The workshop will bring together leading researchers from different areas of Theoretical Computer Science
with the goal of presenting the latest research to a broad TCS audience from Chicago and surrounding areas, and increasing the interaction between different areas
of Theoretical Computer Science.

All researchers interested in theoretical computer science are invited to attend.
Attending the workshop is free, but please
register via this
form before January 15th.

Confirmed Speakers:

• Nima Anari (Stanford University)

• Sebastien Bubeck (Microsoft Research Redmond)

• Arkadev Chattopadhyay (Tata Institute of Fundamental Research)

• Ilias Diakonikolas (University of Wisconsin-Madison)

• Sebastian Forster (University of Salzburg)

• Ankit Garg (Microsoft Research India)

• Nika Haghtalab (Cornell University)

• Prahladh Harsha (Tata Institute of Fundamental Research)

• Piotr Indyk (Massachusetts Institute of Technology)

• Sanjeev Khanna (University of Pennsylvania)

• Dakshita Khurana (University of Illinois at Urbana-Champaign)

• Pravesh Kothari (Carnegie Mellon University)

• Robert Krauthgamer (The Weizmann Institute of Science)

• Marvin Künnemann (Max Planck Institute for Informatics)

• Tengyu Ma (Stanford University)

• Rafael Oliveira (University of Toronto and University of Waterloo)

• Sofya Raskhodnikova (Boston University)

• Noga Ron-Zewi (University of Haifa)

• Thatchaphol Saranurak (Toyota Technological Institute at Chicago)

• Balasubramanian Sivan (Google Research)

• Omri Weinstein (Columbia University)

• Henry Yuen (University of Toronto)

Tentative Schedule

8:30 -- 9:00

Registration + Light Breakfast

Session 1

9:00 -- 9:20

Thatchaphol Saranurak

A Deterministic Algorithm for Balanced Cut with Applications

Finding a minimum balanced cut is a powerful method for implementing the divide-and-conquer paradigm
on graphs.We give a new deterministic algorithm for finding an approximate minimum balanced cut in
almost-linear time. Previous algorithms are either randomized or take quadratic time. This implies
near-optimal deterministic algorithms for a whole range of important graph problems, including approximate
max flow, electric flow, Laplacian solvers, expander decomposition, dynamic connectivity, etc.

Joint work with Julia Chuzhoy, Yu Gao, Jason Li, Danupon Nanongkai, and Richard Peng.

9:20 -- 9:40

Sanjeev Khanna

Polynomial Pass Lower Bounds for Graph Streaming Algorithms

We present new lower bounds that show that a polynomial number of passes
are necessary for solving some fundamental graph problems in the streaming
model of computation. For instance, we show that any streaming algorithm
that finds a minimum s-t cut in a weighted undirected graph needs essentially
quadratic space unless it makes a polynomial number of passes over the graph stream.

To prove our lower bounds, we introduce and analyze a new four-player
communication problem that we refer to as the hidden-pointer chasing problem.
The hidden-pointer chasing problem appears flexible enough to find other
applications and is therefore interesting in its own right. To showcase this,
we present an interesting application of this problem beyond streaming algorithms.
Using a reduction from hidden-pointer chasing, we prove that any algorithm for
submodular function minimization needs to make essentially a quadratic number
of value queries to the function unless it has a polynomial degree of adaptivity.

This is joint work with Sepehr Assadi and Yu Chen.

9:40 -- 10:00

Sebastian Forster

Computing and Testing Small Connectivity in Near-Linear Time and
Queries via Fast Local Cut Algorithms

Consider the following "local" cut-detection problem in a directed
graph: We are given a seed vertex x and need to remove at most k edges
so that at most \nu edges can be reached from x (a "local" cut) or
output \bot to indicate that no such cut exists. If we are given query
access to the input graph, then this problem can in principle be solved
without reading the whole graph and with query complexity depending on k
and \nu. In this paper we consider a slack variant of this problem
where, when such a cut exists, we can output a cut with up to O(k\nu)
edges reachable from x.

