Can someone explain what is "interpolation threshold"? Both articles talk about it, but none defines.
Where the "Effective Model Complexity (EMC)" of a model + training procedure (w.r.t an input distribution) is the maximum number of samples from the distribution that the model+training can fit to ~0 train error.
Our experiments are consistent with the hypothesis that the double-descent peak occurs when EMC = n; that is, when the model+training is just barely able to fit the train set.
It's almost certainly possible to break this by pathological choice of a data distribution or model/initialization/optimization scheme. But, I don't think this is interesting -- what I think is interesting is that this seems to hold true in real life, in "natural settings".
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(^) Whatever "natural distributions" means... (which I think is a good research direction in itself).
But that doesn't mean there's a single structure determined by a single set of parameters. Quite possibly there are numerous structures with not-compatible parameter structures.
Moreover, common AI data sets share parameters in a fashion that isn't always obvious - most images on the web are photos taken by human photographers who tend to center their subject, effectively giving them different parameters than, say, security camera footage. IE, "normal data" may not mean what we imagine.