Related papers: Fast Matrix Multiplication meets the Submodular Wi…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
Matrix multiplication is a fundamental task in almost all computational fields, including machine learning and optimization, computer graphics, signal processing, and graph algorithms (static and dynamic). Twin-width is a natural complexity…
In this paper we propose models of combinatorial algorithms for the Boolean Matrix Multiplication (BMM), and prove lower bounds on computing BMM in these models. First, we give a relatively relaxed combinatorial model which is an extension…
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…
Matrix completion problems arise in many applications including recommendation systems, computer vision, and genomics. Increasingly larger neural networks have been successful in many of these applications, but at considerable computational…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…
In recent years it has become popular to study dynamic problems in a sensitivity setting: Instead of allowing for an arbitrary sequence of updates, the sensitivity model only allows to apply batch updates of small size to the original input…
Statistical query (SQ) algorithms are algorithms that have access to an {\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $\phi:X \rightarrow [-1,1]$, the oracle returns an estimate…
Maximum-likelihood (ML) decoding for arbitrary block codes remains fundamentally hard, with worst-case time complexity-measured by the total number of multiplications-being no better than straightforward exhaustive search, which requires…
Quantum Annealing (QA) can efficiently solve combinatorial optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations. For broader applicability of QA, quadratization…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
Low-bit quantized neural networks are of great interest in practical applications because they significantly reduce the consumption of both memory and computational resources. Binary neural networks are memory and computationally efficient…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
The conjectured hardness of Boolean matrix-vector multiplication has been used with great success to prove conditional lower bounds for numerous important data structure problems, see Henzinger et al. [STOC'15]. In recent work, Larsen and…
Quality diversity~(QD) is a branch of evolutionary computation that gained increasing interest in recent years. The Map-Elites QD approach defines a feature space, i.e., a partition of the search space, and stores the best solution for each…
The Boolean product $R = P \cdot Q$ of two $\{ 0, 1\} \; m \times m \; $ matrices is $$R(j,k) = 1 \; \mathrm{\ IF\ for\ some\ } \; t \; \,P(j, t) = Q(t, k) = 1\; \; \mathrm{ELSE\ } \, R(j, k) = 0. $$ The near-optimal design reduces the…
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…
We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…