Related papers: XiSort: Deterministic Sorting via IEEE-754 Total O…
While Transformers have achieved remarkable success in LLMs through superior scalability, their application in industrial-scale ranking models remains nascent, hindered by the challenges of high feature sparsity and low label density. In…
Sorting is one of the oldest computing problems and is still very important in the age of big data. Various algorithms and implementation techniques have been proposed. In this study, we focus on comparison based, internal sorting…
Current methods which compress multisets at an optimal rate have computational complexity that scales linearly with alphabet size, making them too slow to be practical in many real-world settings. We show how to convert a compression…
Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…
We present a scalable algorithm for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our quantum…
We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…
Posit arithmetic has emerged as a promising alternative to IEEE 754 floating-point representation, offering enhanced accuracy and dynamic range. However, division operations in posit systems remain challenging due to their inherent hardware…
Many scientific codes and instruments generate large amounts of floating-point data at high rates that must be compressed before they can be stored. Typically, only lossy compression algorithms deliver high-enough compression ratios.…
This paper introduces a new comparison base stable sorting algorithm, named RS sort. RS Sort involves only the comparison of pair of elements in an array which ultimately sorts the array and does not involve the comparison of each element…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…
Sorting is a fundamental operation in computer systems and is widely used in applications such as databases, data analytics, and hardware accelerators. Unary computing has recently emerged as a low-cost and power-efficient paradigm for…
We investigate array separation logic (ASL), a variant of symbolic-heap separation logic in which the data structures are either pointers or arrays, i.e., contiguous blocks of allocated memory. This logic provides a language for…
The increasing complexity of autonomous systems has driven a shift to integrated heterogeneous SoCs with real-time and safety demands. Ensuring deterministic WCETs and low-latency for critical tasks requires minimizing interference on…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…
At the core of any inference procedure in deep neural networks are dot product operations, which are the component that require the highest computational resources. A common approach to reduce the cost of inference is to reduce its memory…
Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
Sensor-based sorting systems enable the physical separation of a material stream into two fractions. The sorting decision is based on the image data evaluation of the sensors used and is carried out using actuators. Various process…
Much of the copious literature on the subject of sorting has concentrated on minimizing the number of comparisons and/or exchanges/copies. However, a more appropriate yardstick for the performance of sorting algorithms is based on the total…