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Comment by anewhnaccount2 | Hacker News Reader

Should the Pareto front not be drawn with line perpendicular to the axes rather than diagonal lines?

Often with this kind of pareto it can be argued that even when continuous decisions are not available, a compression system could keep choosing every second at effort 7 and every second at effort 6 (or any ratio), leading, on the average interpolated results. Naturally such interpolation does not produce straight lines in log space.

Yes, it should, but it looks like they just added a line to the jxl 0.10 series of data on whatever they used to make the graph, and labelled it the Pareto front. Looking closely at the graphs, they actually miss some points where version 0.9 should be included in the frontier.

I think it can be understood as an expected Pareto frontier if enough options are added to make it continuous, which is often implied in this kind of discussions.

I'm not sure that's reasonable - The effort parameters are integers between 1 and 10, with behavior described here: https://github.com/libjxl/libjxl/blob/main/doc/encode_effort..., the intermediate options don't exist as implemented programs. This is a comparison of concrete programs, not an attempt to analyze the best theoretically achievable.

Also, the frontier isn't convex, so it's unlikely that if intermediate options could be added then they would all be at least as good as the lines shown; and the use of log(speed) for the y-axis affects what a straight line on the graph means. It's fine for giving a good view of the dataset, but if you're going to make a guess about intermediate possibilities, 'speed' or 'time' should also be considered.

You are right, but that would make an uglier plot :)

Some of the intermediate options are available though, through various more fine-grained encoder settings than what is exposed via the overall effort setting. Of course they will not fall exactly on the line that was drawn, but as a first approximation, the line is probably closer to the truth than the staircase, which would be an underestimate of what can be done.

Perpendicular to which axis?

both - staircase style.

Good grief. A poorly phrased question, and an answer that doesn't narrow the possibilities.

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… and why?

Whichever is more pessimistic. So for the axes in this article, the first one. If you have an option on the "bad" side of the Pareto curve, you can always find an option that is better in both axes. If a new option is discovered that falls on the good side of the curve, well, then the curve needs to be updated to pass thru that new option.

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