Related papers: Exponential Separation between Quantum and Classic…
In this paper, we present several new results on minimizing a nonsmooth and nonconvex function under a Lipschitz condition. Recent work shows that while the classical notion of Clarke stationarity is computationally intractable up to some…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
We exhibit a Boolean function for which the quantum communication complexity is exponentially larger than the classical information complexity. An exponential separation in the other direction was already known from the work of Kerenidis…
Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
In the recent years, researchers proposed a number of successful methods to perform out-of-distribution (OOD) detection in deep neural networks (DNNs). So far the scope of the highly accurate methods has been limited to image level…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
A key component of a quantum machine learning model operating on classical inputs is the design of an embedding circuit mapping inputs to a quantum state. This paper studies a transfer learning setting in which classical-to-quantum…
We demonstrate that the recently developed Optimal Uncertainty Quantification (OUQ) theory, combined with recent software enabling fast global solutions of constrained non-convex optimization problems, provides a methodology for rigorous…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
In this paper, we study the OOD generalization of neural algorithmic reasoning tasks, where the goal is to learn an algorithm (e.g., sorting, breadth-first search, and depth-first search) from input-output pairs using deep neural networks.…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
We prove lower bounds for higher-order methods in smooth non-convex finite-sum optimization. Our contribution is threefold: We first show that a deterministic algorithm cannot profit from the finite-sum structure of the objective, and that…
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…
We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) capability, two properties of fundamental importance to the physics and practical use of quantum many-body systems,…
Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…