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Algorithm evaluation and comparison are fundamental questions in machine learning and statistics -- how well does an algorithm perform at a given modeling task, and which algorithm performs best? Many methods have been developed to assess…
Context: Differential testing is a useful approach that uses different implementations of the same algorithms and compares the results for software testing. In recent years, this approach was successfully used for test campaigns of deep…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
Fair algorithm evaluation is conditioned on the existence of high-quality benchmark datasets that are non-redundant and are representative of typical optimization scenarios. In this paper, we evaluate three heuristics for selecting diverse…
Neural algorithmic reasoners are parallel processors. Teaching them sequential algorithms contradicts this nature, rendering a significant share of their computations redundant. Parallel algorithms however may exploit their full…
Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most…
Incorporating geometric invariance into neural networks enhances parameter efficiency but typically increases computational costs. This paper introduces new equivariant neural networks that preserve symmetry while maintaining a comparable…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
The ability of machine learning (ML) classification models to resist small, targeted input perturbations -- known as adversarial attacks -- is a key measure of their safety and reliability. We show that floating-point non-associativity…
In a typical Internet-of-Things setting that involves scientific applications, a target computation can be evaluated in many different ways depending on the split of computations among various devices. On the one hand, different…
Algorithms operating on real numbers are implemented as floating-point computations in practice, but floating-point operations introduce roundoff errors that can degrade the accuracy of the result. We propose $\Lambda_{num}$, a functional…
Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one-…
Reliable numerical computations are central to scientific computing, but the floating-point arithmetic that enables large-scale models is error-prone. Numeric exceptions are a common occurrence and can propagate through code, leading to…
With distributed computing and mobile applications, synchronizing diverging replicas of data structures is a more and more common problem. We use algebraic methods to reason about filesystem operations, and introduce a simplified definition…
Performance prediction, the task of estimating a system's performance without performing experiments, allows us to reduce the experimental burden caused by the combinatorial explosion of different datasets, languages, tasks, and models. In…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
We review strategies for differentiating matrix-based computations, and derive symbolic and algorithmic update rules for differentiating expressions containing the Cholesky decomposition. We recommend new `blocked' algorithms, based on…
Evaluating the programming robustness of large language models (LLMs) is paramount for ensuring their reliability in AI-based software development. However, adversarial attacks exhibit fundamental limitations that compromise fair robustness…
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…