Related papers: Monotonicity of Multi-Term Floating-Point Adders

Combinatorial mixed valuations associated to translation-invariant valuations on polytopes are introduced. In contrast to the construction of mixed valuations via polarization, combinatorial mixed valuations reflect and often inherit…

This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…

The use of aggregates in recursion enables efficient and scalable support for a wide range of BigData algorithms, including those used in graph applications, KDD applications, and ML applications, which have proven difficult to be expressed…

Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…

In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are…

In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz generalized symmetric matrix factorization model that unifies a broad class of matrix factorization formulations arising in machine learning, image science, engineering, and…

The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been…

Transformers have significantly advanced AI and machine learning through their powerful attention mechanism. However, computing attention on long sequences can become a computational bottleneck. FlashAttention mitigates this by fusing the…

We provide an optimization-based argument for the monotonicity of the multiplicative algorithm (MA) for a class of optimal experimental design problems considered in Yu (2010). Our proof avoids introducing auxiliary variables (or problems)…

In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…

Let $A$ be a set of finite integers, define $$A+A \ = \ \{a_1+a_2: a_1,a_2 \in A\}, \ \ \ A-A \ = \ \{a_1-a_2: a_1,a_2 \in A\},$$ and for non-negative integers $s$ and $d$ define $$sA-dA\ =\ \underbrace{A+\cdots+A}_{s}…

Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…

We extend our recent results on ordinary su(N) tensor product multiplicities to higher su(N) tensor products. Particular emphasis is put on four-point couplings where the tensor product of four highest weight modules is considered. The…

This paper introduces the multiplicative variant of the recently proposed asynchronous additive coarse-space correction method. Definition of an asynchronous extension of multiplicative correction is not straightforward, however, our…

Training Deep Neural Networks (DNNs) can be computationally demanding, particularly when dealing with large models. Recent work has aimed to mitigate this computational challenge by introducing 8-bit floating-point (FP8) formats for…

Monotonicity constraints are powerful regularizers in statistical modelling. They can support fairness in computer-aided decision making and increase plausibility in data-driven scientific models. The seminal min-max (MM) neural network…

In this paper, we study a fundamental problem in submodular optimization, which is called sequential submodular maximization. Specifically, we aim to select and rank a group of $k$ items from a ground set $V$ such that the weighted…

A robust summarization system should be able to capture the gist of the document, regardless of the specific word choices or noise in the input. In this work, we first explore the summarization models' robustness against perturbations…

A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with…

We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited…