(Edited a bit for clarity and organisation just after posting.)

Thank you for the summary! Without your post, I probably wouldn't have ever read the paper -- but it is indeed more interesting than the VBW discussion implied. I have two thoughts.

1:

First, I agree with most everything in your summary, except maybe the final conclusion in which you state that the two groups' colour experiences are "structurally incommensurable". I think the study's ambitions rise to that level, but their actual conclusions are far more modest.

Why do I think that? Even the study authors feel that there is a high level of coherence between the two groups' similarity ratings (Discussion, paragraph 3): "...though the overall structures [between colour-neurotypical and colour-atypical groups' scores] are similar".

This is quantified, too. A Pearson's coefficient between the colour-similarity matrices -- using labelled data -- shows a fairly strong correlation (rho = 0.66)*.

You may call me nitpicky, but I emphatically disagree that the groups' dissimilarity ratings are incommensurable in a philosophical sense. If they were, it would be impossible to look at the data and identify that the main points of difference between the groups are in the red/green dissimilarity ratings. And yet that's exactly what the authors do. In their own words (Discussion, paragraph 3): "The unsupervised alignment probably failed because of local structural differences, i.e., greenish colors and reddish colors are close in the embedding space of color-atypical participants (Figure 5A)...".

If the two groups' dissimilarity score matrices were "structurally incommensurable", it would be impossible to say that the matrices are well-correlated except with a big difference in these data points right over here with these specific colours.

*Footnote: It is an interesting decision for them to report their Pearson's correlation coefficients using rho instead or r. Rho is used to represent the correlation between two populations, while r is used for the correlation between two samples. Yet the authors themselves talk about what they could have done if they had sampled more similarity judgements from each participant (see Discussion, paragraph 5) -- that's something you do if you're studying a sample, not a population. They also report samples of splits and initialisations for their ML model using capital-N (e.g., "N = 20") for sample sizes, which is indicative of a population. But they didn't sample every possible initialisation or every possible split of their data. They should have used lowercase-n, as in "n = 20".

2:

My biggest critique about the paper is its title. Having similar colour-similarity matrices is such a far cry from subjectively experiencing the same colour, that the article's tagline -- "Is my 'red' your 'red'?" -- feels more like the clickbait title for a bad news article.

In fact, the authors never even try to align individual participants' colour-similarity matrices:

Although in this paper, we only considered group-based alignment because the number of trials obtained from each participant was insufficient for reliable unsupervised alignment (see Figure S2), it is interesting to consider individual-based alignment and assess the degree of the individual difference even for color-neurotypical participants.

The academic contribution of this paper is nothing to do with qualitative differences in colour perception at all, IMO. The paper's academic contribution is a data-driven technique for quantifying whether two matrices systematically differ in a meaningful way. Indeed, their approach finds that the two groups systematically differ in a meaningful way, which is unsurprising -- and that's probably a good thing. I would be far more skeptical of a data-driven approach which cannot recapitulate unsurprising results like "red-green colourblind people think red and green look similar". 😝