We present a simple randomized algorithm spending O(k^2\nu) time and
O(k\nu) queries for the above variant, improving in particular a
previous time bound of (k^{O(k)}\nu) by Chechik et al. [SODA '17]. We
also extend our algorithm to handle an approximate variant. We
demonstrate that these local algorithms are versatile primitives for
designing substantially improved algorithms for classic graph problems
by providing the following three applications. (1) A randomized
algorithm for the classic k-vertex connectivity problem that takes
near-linear time when k=polylog(n), namely \tilde O(m+nk^3) time in
undirected graphs and \tilde O(mk^2) time in directed graphs. Our
techniques also yield an improved approximation scheme. (2) Property
testing algorithms for k-edge and -vertex connectivity with query
complexities that are near-linear in k, exponentially improving the
state of the art. This resolves two open problems, one by Goldreich and
Ron [STOC '97] and one by Orenstein and Ron [Theor. Comput Sci. '11].
(3) A faster algorithm for computing the maximal k-edge connected
subgraphs, improving prior work of Chechik et al. [SODA '17].

10:00 -- 10:20

Prahladh Harsha

High Dimensional Expander and some coding applications

Expander graphs, over the last few decades, have played a pervasive
role in almost all areas of theoretical computer science. Recently,
various high-dimensional analogues of these objects have been studied
in mathematics and even more recently, there have been some surprising
applications in computer science, especially in the area of coding
theory. In this talk, we will explore these high-dimensional expanders
from a spectral viewpoint and give an alternate characterization if
terms of random walks. We will then see an application of
high-dimensional expanders towards local testability and
list-decoding.

10:20 -- 10:45

Break

Session 2

10:45 -- 11:05

Dakshita Khurana

New Techniques for Zero-Knowledge Proofs

Zero-knowledge is one of the central areas of research in cryptography.
A zero-knowledge proof allows a prover to convince a verifier about the truth
of an NP statement while revealing no information beyond the truth of the statement.
In the first part of this talk, I will give an overview of how zero-knowledge is
defined, and of different techniques that we know, that help us build zero-knowledge
proof systems. In the second part of the talk, I will give an overview of a new
non-black-box simulation technique. I will describe how this gives us the first
constructions of witness hiding proof systems requiring only a single message each
from the verifier and the prover. Part 2 of the talk is based on joint work with
Nir Bitansky and Omer Paneth.

11:05 -- 11:25

Noga Ron-Zewi

Local Proofs Approaching the Witness Length

Interactive oracle proofs are a hybrid between interactive proofs
and probabilistically-checkable proofs, where the prover is allowed
to interact with a verifier by sending relatively long messages to
the verifier, who in turn is only allowed to query a few of the bits
that were sent.

In this work we construct, for any NP relation for which membership
can be decided in polynomial-time and bounded polynomial space
(e.g., SAT, Hamiltonicity, Clique, Vertex-Cover, etc.), interactive
oracle proofs in which the proof length approaches the witness length.
The number of rounds, as well as the number of queries made by the verifier,
are constant. Our proof leverages recent constructions of high-rate locally
testable tensor codes. In particular, we bypass the barrier imposed by the
low rate of multiplication codes (e.g., Reed-Solomon, Reed-Muller or AG codes)
- a core component in prior constructions.

Joint work with Ron Rothblum.

11:25 -- 11:45

Pravesh Kothari

Efficient List-Decodable Estimation Via Sum-of-Squares

List-decodable learning studies high dimensional statistical estimation in the setting where
an α (< 1/2) fraction of the input sample are drawn according to the model and the remaining (
possibly majority) points are arbitrary, potentially adversarially chosen inliers. Since only a
minority of the sample are inliers, it is not possible to recover the unknown parameters uniquely.
Thus, the goal in list-decodable learning is to recover a small - a fixed constant depending on
α - list of parameters that contains the true parameters.

In this talk, I will survey a unified approach based on the sum of squares method for
list-decodable learning. This is a single unified approach that yields the state of the
art efficient algorithms for the problems of mean estimation/clustering spherical mixture
models, linear regression and subspace recovery in the list-decodable setting.

