Related papers: A Test for FLOPs as a Discriminant for Linear Alge…

The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…

Neural networks performance has been significantly improved in the last few years, at the cost of an increasing number of floating point operations per second (FLOPs). However, more FLOPs can be an issue when computational resources are…

In introductory programming courses, it is challenging for instructors to provide debugging feedback on students' incorrect programs. Some recent tools automatically offer program repair feedback by identifying any differences between…

Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…

Many classification problems consider classes that form a hierarchy. Classifiers that are aware of this hierarchy may be able to make confident predictions at a coarse level despite being uncertain at the fine-grained level. While it is…

Selective classifiers improve model reliability by abstaining on inputs the model deems uncertain. However, few practical approaches achieve the gold-standard performance of a perfect-ordering oracle that accepts examples exactly in order…

Basic Linear Algebra Subprograms (BLAS) is a core library in scientific computing and machine learning. This paper presents FT-BLAS, a new implementation of BLAS routines that not only tolerates soft errors on the fly, but also provides…

Solving large-scale Mixed Integer Programs (MIP) can be difficult without advanced algorithms such as decomposition based techniques. Even if a decomposition technique might be appropriate, there are still many possible decompositions for…

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,…

We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…

The ability of large language models (LLMs) to validate their output and identify potential errors is crucial for ensuring robustness and reliability. However, current research indicates that LLMs struggle with self-correction, encountering…

The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…

As machine learning becomes prevalent, mitigating any unfairness present in the training data becomes critical. Among the various notions of fairness, this paper focuses on the well-known individual fairness, which states that similar…

Empirical investigations into unintended model behavior often show that the algorithm is predicting another outcome than what was intended. These exposes highlight the need to identify when algorithms predict unintended quantities - ideally…

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…

Many logic programming languages have delay primitives which allow coroutining. This introduces a class of bug symptoms -- computations can flounder when they are intended to succeed or finitely fail. For concurrent logic programs this is…

We observe a disconnect between the developers and the end users of linear algebra libraries. On the one hand, the numerical linear algebra and the high-performance communities invest significant effort in the development and optimization…

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

Reinforcement learning (RL) approaches for Large Language Models (LLMs) frequently use on-policy algorithms, such as PPO or GRPO. However, policy lag from distributed training architectures and differences between the training and inference…

Precise estimation of downstream performance in large language models (LLMs) prior to training is essential for guiding their development process. Scaling laws analysis utilizes the statistics of a series of significantly smaller sampling…