck (Averaged over millions of games this one seems very unlikely, but it’s a possibility)?

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AMAT using Local miss rate, global miss rate, local hit rate, global hit rate

Consider the following scenario as shown in image:

enter image description here

I have summarized the above Memory layout in terms of Miss rates and hit rates:

.---.----------------.------------.------------.------------.--------. |   |                |     0      |     1      |     2      |   3    | :---+----------------+------------+------------+------------+--------: |   |                | LMR        | GMR        | LHR        | GHR    | :---+----------------+------------+------------+------------+--------: | 0 | L1 cache       | 10/100     | 10/100     | 90/100     | 90/100 | :---+----------------+------------+------------+------------+--------: | 1 | L2 cache       | 3/10       | 3/100      | 7/10       | 7/100  | :---+----------------+------------+------------+------------+--------: | 2 | Main Memory    | 0/3        | 0/100      | 3/3        | 3/100  | :---+----------------+------------+------------+------------+--------: | 3 | Sum of columns | Not useful | Not useful | Not useful | 1      | '---'----------------'------------'------------'------------'--------' 

Here LMR – local miss rate, GMR – global miss rate, LHR – local hit rate, GHR – global hit rate. From the above table I deduced the following insights:

  1. Sum of the Global Hit rates (GHR) of all caches and Main Memory is 1.
  2. The formula for AMAT(Average Memory Access Time) can be interpreted as follows:

AMAT = t1 + m1t2 + m1m2t3


AMAT = t1 + M1t2 + M2t3

. where m1,m2 are local miss rates of Level 1 and Level 2 caches respectively. M1,M2 are global miss rates of Level 1 and Level 2 caches respectively. t1, t2, t3 are access times for level 1 cache, level 2 cache and Main Memory. For the given example,

AMAT = t1 + 10/100t2 + 3/100t3

  1. From point 2 it can be said that

M1 = m1; M2 = m1*m2; and so on

  1. Local Hit rate of Main Memory (or final level cache) is always 1. Here it is assumed that required word is surely found in Main Memory ( or final level cache).
    • Local Hit rate of level 1 cache = Global Hit rate of level 1 cache.

    • Local Miss rate of level 1 cache = Global Miss rate of level 1 cache.

Now my question is “Are these points correct?”. I did not find any information relevant to the above points. Also are there any more insights I can get from the table? Like relation between GHR and lmr, lhr.

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