Based on joint works with Ainesh Bakshi, Sushrut Karmalkar, Adam Klivans, and Jacob Steinhardt.

11:45 -- 1:15

Lunch (Provided)

Session 3

1:15 -- 1:35

Ilias Diakonikolas

Distribution-Independent PAC Learning of Halfspaces with Massart Noise

I will describe recent algorithmic progress on the problem
of learning halfspaces in the distribution-independent PAC model,
when the labels of the examples have been corrupted by Massart noise.

1:35 -- 1:55

Piotr Indyk

Learning-augmented algorithms

1:55 -- 2:15

Tengyu Ma

Optimization of Regularized Wide Neural Networks

We will show that gradient descent can optimize a regularized infinite-width two-layer
neural network in polynomial iterations. We will also discuss recent progress on the
theory of deep learning very briefly as the context of this result as well as
interesting open questions.

2:15 -- 2:35

Balasubramanian Sivan

Strategizing against No-regret Learners

How should a player who repeatedly plays a game against a no-regret
learner strategize to maximize his utility? We study this question and
show that under some mild assumptions, the player can always guarantee
himself a utility of at least what he would get in a Stackelberg equilibrium
of the game. When the no-regret learner has only two actions, we show that
the player cannot get any higher utility than the Stackelberg equilibrium
utility. But when the no-regret learner has more than two actions and plays
a mean-based no-regret strategy, we show that the player can get strictly
higher than the Stackelberg equilibrium utility. We provide a characterization
of the optimal game-play for the player against a mean-based no-regret learner
as a solution to a control problem. When the no-regret learner's strategy also
guarantees him a no-swap regret, we show that the player cannot get anything
higher than a Stackelberg equilibrium utility.

Joint work with Yuan Deng, Jon Schneider

2:35 -- 2:55

Ankit Garg

Learning arithmetic circuits in the average case via lower bounds

The problem of learning arithmetic circuits is the following: given a
polynomial as a black box that is promised to have a small arithmetic circuit
computing it, can we find this arithmetic circuit? This problem is hard in the
worst case and so previous works have focused on regimes where the NP-hardness does not
kick in (e.g. constant top fan-in etc.). We focus on the average case where one assumes
certain non-degeneracy assumptions on the circuit (formally these amount to assuming the
circuit parameters lie outside a certain variety and hence if they are chosen randomly
according to any reasonable distribution, the non-degeneracy condition is satisfied
whp). Kayal and Saha gave a meta framework for designing these algorithms for circuit
classes where we have lower bounds. They carried this out for depth 3 circuits (sums
of products of linear forms) and we (in joint work with Kayal and Saha) carry it out for depth
4 powering circuits (sums of powers of low degree polynomials). I will talk about the meta framework
and then about our specific results.
I will also talk about a potential application to learning mixtures of general Gaussians.

2:55 -- 3:20

Break

Session 4

3:20 -- 3:40

Henry Yuen

Connes' Embedding Problem through the lens of complexity theory

The Connes Embedding Problem (CEP) is a long-standing question in the field
of operator algebras, and is known to be equivalent to a number of other
conjectures across mathematics. Remarkably, the CEP is also connected to
fundamental questions in quantum information theory. In particular, a positive
resolution to the CEP implies the existence of an algorithm to approximately
compute the optimal winning probability of nonlocal games. This motivates an
intriguing complexity-theoretic approach to exploring the CEP: obtaining lower
bounds on the complexity of nonlocal games implies limits on the CEP, whereas
upper bounds gives evidence towards its positive resolution.

I will give an overview of this fascinating connection between the Connes
Embedding Problem, nonlocal games, and computational complexity, and I will
discuss some new results about the complexity of nonlocal games.

3:40 -- 4:00

Marvin Künnemann

A Fine-grained Analogue of Schaefer's Theorem in P

Recent years have seen a surge of methods to analyze the complexity landscape within the
polynomial-time regime, allowing us to classify which problems are unlikely to have faster
solutions than currently known. Unfortunately, most of these results establish relationships
only between isolated problems rather than between general classes of problems. The most
important exception is a recent completeness result that shows that the fundamental Orthogonal
Vectors problem (OV) is complete for the class of model-checking first-order properties
[Gao, Impagliazzo, Kolokolova, and Williams TALG'19].

