Unpopular Opinion
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There are multiple facets here that all kinda get mashed together when people discuss this topic and the publicly available/public domain difference kinda gets at that.
An AI model could be seen as an efficient but lossy compression scheme, especially when it comes to images... And a compressed jpeg of an image is still seen as a copy so why would an AI model trained on reproducing it be different?
Are you suggesting that the model itself is a compressed version of its training data? I think it requires some stretches of how training works to accept that.
It depends on how much you compress the jpeg. If it gets compressed down to 4 pixels, it cannot be seen as infringement. Technically, the word cloud is lossy compression too: it has all of the information of the text, but none of the structure. I think it depends largely on how well you can reconstruct the original from the data. A word cloud, for instance, cannot be used to reconstruct the original. Nor can a compressed jpeg, ofc; that’s the definition of lossy. But most of the information is still there, so a casual observer can quickly glean the gist of the image. There is a line somewhere between finding the average color of a work (compression down to one pixel) and jpeg compression levels.
Is the line where the main idea of the work becomes obscured? Surely not, since a summary hardly infringes on the copyright of a book. I don’t know where this line should be drawn (personally, I feel very Stallman-esque about copyright: IP is not a coherent concept), but if we want to put rules on these things, we need to well-define them, which requires venturing into the domain of information theory (what percentage of the entropy in the original is part of the redistributed work, for example), but I don’t know how realistic that is in the context of law.