4,201 Works

Inference in "Likelihood-Free" Bayesian Networks

Marco Cusumano-Towner

Dongzhen miao (東鎮廟)

Chenxi Huang & Yuanjing Zhang
This video presents the history, structure, architecture and stele corridors of the Dongzhen Temple. Current attitudes toward folk beliefs and contemporary sacrificial scenes in Dongzhen were logged as well. Bilingual editions available.

Topological free entropy

Dan Voiculescu
Free entropy is the analogue of entropy in the setting of free probability. I will take a look back at the topoloical version of free entropy based on norm-microstates. This will include a discussion of the associated topological free entropy dimension, some connections with potential theory, random matrices and some problems,

Operator algebras meet Quantum information theory: a survey on factorizable channels and their applications

Magdalena Musat
Factorizable quantum channels, introduced by C. Anantharaman-Delaroche within the framework of operator algebras, have proven to have important applications in the analysis of quantum information theory, leading also to reformulations of the Connes Embedding Problem. I will survey these results, and address the question whether (infinite dimensional) von Neumann algebras are really needed to describe such channels.

Geometry of the set of synchronous quantum correlations

Travis Russell
We provide a complete geometric description of the set of synchronous quantum correlations for the three experiment two outcome scenario. We show that these correlations form a closed set. Moreover, every correlation in this set can be realized using projection valued measures on a Hilbert space of dimension no more than 16. Along the way we discuss potential implications for Connes' embedding conjecture.

Matrix models for quantum permutations

Michael Brannan
A quantum permutation (or magic unitary) is given by a square matrix whose entries are self-adjoint projections acting on a common Hilbert space $H$ with the property that the row and column sums each add up to the identity operator. Quantum permutations are operator-valued analogues of ordinary permutation matrices and they arise naturally in both quantum group theory and also in the study of quantum strategies for certain non-local games. From the perspective of non-local...

Nonlocal games are harder to approximate than we thought!

John Wright
One of the most confounding open problems in quantum computing is whether we can approximate the quantum value of a nonlocal game, and, if so, how quickly. So far, our progress has been dismal: in spite of decades of work on this problem, we still have not even devised a *finite* time algorithm to solve it! Recent results have hinted that this might not be due to a failing of our imagination, but rather that...

You must have n qubits or more to win: efficient self-tests for high-dimensional entanglement

Anand Natarajan
How much, and what sort of entanglement is needed to win a non-local game In many ways this is the central question in the study of non-local games, and as we've seen in the previous talks, a full understanding of this question could resolve such conundrums as Tsirelson's problem, the complexity of MIP*, and Connes' embedding conjecture. One approach to this question which has proved fruitful is to design *self-tests*: games for which players who...

Kirchberg's contributions to Connes' Embedding Problem

Thomas Sinclair
I will give a treatment of tensor norms of C*-algebras and operator systems with the goal of explaining the major ideas behind Kirchberg's famous tensor product reformulation of Connes' Embedding Problem.

An Algebraic Framework for XOR Games

Adam Bene Watts
One promising technique for understanding features of nonlocal games is to study constraints placed on the players' measurement operators using techniques from algebraic combinatorics. In this talk, I will show an XOR game has commuting operator value 1 iff an instance of the subgroup membership problem on a finitely presented group corresponding to the game has a solution. This relationship can be used to show that the value one question is decidable for interesting sub-cases...

Slofstraâ s Contributions to the Connes Embedding Problem

Vern Paulsen
We will start with an expository overview of various approaches and equivalences to the Connes Embedding Problem and then focus on three of Slofstraâ s contributions.

A complexity-theoretic approach to disproving Connes' Embedding Problem

Thomas Vidick
Tsirelson's problem asks a question about modeling locality in quantum mechanics; roughly speaking, whether the tensor product and commuting models for specifying bipartite correlations are equivalent. Ozawa showed that Tsirelson's problem is equivalent to Connes' Embedding Problem In the talk I will start from Tsirelson's problem and outline a possible approach to its resolution that goes through the theory of nonlocal games in quantum information and interactive proofs in complexity theory. The talk will be...

The Hagedorn-Hermite Correspondence

Tomoki Ohsawa
I will explain the correspondence between the semiclassical wave packets of Hagedorn and the Hermite functions by looking into the relationship between their ladder operators. The correspondence provides simple derivations of some fundamental properties of the Hagedorn wave packets-such as its completeness, transformation properties, and their generating functions-by linking them to the corresponding properties of the Hermite functions.

Reconstructing arithmetic formulas using lower bound proof techniques

Neeraj Kayal
What is the smallest formula computing a given multivariate polynomial f(x)= In this talk I will present a paradigm for translating the known lower bound proofs for various subclasses of formulas into efficient proper learn= ing algorithms for the same subclass. Many lower bounds proofs for various subclasses of arithmetic formulas redu= ce the problem to showing that any expression for f(x) as a sum of =93simpl= e=94 polynomials T_i(x): f(x) =3D T_1(x) + T_2(x)...

