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pm_me_your_pay_slips OP t1_j6yl0wq wrote

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

The first paper proposes a way of quantifying memorization by looking at pairs of prefixes and postfixes and observing whether the postfixes wer generated by the model when the prefixes were used as prompts.

The second paper has this to say about generalization:

> A natural question at this point is to ask why larger models memorize faster? Typically, memorization is associated with overfitting, which offers a potentially simple explanation. In order to disentangle memorization from overfitting, we examine memorization before overfitting occurs, where we define overfitting occurring as the first epoch when the perplexity of the language model on a validation set increases. Surprisingly, we see in Figure 4 that as we increase the number of parameters, memorization before overfitting generally increases, indicating that overfitting by itself cannot completely explain the properties of memorization dynamics as model scale increases.

In fact, this is the title of the paper: "Memorization without overfitting".

> Anyway, need to read this closer, but "lower posterior likelihood" to me seems fundamentally different from "memorized".

The memorization score is not "lower posterior likelihood", but the log density ratio for a sample: log( p(sample| dataset including sample)/p(sample| dataset excluding sample) ) . Thus, a high memorization score is given to samples that go from very unlikely when not included to as likely as the average sample when included in the training data, or from as likely as the average training sample when not included in the training data to above-average likelihood when included.

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DigThatData t1_j6ynesq wrote

> p(sample| dataset including sample)/p(sample| dataset excluding sample) )

which, like I said, is basically identical to statistical leverage. If you haven't seen it before, you can compute LOOCV for a regression model directly from the hat matrix (which is another name for the matrix of leverage values). This isn't a good definition for "memorization" because it's indistinguishable from how we define outliers.

> What's the definition of memorization here? how do we measure it?

I'd argue that what's at issue here is differentiating between memorization and learning. My concern regarding the density ratio here is that a model that had learned to generalize well in the neighborhood of the observation in question would behave the same way, so this definition of memorization doesn't differentiate between memorization and learning, which I think effectively renders it useless.

I don't love everything about the paper you linked in the OP, but I think they're on the right track by defining their "memorization" measure by probing the model's ability to regenerate presumably memorized data, especially since our main concern wrt memorization is in regards to the model reproducing memorized values.

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pm_me_your_pay_slips OP t1_j6ypajq wrote

>This isn't a good definition for "memorization" because it's indistinguishable from how we define outliers.

The paper has this to say about your point

> If highly memorized observations are always given a low probability when they are included in the training data, then it would be straightforward to dismiss them as outliers that the model recognizes as such. However, we find that this is not universally the case for highly memorized observations, and a sizable proportion of them are likely only when they are included in the training data.

> Figure 3a shows the number of highly memorized and “regular” observations for bins of the log probability under the VAE model for CelebA, as well as example observations from both groups for different bins. Moreover, Figure 3b shows the proportion of highly memorized observations in each of the bins of the log probability under the model. While the latter figure shows that observations with low probability are more likely to be memorized, the former shows that a considerable proportion of highly memorized observations are as likely as regular observations when they are included in the training set. Indeed, more than half the highly memorized observations fall within the central 90% of log probability values.

TLDR if this method was giving you a high score to outliers only, then these samples would have low likelihood when they were included in the training data (because they are outliers). But the authors observed sizeable proportion of the samples with high memorization score to be as likely as regular (inlier) data.

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