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This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…

We consider the famous Strassen algorithm for fast multiplication of matrices. We show that this algorithm has a nontrivial finite group of automorphisms of order 36 (namely the direct product of two copies of the symmetric group on 3…

High dimensional integration is essential to many areas of science, ranging from particle physics to Bayesian inference. Approximating these integrals is hard, due in part to the difficulty of locating and sampling from regions of the…

Automatically constructing taxonomy finds many applications in e-commerce and web search. One critical challenge is as data and business scope grow in real applications, new concepts are emerging and needed to be added to the existing…

Data augmentation is a powerful technique to enhance the performance of a deep learning task but has received less attention in 3D deep learning. It is well known that when 3D shapes are sparsely represented with low point density, the…

Medical image data are often limited due to the expensive acquisition and annotation process. Hence, training a deep-learning model with only raw data can easily lead to overfitting. One solution to this problem is to augment the raw data…

Deep hedging uses recurrent neural networks to hedge financial products that cannot be fully hedged in incomplete markets. Previous work in this area focuses on minimizing some measure of quadratic hedging error by calculating pathwise…

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…

We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the rank of the tensor decomposition suggests. In particular for…

While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…

Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance…

Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we…

The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…

We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a…

The main contribution of this paper is a new improved variant of the laser method for designing matrix multiplication algorithms. Building upon the recent techniques of [Duan, Wu, Zhou, FOCS 2023], the new method introduces several new…

We present a new improvement on the laser method for designing fast matrix multiplication algorithms. The new method further develops the recent advances by [Duan, Wu, Zhou FOCS 2023] and [Vassilevska Williams, Xu, Xu, Zhou SODA 2024].…

Recently Dutta and Bhattacharya (2013) introduced a novel Markov Chain Monte Carlo methodology that can simultaneously update all the components of high dimensional parameters using simple deterministic transformations of a one-dimensional…

We present a new method to bound the cardinality of triple product sets in groups and give three applications. A new and unexpectedly short proof of the Plunnecke-Ruzsa sumset inequalities for Abelian groups. A new proof of a theorem of Tao…

Utilizing the notion of property (T) we construct new examples of quantum group norms on the polynomial algebra of a compact quantum group, and provide criteria ensuring that these are not equal to neither the minimal nor the maximal norm.…

A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related…