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znihilist t1_j6uz705 wrote

Reply to comment by znihilist in [R] Extracting Training Data from Diffusion Models by pm_me_your_pay_slips

If you have a set of pair numbers: (1,1)..(2,3.95)..(3,9.05)..(4, 16.001)..etc These can be fitted with x^2, but x^2 does not contain anywhere the four pairs of numbers, but can recreate them to a certain degree of precision if you try to guess the x values.

Is f(x) = x^2 memorizing the inputs or just able to recreate them because they are in the possible outcome space?

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Ronny_Jotten t1_j6wsav3 wrote

If I remember your face, does my brain contain your face? Can your face be found anywhere inside my brain? Or has my brain created a sort of close-fit formula, embodied in connections of neurons, that can reproduce it to a certain degree of precision? If the latter, does that mean that I haven't memorized your face, even though I can draw a pretty good picture of it?

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visarga t1_j6x0qcm wrote

I think their argument goes like this - when you encode an image to JPEG the actual image is replaced by DCT coefficients and reconstruction is only approximate. That doesn't make the image free of copyright.

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znihilist t1_j6xa0o3 wrote

My point is more to the fact that f(x) doesn't have 3.95 in it anywhere. Because another option would be to write f(x) as -(x-2)(x-3)(x-4)*1/6 -(x-1)(x-3)(x-4)*3.95/2 -(x-1)(x-2)(x-4)*9.05/2 + (x-1)(x-2)(x-3)*16.001/6 this recreates the original points, plug in 1 and you get -(-1)(-2)(-3)*1/6 -(0)(-2)(-3)*3.95/2 -(0)(-1)(-3)*9.05/2 + (0)(-1)(-2)*16.001/6 which is just 1.

This version of f(x) has "memorized" the inputs and is written as a direct function of these inputs, versus x^2 which has nothing in it that is retraced to the original inputs. Both of these functions are able to recreate the original inputs. Although one to infinite precision (RMSE = 0) and the other to an RMSE of ~0.035.

I think intuitively we recognize that these two functions are not the same even beyond their obvious differences (first is a 4th order power function, and the other is a 2nd order power function), either way. Point is, I think "memorize" while applicable in both cases, one stores a copy and the other is able to recreate from scratch, and I believe they do mean different things in their legal implications.

Also, I think it is very interesting the divide on this from a philosophical point of view, and with the genie being out of the bottle, then beside strong societal change and pressure that genie is never going back to the bottle.

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