In this talk, we discuss advances towards a detailed understanding of this class
of problems, to strengthen our class-based understanding of hardness within P.
In particular, for a notable subclass, we determine precisely which first-order properties
admit a polynomial-factor improvement over the natural baseline algorithm (conditional on
a plausible assumption on the hardness of finding cliques in hypergraphs). This establishes
a dichotomy in P that is analogous to Schaefer's Theorem for constraint satisfaction problems.

Joint work with Karl Bringmann and Nick Fischer.

4:00 -- 4:20

Omri Weinstein

An Adaptive Step Toward the Multiphase Conjecture

In 2010, Patrascu proposed the Multiphase problem as a candidate for proving *polynomial*
lower bounds on the operational time of dynamic data structures, and showed it would imply
unconditional lower bounds on many important dynamic data structure problems. After 10
years, there has been almost no progress on this conjecture. We show an ~\Omega(\sqrt{n})
cell-probe lower bound on the Multiphase problem for data structures with general (adaptive)
updates, and queries with unbounded but "layered" adaptivity. This captures all known
set-intersection data structures and significantly strengthens previous Multiphase lower
bounds, which only captured non-adaptive data structures. Our main technical result is a
communication lower bound on a 4-party variant of Patrascu's Number-On-Forehead game,
using information complexity techniques.

Joint work with Young Kun Ko.

4:20 -- 4:40

Arkadev Chattopadhyay

The Log-Approximate-Rank Conjecture is False

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) as a very natural analogue for randomized communication of the
still unresolved Log-Rank Conjecture for deterministic communication. The best known
previous gap for any total function between the two measures was a recent 4th-power
separation by Goos, Jayram, Pitassi and Watson (2017).

Additionally, our function F refutes Grolmusz's Conjecture (1997) and a variant of the
Log-Approximate-Nonnegative-Rank Conjecture, suggested by Kol, Moran, Shpilka and
Yehudayoff (2014), both of which are implied by the LARC. The complement of F has
exponentially large approximate nonnegative rank. This answers a question of Lee (2012)
and Kol et al. (2014), showing that approximate nonnegative rank can be exponentially
larger than approximate rank. The function F also falsifies a conjecture about parity
measures of Boolean functions made by Tsang, Wong, Xie and Zhang (2013). The latter
conjecture implied the Log-Rank Conjecture for XOR functions.

Remarkably, after our manuscript was published in the public domain, two groups of
researchers, Anshu-Boddu-Touchette (2018) and Sinha-de-Wolf (2018), showed independently
that the function F even refutes the Quantum-Log-Approximate-Rank Conjecture.

(This is joint work with Nikhil Mande and Suhail Sherif)

4:40 -- 5:00

Rafael Oliveira

Towards a theory of non-commutative optimization

Scaling problems, such as operator scaling and tensor scaling, have recently found several
applications in diverse areas of math and CS. They have been used to give efficient algorithms
for non-commutative rational identity testing, compute the optimal constant in Brascamp-Lieb
inequalities, one-body quantum marginal problem, solution to the Paulsen problem, and the
search version of the Horn's problem, to name a few. Scaling problems are natural geodesic
convex optimization problems on Riemannian manifolds that arise from the symmetries of
non-commutative groups, and the algorithms (and their analyses) developed in these previous
works heavily relied on this general form of convexity.

In this talk we discuss our recent systematic development of a theory of non-commutative
optimization, which greatly extends ordinary (Euclidean) convex optimization. We will see
how NC optimization unify and generalize the algorithms developed for the uniform and
non-uniform versions of the operator scaling and tensor scaling problems.

Based on joint work with Peter Buergisser, Cole Franks, Ankit Garg, Michael Walter and Avi Wigderson.