Tensor Isomorphism: completeness, graph-theoretic methods, and consequences for Group Isomorphism

Joshua Grochow
We consider the problems of testing isomorphism of tensors, p-groups, cubic forms, algebras, and more, which arise from a variety of areas, including machine learning, group theory, and cryptography. Despite a perhaps seeming similarity with Graph Isomorphism, the current-best algorithms for these problems (when given by bases) are still exponential - for most of them, even q^{n^2} over GF(q). Similarly, while efficient practical software exists for Graph Isomorphism, for these problems even the best current...

The sunflower conjecture and connections to TCS

Shachar Lovett
The sunflower conjecture is one of the famous open problems in combinatorics. In attempting to improve the current known bounds, we discovered connections to objects studies in TCS, such as randomness extractors and DNFs, as well as to new questions in pseudo-randomness. I will describe some of these connections and the many open problems that arise. Based on joint works with Ryan Alweiss, Xin Li, Noam Solomon and Jiapeng Zhang.

The Log-Approximate-Rank Conjecture is False

Arkadev Chattopadhyay
We construct a simple and total XOR function F on 2n variables that has only O(n) spectral norm, O(n^2) approximate rank and O(n^{2.5}) approximate nonnegative rank. We show it has polynomially large randomized bounded-error communication complexity of Omega(sqrt(n)). This yields the first exponential gap between the logarithm of the approximate rank and randomized communication complexity for total functions. Thus, F witnesses a refutation of the Log-Approximate-Rank Conjecture which was posed by Lee and Shraibman (2007)...

Private hypothesis selection

Mark Bun
We investigate the problem of differentially private hypothesis selection: Given i.i.d. samples from an unknown probability distribution P and a set of m probability distributions H, the goal is to privately output a distribution from H whose total variation distance to P is comparable to that of the best such distribution. We present several algorithms for this problem which achieve sample complexity similar to those of the best non-private algorithms. These give new and improved...

Query-to-Communication lifting using low-discrepancy gadgets

Sajin Koroth
Lifting theorems are theorems that relate the query complexity of a function f : {0, 1}^n â {0, 1} to the communication complexity of the composed function f â ¦ g^n, for some â gadgetâ g : {0, 1}^b à {0, 1}^b â {0, 1}. Such theorems allow transferring lower bounds from query complexity to the communication complexity, and have seen numerous applications in the recent years. In addition, such theorems can be viewed as...

Sylvester-Gallai Type Theorems for Quadratic Polynomials

Amir Shpilka
We prove Sylvester-Gallai type theorems for quadratic polynomials. Specifically, we prove that if a finite collection Q, of irreducible polynomials of degree at most 2, satisfy that for every two polynomials Q1,Q2 â Q there is a third polynomial Q3â Q so that whenever Q1 and Q2 vanish then also Q3 vanishes, then the linear span of the polynomials in Q has dimension O(1). We also prove a colored version of the theorem: If three...

Efficient Construction of Rigid Matrices Using an NP Oracle

Josh Alman
If H is a matrix over a field F, then the rank-r rigidity of H, denoted R_{H}(r), is the minimum Hamming distance from H to a matrix of rank at most r over F. Giving explicit constructions of rigid matrices for a variety of parameter regimes is a central open challenge in complexity theory. In this work, building on Williams' seminal connection between circuit-analysis algorithms and lower bounds [Williams, J. ACM 2014], we give a...

Nearly Optimal Pseudorandomness From Hardness

Dana Moshkovitz
Existing proofs that deduce BPP=P from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with little slowdown. Specifically, assuming exponential lower bounds against nondeterministic circuits, we convert any randomized algorithm that errs rarely into a deterministic algorithm with a similar running time (with pre-processing), and any general randomized algorithm into a deterministic algorithm whose runtime is slower by a nearly linear multiplicative...

Near-Optimal Pseudorandom Generators for Constant-Depth Read-Once Formulas

William Hoza
We give an explicit pseudorandom generator (PRG) for read-once $\mathbf{AC}^0$, i.e., constant-depth read-once formulas over the basis $\{\wedge, \vee, \neg\}$ with unbounded fan-in. The seed length of our PRG is $\widetilde{O}(\log(n/\varepsilon))$. Previously, PRGs with near-optimal seed length were known only for the depth-$2$ case (Gopalan et al. FOCS '12). For a constant depth $d > 2$, the best prior PRG is a recent construction by Forbes and Kelley with seed length $\widetilde{O}(\log^2 n + \log...

Pseudorandomness from the Fourier Spectrum

Eshan Chattopadhyay
We describe new ways of constructing pseudorandom generators for Boolean functions that satisfy certain bounds on their Fourier spectrum. We discuss the possibility of using this approach to construct pseudorandom generators for complexity classes that have eluded researches for decades. Based on joint works with Pooya Hatami, Kaave Hosseini, Shachar Lovett and Avishay Tal.

Derivation of the Ion equation

Benoit Pausader
(Joint work with Y. Guo, E. Grenier and M. Suzuki) We consider the 2 fluid Euler-Poisson equation in 3d space and show that, when the mass of electron tends to 0, the solutions can be well approximated by the strong limit which solves the (1 fluid) Euler-Poisson equation for ions and an initial layer which disperses the excess electron density and velocity in short time. This is a singular limit, somewhat akin to the low-Mach...

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