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Leela Chess Zero (Elo improvement)

Posted 7 months ago
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LC0 is an artificial intelligence chess engine in the spirit of alpha zero. Here is the improvement of elo performance (http://162.217.248.187/networks) The list is imported into Mathematica and visualized.

elo = Reverse[{5582.24, 5599.02, 5595.76, 5587.37, 5575.35, 5578.86, 
    5578.41, 5559.51, 5558.62, 5547.21, 5544.44, 5520.53, 5525.25, 
    5529.51, 5512, 5506.45, 5512.17, 5506.03, 5499.74, 5501.1, 
    5501.53, 5403.39, 5465.7, 5390.71, 5408.78, 5449.13, 5393.27, 
    5405.26, 5402.22, 5396.25, 5405.12, 5388.28, 5373.22, 5373.22, 
    5382.08, 5376.9, 5389.56, 5385.24, 5388.75, 5377.15, 5362.19, 
    5372.96, 5358.95, 5361.91, 5362.32, 5373.95, 5371.42, 5357.75, 
    5364.27, 5356.47, 5339.32, 5359.03, 5341.32, 5345.33, 5320.59, 
    5322.68, 5323.93, 5329.32, 5323.33, 5308.89, 5297.69, 5270.72, 
    5284.89, 5252.59, 5260, 5276.7, 5267.33, 5260.23, 5246.83, 5235.3,
     5220.19, 5213.11, 5191.5, 5182.34, 5176.54, 5160.91, 5174, 
    5179.87, 5169.23, 5155.79, 5160.24, 5162.81, 5169.7, 5160.77, 
    5180.88, 5186.43, 5193.7, 5160.59, 5186.78, 5140.89, 5137.88, 
    5134.54, 5127.34, 5116.73, 5121.87, 5120.67, 5071.68, 5073.65, 
    5062.54, 5105.09, 5079.68, 5012.99, 4968.4, 4944.51, 4931.96, 
    4865.13, 4893.65, 4902.49, 4897.91, 4867.15, 4817.83, 4847.71, 
    4828.7, 4815.66, 4790.06, 4803.49, 4783.36, 4805.28, 4806.17, 
    4828.25, 4794.17, 4871.79, 4766.88, 4838.96, 4861.16, 4827.88, 
    4843.98, 4779.94, 4686.33, 4694.95, 4635.64, 4662.68, 4710.17, 
    4691, 4714.87, 4707.12, 4666.22, 4770.97, 4714.4, 4723.58, 
    4717.13, 4764.19, 4771.39, 4780.76, 4732.06, 4644.06, 4593.21, 
    4693.56, 4550.2, 4662.17, 4567.69, 4635.73, 4565.3, 4501.65, 
    4561.74, 4526.5, 4610.17, 4608.94, 4583.81, 4563.67, 4602.39, 
    4579.44, 4606.92, 4651.24, 4538.57, 4581.63, 4590.44, 4553.47, 
    4694.18, 4656.61, 4497.8, 4505.81, 4478.08, 4474.75, 4419.34, 
    4323.89, 4360.11, 4388.26, 4341.03, 4368.6, 4357.52, 4414.23, 
    4431.85, 4380.64, 4393.54, 4257.54, 4343.33, 4214.81, 4279.98, 
    4241.64, 4224.83, 4081.69, 4184.84, 4095.81, 4228.57, 4245.95, 
    4230.28, 3967.87, 3948.48, 3751.33, 4183.65, 4182.35, 4195.82, 
    4157.42, 4153.53, 4163.83, 4173.35, 4112.7, 4048.49, 3999.11, 
    3920.26, 3885.54, 3836.56, 3889.04, 3802.18, 3742.72, 3678.26, 
    3705.96, 3740.53, 3619.69, 3693.05, 3670, 3654.16, 2739.26, 
    3651.31, 3624.36, 3550.36, 3501.08, 3576.92, 3498.75, 3348.85, 
    3368.34, 3319.15, 3281.91, 3107.95, 3135.62, 3033.11, 2825.47, 
    2860.33, 2764.14, 2476.07, 2039.64, 1724.29, 1555.89, 1424.95}];

  lp = ListPlot[elo, Filling -> Axis, 
     AxesLabel -> {"Network", "Leela Elo"}, 
     AxesStyle -> Arrowheads[{0, 0.02}], PlotRange -> All]

enter image description here

It seems it grows like a powerfunction, so lets check it with WL

data = MapIndexed[{#2[[1]], #1} &, elo];
expr = Normal[NonlinearModelFit[data, b x^a, {a, b}, x]]

1945.17 x^0.191238

This is the powerfunction, now lets visualize it:

pp1 = Plot[expr, {x, 0, Length[elo]}, 
   PlotStyle -> Directive[Blue, Thick], PlotRange -> All];
Show[lp, pp1, PlotRange -> All, AxesOrigin -> {0, 0}]

enter image description here

2 Replies

In my opinion, if you want to test if two quantities are related by a power law, the best way is to do a log-log plot since this will immediately show you a straight line if you're right. Humans are very good at recognizing straight lines by eye. Fitting a non-straight line to data can be deceiving since it can be difficult to judge if the data follow the relation accurately (especially at the extremes of the range and domain).

ListLogLogPlot[elo, Filling -> Axis, 
 AxesLabel -> {"Network", "Leela Elo"}, 
 AxesStyle -> Arrowheads[{0, 0.02}], PlotRange -> All]

log log plot

As you can see from this plot, the data seem to satisfy the power law quite well in the higher regions, but closer to the origin there are is a significant departure from the overall trend. If you just fit a power law line, you wouldn't see this quite as clearly. The ScalinFunctions option in plotting functions can also help you quite a lot in the exploration of dependencies between variables.

Posted 7 months ago

yeah true enough

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