4 ms·

Because the dual of a structure is clearly not another representation of the structure. Isomorphism means nothing. /s Your intuition is correct, fitting for th

by babel_ 4y ago

Because the dual of a structure is clearly not another representation of the structure. Isomorphism means nothing. /s Your intuition is correct, fitting for the data will lead to this arising. However, you misunderstand the interpretation. What is being fit is exactly an encoding of the dataset (a dual of it, like switching from edges of a cube to faces), so the "coincidence" is which specific images show up with extremely high similarity after similar prompting; likely meaning nothing related showed up in the testing, so it never got pushed around and settled nearby. For many images, that encoding was lossy and sufficiently moved that they are not matches to the training data, however for some they have ended up essentially encoded in these "lines" (as your analogy goes) and can therefore be reconstructed with not that much effort.

kilgnad 4y ago
>Because the dual of a structure is clearly not another representation of the structure. Isomorphism means nothing. /s But it's not an isomorphism. I have a function that has a range that covers every single number in existence. Does that mean that function is A copy of every single number in existence? No. Is that function an isomorphism of every number in existence? No mathematician would use the term "isomorphism" in such a way. You could say that if F(3) = 4, then (4, F(3)) are two things that are isomorphic. But, again, no mathematician would call F(X) isomorphic to 4. Technically in terms of law, what this would mean is that USING the model to generate a COPY would be illegal. The model itself does not hold a copy until function application is executed. Therefore existence of the model itself IS not illegal. To say it's illegal is to say that a copy of the mona lisa exists in paint and paint brushes. F(X) is the paint and paint brush. F(3) is the painting. I will say this, I don't think most people in the jury will be technical enough to get this distinction and the technical part isn't even really important in my opinion. The laws should be made based off of what's better for society/humanity not what's technically valid. Still my comment here is on what is technically happening which SHOULD remain completely separate from the politics surrounding it.
- babel_ 4y ago
  I mentioned isomorphism in reference to representation, which was kinda the point. And, not to belabour the point, but a function F that has an isomorphism to the real numbers means that F does indeed encode all numbers (and, when defined as a set, exactly contains a copy of each). That's literally the point of isomorphism. To demonstrate simply, the integers have an isomorphism to the natural numbers: you count them in an alternating pattern. That's an isomorphism between them (and it need not be relation preserving). So, with that, you can interpret all integers as natural numbers; we say they're the same up to their isomorphism. Isomorphisms also exist for the real numbers with other structures, via bijective maps, and so forth. I'm not going to respond to the other stuff since it's nothing to do with what I said or responded to (even when it was a misinterpretation).
  - kilgnad 4y ago
    Ok sure. This makes sense. Let's be clear so I don't get off track again. Your point is that an isomorphism means an encoding of the picture exists in the network and is therefore a copy. My point of contention is that it's not a copy. But imagine this scenario. The model produces a picture that is identical to a picture in the real world, but that picture was NOT part of the training data. This is certainly possible. It's fuzzy but there comes a point where the layers of abstraction between two entities that are isomorphic become big enough such that they don't violate copyright law.
    - babel_ 4y ago
      Outside the scope of the paper, but sure, it's a valid and interesting question. If a model were to produce a pre-existing image not in its dataset, then we can strongly suspect that two behaviours have occurred (for the sake of establishing provenance). First, it was just the ever so small, non-zero chance that it was produced by a random process that was not based on anything learnt, and within the finite resolution and some accuracy of colour, happens to match up to something already existing which, for example, may have been produced independently by a human artist - say, after the dataset was collected, but before the model was trained, such that it is emphatically a "coincidence" and nothing else, no collusion, no learning, no intelligence. Just chance. Second, and I believe far more likely, this image has been encoded into the model by indirect learning and proxy. For example, say some notable and famous work of art is not part of your dataset (which is believable). However, say that there exist, say, art that references this famous work in some way (as artists sometimes do), which may be up to the point of parody (or some a gag), or may be some small aspect (colour scheme, notable style, outfits, lighting & composition, certain people, etc). Especially if it is what we would literally call "influential", is it not possible to reconstruct the famous work (that was not in the dataset) by indirectly learning about it from other pieces? Now, exact (or near-exact) matches are unlikely, for the most part it would probably tend more towards similarly repeating the references and parody of its dataset, but I feel this would strongly increase the likelihood of randomly producing it as in the first behaviour, and we're inflating the chances certain works are reconstructed entirely by "coincidence"; at least, as according to all observers that merely look at the binary presence of the original in the dataset. Is this a copy? Is it not a copy? In all honesty, the notion of copy or not is insufficiently defined, because there's always some angle that can be part of it, or may not be, as most copyright law is handled on a case by case basis. Is it a copy because its provenance was an attempt to copy? Was it a copy by cosmic accident or just an independent work? Was it a copy by inferred reconstruction, thus not literal copying from the source, even if a verbatim reproduction is made? Is a vector version of a raster image a copy, and vice versa? What is "sufficiently" transformative to no longer be a copy? Does a copy of the Mona Lisa exist in the mind of a person that experiences it, while as a subject in a photograph it has grounds to not be? I'm trying to avoid anthropomorphising it and state whichever way what this is, I'd rather just illustrate how what we learn, what we experience, what we produce replicas of, and all of this is generally part of an unsolved problem/field: epistemology. Do we understand diffusion models fully? No. Therefore, weighing on one side or another should merely be for the purpose of a leading research question, or to exist on either side of a dialectic; such as in the courtroom. Perhaps we're still just too immature on this topic to really say anything about copying. Really, the only thing we do know about copying, is that you should never get caught doing it. (For legal reasons, that was a joke.)

