Also, Should the simplicity prior they use is akin to kolmogorov complexity-based mostly priors, then Which means the things they are executing is akin to what e.g. Solomonoff Induction does. And I've by no means listened to any individual try and argue that Solomonoff Induction "basically interpolates" just before!
The remainder of the remark is about things which i did not have a strong belief on, so I am going to go away it for Zach to answer if he would like.
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As for the rest of your remark -- That which you’re expressing below looks correct to me, but I’m not sure I see how any of this can be a counterpoint to everything we’re indicating?
Also: because we’re estimating several probabilities by sampling, we in essence must discretise the operate Room. If you have any concrete ideas for ways to get close to this then we’re all ears!
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For an random function on an input space of dimension 2n, you'll want to roll 2n unbiased random variables.  Just about every roll affects just one enter aspect.
As an example, if you have a look at Determine 6 in the submit I url, you'll be able to see that unique versions of SGD do give a rather various inductive bias. Having said that, this impact is apparently fairly modest relative to what's provided by the "prior".
SI is bayesianism + universal prior, IIRC. The way that solomonoff induction generalizes to new knowledge is just that it takes the prior and cuts out the many features that contradict The brand new facts. (i.e. it does bayesian update). So insofar since it generalizes well, it's as it is made up of functions in the initial common prior that generalize very well, and they have got comparatively superior prior when compared to the features that don't.
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Precisely, I am wary of the main focus on measuring complexity for features amongst finite sets, for instance binary features.
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