Related papers: Smoothing Structured Decomposable Circuits
Towards better understanding of gate elimination, the only method known that can prove complexity lower bounds for explicit functions against unrestricted Boolean circuits, this work contributes: (1) formalizing circuit simplifications as a…
Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…
We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting…
In this exploration paper, we design algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete sphere. Such a contraction is a kind of shrinking or reducing process. In our algorithms, we need to…
A quantum circuit may be strongly classically simulated with the aid of ZX-calculus by decomposing its $t$ T-gates into a sum of $2^{\alpha t}$ classically computable stabiliser terms. In this paper, we introduce a general procedure to find…
The goal of a denoising algorithm is to reconstruct a signal from its noise-corrupted observations. Perfect reconstruction is seldom possible and performance is measured under a given fidelity criterion. In a recent work, the authors…
Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
Due to the unreliability and limited capacity of existing quantum computer prototypes, quantum circuit simulation continues to be a vital tool for validating next generation quantum computers and for studying variational quantum algorithms,…
Sparse decomposition has been widely used for different applications, such as source separation, image classification and image denoising. This paper presents a new algorithm for segmentation of an image into background and foreground text…
We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…
During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as points-set or triangulated mesh). The noise-removal…
In this work, we present an efficient way to decouple the multicontinuum problems. To construct decoupled schemes, we propose Implicit-Explicit time approximation in general form and study them for the fine-scale and coarse-scale space…
In this paper, we consider the following graph partitioning problem: The input is an undirected graph $G=(V,E),$ a balance parameter $b \in (0,1/2]$ and a target conductance value $\gamma \in (0,1).$ The output is a cut which, if non-empty,…
Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…