by babel_ 4y ago

kilgnad 4y ago

>Because the dual of a structure is clearly not another representation of the structure. Isomorphism means nothing. /s But it's not an isomorphism. I have a function that has a range that covers every single number in existence. Does that mean that function is A copy of every single number in existence? No. Is that function an isomorphism of every number in existence? No mathematician would use the term "isomorphism" in such a way. You could say that if F(3) = 4, then (4, F(3)) are two things that are isomorphic. But, again, no mathematician would call F(X) isomorphic to 4. Technically in terms of law, what this would mean is that USING the model to generate a COPY would be illegal. The model itself does not hold a copy until function application is executed. Therefore existence of the model itself IS not illegal. To say it's illegal is to say that a copy of the mona lisa exists in paint and paint brushes. F(X) is the paint and paint brush. F(3) is the painting. I will say this, I don't think most people in the jury will be technical enough to get this distinction and the technical part isn't even really important in my opinion. The laws should be made based off of what's better for society/humanity not what's technically valid. Still my comment here is on what is technically happening which SHOULD remain completely separate from the politics surrounding it.

babel_ 4y ago
I mentioned isomorphism in reference to representation, which was kinda the point. And, not to belabour the point, but a function F that has an isomorphism to the real numbers means that F does indeed encode all numbers (and, when defined as a set, exactly contains a copy of each). That's literally the point of isomorphism. To demonstrate simply, the integers have an isomorphism to the natural numbers: you count them in an alternating pattern. That's an isomorphism between them (and it need not be relation preserving). So, with that, you can interpret all integers as natural numbers; we say they're the same up to their isomorphism. Isomorphisms also exist for the real numbers with other structures, via bijective maps, and so forth. I'm not going to respond to the other stuff since it's nothing to do with what I said or responded to (even when it was a misinterpretation).
- kilgnad 4y ago
  Ok sure. This makes sense. Let's be clear so I don't get off track again. Your point is that an isomorphism means an encoding of the picture exists in the network and is therefore a copy. My point of contention is that it's not a copy. But imagine this scenario. The model produces a picture that is identical to a picture in the real world, but that picture was NOT part of the training data. This is certainly possible. It's fuzzy but there comes a point where the layers of abstraction between two entities that are isomorphic become big enough such that they don't violate copyright law.
  - babel_ 4y ago
    Outside the scope of the paper, but sure, it's a valid and interesting question. If a model were to produce a pre-existing image not in its dataset, then we can strongly suspect that two behaviours have occurred (for the sake of establishing provenance). First, it was just the ever so small, non-zero chance that it was produced by a random process that was not based on anything learnt, and within the finite resolution and some accuracy of colour, happens to match up to something already existing which, for example, may have been produced independently by a human artist - say, after the dataset was collected, but before the model was trained, such that it is emphatically a "coincidence" and nothing else, no collusion, no learning, no intelligence. Just chance. Second, and I believe far more likely, this image has been encoded into the model by indirect learning and proxy. For example, say some notable and famous work of art is not part of your dataset (which is believable). However, say that there exist, say, art that references this famous work in some way (as artists sometimes do), which may be up to the point of parody (or some a gag), or may be some small aspect (colour scheme, notable style, outfits, lighting & composition, certain people, etc). Especially if it is what we would literally call "influential", is it not possible to reconstruct the famous work (that was not in the dataset) by indirectly learning about it from other pieces? Now, exact (or near-exact) matches are unlikely, for the most part it would probably tend more towards similarly repeating the references and parody of its dataset, but I feel this would strongly increase the likelihood of randomly producing it as in the first behaviour, and we're inflating the chances certain works are reconstructed entirely by "coincidence"; at least, as according to all observers that merely look at the binary presence of the original in the dataset. Is this a copy? Is it not a copy? In all honesty, the notion of copy or not is insufficiently defined, because there's always some angle that can be part of it, or may not be, as most copyright law is handled on a case by case basis. Is it a copy because its provenance was an attempt to copy? Was it a copy by cosmic accident or just an independent work? Was it a copy by inferred reconstruction, thus not literal copying from the source, even if a verbatim reproduction is made? Is a vector version of a raster image a copy, and vice versa? What is "sufficiently" transformative to no longer be a copy? Does a copy of the Mona Lisa exist in the mind of a person that experiences it, while as a subject in a photograph it has grounds to not be? I'm trying to avoid anthropomorphising it and state whichever way what this is, I'd rather just illustrate how what we learn, what we experience, what we produce replicas of, and all of this is generally part of an unsolved problem/field: epistemology. Do we understand diffusion models fully? No. Therefore, weighing on one side or another should merely be for the purpose of a leading research question, or to exist on either side of a dialectic; such as in the courtroom. Perhaps we're still just too immature on this topic to really say anything about copying. Really, the only thing we do know about copying, is that you should never get caught doing it. (For legal reasons, that was a joke.)