Anyway I’m sure you’re all dying to know what exactly the title means. For the lay-person, computational hardness results typically come in two flavors, “worst-case” and “average-case”. “Worst-case” hardness means that no matter what algorithm you try to use to solve a problem, there exists at least one input on which the algorithm makes a mistake. “Average-case” hardness says that no mater what algorithm you try to use to solve a problem, there exist many inputs on which the algorithm makes a mistake. So average-case hardness implies worst-case hardness, but in most cases the reverse implication is unknown.

In general, when we want to prove a statement X and we can’t do it unconditionally, then we try to show that some kind of hardness implies X. We prefer to show that worst-case hardness implies X because worst-case hardness is a more reasonable assumption than average-case hardness.

However, in many situations we only know how to prove that average-case hardness implies X. In our case, we know that some versions of average-case hardness imply that the task of learning how to label (for example, label pictures as “landscape” or not) is difficult, but it’s unknown whether we can show that learning is hard based only on worst-case assumptions. Our paper tries to address this, and basically we show that a wide range of proof techniques, including all hardness of learning proof techniques known in the literature, cannot be used to resolve this question. I know, there’s a lot of double negatives going on, but trust me it makes sense!

Anyway I’m unable to access my blog from my office because of this connerie because in order to access foreign sites at the office we have to go through a proxy. I can access the blog at the hotel by tunneling through Princeton’s servers, but since I have to pay for Internet here I’m probably only going to update the blog on the weekends. Sadness

Sometimes your aisles are so crowded that I can barely squeeze through past the exasperated soccer mom looking at her kids and wondering that maybe, just maybe, she could get out of the parking lot before they realize she’s abandoned them in the freezer room, or the white guy trying to impress his Asian girlfriend with his knowledge about light vs dark soy sauce. And sometimes it’s just so damn cold out that the thought of trekking over to 12th Ave through the gauntlet of bums, projects, and police stations almost seems not worth it.

But then I remember that crunchy and sweet Gala apple you gave me two weeks ago. Or that tender asparagus you gave me on Valentine’s day. Or even that heavenly stinky cheese you proffered over the holidays that forced my roommate to declare a DMZ across the middle of the fridge. And I know that I can try to resist as hard as I can, but there’s no way that I could ever tear myself away from you for another supermarket. Whole Foods’ yuppie luxury tree-hugging self-indulgence and Gristede’s overpriced trash heap just can’t compare to you.

BUT the funniest part of todays talk was when someone asked Silvio Micali why we should care about the sealed envelopes and ballot box paradigm if it can’t be implemented over the Internet, to which Silvio asked, “Well we can’t have sex over the Internet, so why do we care about sex?” Which of course led to the comment, “Well you can find sex over the Internet” and… well… I’ll stop there.

The other highlight of the day was watching a bunch of computer scientists do the YMCA, or, in this case, the IACR. I’ll let the picture speak for itself.