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# [theory-seminar] The Practice of Theory Research - Final Talks

Omer Reingold reingold at stanford.edu
Thu Mar 3 16:34:16 PST 2022

And the location of the talks is very close to Gates in Sequoia Hall 200
<http://campus-map.stanford.edu/?srch=Sequoia+Hall+200> 🙄   No zoom.

Omer

On Thu, Mar 3, 2022 at 11:16 AM Omer Reingold <reingold at stanford.edu> wrote:

> Hello everybody,
>
> CS 163 is a "research methods in theory of CS" course. There were 5 groups
> doing research throughout the quarter, and they will be telling about their
> progress next week. I append the talk schedules as well as abstracts. The
> students will really appreciate an external audience so please let me know
> if you can make it for any of the talks (even if you can attend a single
> talk it will be great).
>
> Thanks
> Omer
>
> *Tuesday, March 8th*
>
>
>
> 11:30-12: *Low-Bandwidth Evaluation of High-Degree Polynomials Using
> High-Rate Error-Correcting Codes, *Connor Meany, Agustin Otero, Abraham
> Ryzhik
>
> 12-12:30: *Weak Group Isomorphism in Almost-Quadratic Time, *Hanson Hao,
> Ben Heller, Wenqi Li
>
> 12:30-1pm: *Card Guessing Game with Riffle Shuffles and an Adversarial
> Perspective, *Suzy Lou, Josh Nkoy, Joey Rivkin, Colin Sullivan
>
>
>
> *Thursday, March 10th*
>
>
>
> 11:30-12: *More Robust Distributed Merkle's Puzzles, *Christie Di and
> Jamie Song
>
> 12-12:30: *Neural Networks Generalize from Self-Averaging Sub-classifiers
> in the Same Way As Adaptive Boosting, *Peter Chatain and Michael Sun
>
>
>
> * Abstracts:*
>
>
> Title: *Low-Bandwidth Evaluation of High-Degree Polynomials Using
> High-Rate Error-Correcting Codes*
>
> Speakers:  Connor Meany, Agustin Otero, Abraham Ryzhik
>
>
>
> Abstract: The problem of computing functions F:F^k→F on encoded data
> c=C(x) ∈ F^n is the most natural generalization to asking for decodings
> of it: F(x) = x. In [SW22] the problem is solved using less encoded
> information than necessary in trivially first decoding, then evaluating:
> \tilde{c} −“C−1”−→ x-F−→F(x), for F linear over F.  We show how to maintain
> encoding bandwidth gains below trivial while computing nonlinear functions
> of the form F(x) =\sum f_i(x_i) for f_i ∈ F[X] a polynomial of degree at
> most p∈N, ∀i∈[k], without sustaining factors of p losses in encoding rate
> k/n, where C: F^k → F^n. To achieve this, we show that changing the
> encoding function to f(x)^p makes it not much harder to interpolate than
> the original f(x), while tolerating errors as in [SW22]. This stands to
> improve the potency of distributed storage and parallel computation,
> broadening the class of functions that can be computed on desirable-rate
>
>
>
> Title: *Weak Group Isomorphism in Almost-Quadratic Time*
>
> Speakers: Hanson Hao, Ben Heller, Wenqi Li
>
>
>
> Abstract: In DW2020, the group isomorphism problem is solved in nearly
> linear time for a dense set of group orders. Thus, the barrier to improving
> group isomorphism lies in the group orders not contained in this dense set.
> Specifically, the hardest case is thought to be the case of p-groups.
> Although there are not many reductions formalizing that this is the hardest
> case, in GQ2021 there is some progress on this path with a reduction among
> p-groups. The group isomorphism problem is of independent interest, but is
> also motivated by the existence of a reduction from group isomorphism to
> graph isomorphism Miller 1979, the complexity of which is a major unsolved
> problem in complexity theory. Furthermore, the hard case of group
> isomorphism with p-groups is thought to be a hard case of graph isomorphism
> under the reduction from groups to graphs, however there is no reduction
> making this provably true. At the moment, nobody really knows how to handle
> the case of p-groups. And for most group orders that do not contain
> p-groups, there is a nearly linear time algorithm to check for isomorphism.
> In order to find new angles on this sort of problem, we will investigate a
>
> weaker notion than isomorphism.
>
>
>
> Title: *Card Guessing Game with Riffle Shuffles and an Adversarial
> Perspective*
>
> Speakers: Suzy Lou, Josh Nkoy, Joey Rivkin, Colin Sullivan
>
>
>
> Abstract: This paper explores the card guessing game on a riffle-shuffled
> deck. In this game, a dealer orders a deck of n cards numbered 1, . . . ,
> n, and a guesser guesses the cards one at a time, attempting to maximize
> their number of correct guesses in expectation. The paper extends previous
> work on a variant of the card guessing game where the dealer is limited to
> a single riffle shuffle. We show an optimal guesser strategy against
> arbitrarily many riffle shuffles and compute a rough bound on the
> expectation of correct guesses using this strategy. We also introduce an
> adversarial analogue of a riffle shuffle dealer, in which a dealer can
> order the cards in any way consistent with some fixed number of riffle
> shuffles. We give an optimal optimal adversarial dealer strategy using this
> model and compute the upper bound on the number of correct guesses against
> this dealer.
>
>
>
> Title: *More Robust Distributed Merkle's Puzzles*
>
> Speakers: Christie Di and Jamie Song
>
>
>
> Abstract: In 1974, Merkle proposed the first key exchanging scheme based
> on symmetric primitives called “Merkle’s Puzzle”, which allows two players
> to build a secure channel against an eavesdropper. In 2021, Dinur and
> Hassen proposed a distributed merkle’s puzzle protocol but it fails to work
> under constant fraction of semi-honest or malicious players. We will first
> present a basic protocol which should be robust against any number of
> semi-honest or malicious players, then we will proceed with two other
> protocols with better query complexity. Our final goal is to prove the
> optimality for a model against a constant proportion of semi-honest and
> malicious players, or give an impossibility result to show the limit of
> distributed merkle's puzzles in that setting. Our works could potentially
> extend to other highly connected network models.
>
>
>
> Title: *Neural Networks Generalize from Self-Averaging Sub-classifiers in
> the Same Way As Adaptive Boosting*
>
> Speakers: Peter Chatain and Michael Sun
>
>
>
> Abstract: In recent years, neural networks (NN’s) have made giant leaps in
> a wide variety of domains. NN’s are often referred to as “black box”
> algorithms due to how little we can explain their empirical success. Our
> foundational research seeks to explain why neural networks generalize. A
> recent advancement derived a mutual information measure for explaining the
> performance of deep NN’s through a sequence of increasingly complex
> functions. We show deep NN’s learn a series of boosted classifiers whose
> generalization is popularly attributed to self-averaging over an increasing
> number of interpolating sub-classifiers. To our knowledge, we are the first
> work to establish the connection between generalization in boosted
> classifiers and generalization in deep NN’s. Our experimental evidence and
> theoretical analysis suggest NNs trained with dropout exhibit similar
> self-averaging behavior over interpolating sub-classifiers as cited popular
> explanations for the post-interpolation generalization phenomenon in
> boosting.
>
>
>
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