5:00 -- 5:20

Break

Session 5

5:20 -- 5:40

Sofya Raskhodnikova

Approximating the Distance to Monotonicity of Boolean Functions

We study the problem of approximating the distance to monotonicity
of Boolean functions over the hypercube domain. For a function
f:{0,1}^n -> {0,1}, the distance to monotonicity of f is the minimum
fraction of points at which f has to be modified to make it monotone.
We give a nonadaptive algorithm that, given f:{0,1}^n -> {0,1} whose
distance to monotonicity is at least \alpha, makes poly(n, 1/\alpha)
queries and returns an O(\sqrt{n} polylog n)-multiplicative approximation
to the distance to monotonicity of f. Furthermore, we show that for any
constant k > 0, approximating the distance to monotonicity up to
n^{0.5 - k}-factor requires 2^{n^k} nonadaptive queries, thereby ruling out a
poly(n, 1/\alpha)-query nonadaptive algorithm for such approximations. This
answers a question of Seshadhri (Property Testing Review '14) for the case of
nonadaptive algorithms. Approximating the distance to a property is closely
related to tolerantly testing that property. Our lower bound stands in contrast
to standard (non-tolerant) testing of monotonicity that can be
done nonadaptively with O(\sqrt{n} polylog n) queries.

We obtain our lower bound by proving an analogous bound for erasure-resilient
testers. Our method yields the same lower bounds for other properties (unateness
and being a k-junta). These lower bounds improve exponentially on the existing lower
bounds for these properties.

Joint work with Ramesh Krishnan Pallavoor and Erik Waingarten

5:40 -- 6:00

Sebastien Bubeck

How to trap a gradient flow

I will discuss a new strategy to find stationary points of non-convex functions in
low-dimensional spaces. In particular we resolve an open problem from 1993 by Stephen A. Vavasis
on the complexity of this problem in 2D.

Joint work with Dan Mikulincer.

6:00 -- 6:20

Nika Haghtalab

Smoothed Analysis of Online Learning

In the smoothed analysis of algorithms, an adversary chooses an arbitrary input
which is subjected to a small random perturbation before being presented to an
algorithm. The goal is then to design an algorithm that always has good expected
performance, for a worst-case adversary and on average over the perturbation. In
this paper, we apply the smoothed analysis framework to the problem of regret-minimization
in online learning with adaptive adversaries, and show that under the smoothed analysis
framework, online learnability is equivalent to offline learnability. That is, similar
to offline (i.i.d) learning, the VC dimension of a hypothesis class characterizes the
regret obtainable against smoothed adaptive adversaries. This is in stark contrast to
the worse-case regret bounds that are characterized by the Littlestone dimension of a
class of hypotheses, as the Littlestone dimension of even simple classes with constant
VC dimension can be unbounded.

This is based on a joint work with Tim Roughgarden and Abhishek Shetty.

6:20 -- 6:40

Robert Krauthgamer

Coresets for Clustering in Graphs of Bounded Treewidth

We initiate the study of coresets for clustering in graph metrics, i.e., the shortest-path
metric of edge-weighted graphs, which is useful for example for road networks and data
visualization. A coreset is a technique that reduces the data while maintaining a
(1+epsilon)-approximation to the objective, and leads to significantly improved
running time, storage, or communication in various settings.

I will discuss how every graph G of treewidth tw(G) admits a coreset of size
O(tw(G)) for k-Median clustering (omitting dependence on k and epsilon). Moreover,
this coreset can be constructed in near-linear time. We also have a matching lower
bound Omega(tw(G)), which justifies restricting the graph's topology.

Joint work with Vladimir Braverman, Lingxiao Huang, Shaofeng H.-C. Jiang, and Xuan Wu.

6:40 -- 7:00

Nima Anari

Limited Correlations, Fractional Log-concavity, and Fast Mixing Random Walks

The analysis of random walks on high-dimensional expanders has recently
enabled us to answer open questions about sampling/counting in combinatorial
objects like matroids. The key to this connection was showing that matroids
have “spectrally negative” correlations. In this talk, I will show how to go
beyond the setting of matroids and analyze random walks in the presence of
limited positive correlations. I will show how to apply this method to the
hardcore model on bounded-degree graphs and the monomer distribution in
monomer-dimer systems.

Based on joint work with Kuikui Liu and Shayan OveisGharan