(1) the thumbnails indicate that the PDF is available and can be downloaded. This is to promote submissions from pre-print servers and open access journals that make their research readily available. If the PDF is behind a paywall there will not be a thumbnail.
(2) the behavior of the site differs slightly from HN and Reddit. Clicking the title link of a publication takes you to be comment page, whereas the thumbnail takes you to the PDF. Open to hearing what people think about this, but the thumbnail image replaces the title link.
(3) the thumbnails do tend to look similar - but you can often tell what journal it is in and you can recognize familiar papers from it. I like it when authors put figures up front too which some of the ML paper do and which adds some variety.
(2) I don't think this is good enough justification for the huge amount of space wasted by the thumbnail
(3) Recognizing familiar papers isn't all that useful. Making a specific thumbnail for each sub would be better IMO.
Your first and second points could be satisfied by showing a small PDF icon where the thumbnails currently are. Whatever size that allows the listings themselves to be as close together as possible. The PDF icon could also be different colours depending if it has a paywall, or an money symbol over it.
The really big thumbnails that mostly all look the same make the site look very amateurish on first sight.
Here's an example where I on the top row changed the size of the thumbnail to 6em height and width in proportion to the page size and also aligned the votes and upvote button closer to the content. The 2nd and following entries are left with your style.
https://gist.githubusercontent.com/Hultner/e5eb15458e70eecb4...