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Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
Formula-based debugging techniques are becoming increasingly popular, as they provide a principled way to identify potentially faulty statements together with information that can help fix such statements. Although effective, these…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
Recent renewed interest in optimizing and analyzing floating-point programs has lead to a diverse array of new tools for numerical programs. These tools are often complementary, each focusing on a distinct aspect of numerical programming.…
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…
Numerical exceptions, which may be caused by overflow, operations like division by 0 or sqrt(-1), or convergence failures, are unavoidable in many cases, in particular when software is used on unforeseen and difficult inputs. As more…
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…
In recent years, half precision floating-point arithmetic has gained wide support in hardware and software stack thanks to the advance of artificial intelligence and machine learning applications. Operating at half precision can…
Statically reasoning in the presence of and about exceptions is challenging: exceptions worsen the well-known mutual recursion between data-flow and control-flow analysis. The recent development of pushdown control-flow analysis for the…
We analyze stochastic conditional gradient methods for constrained optimization problems arising in over-parametrized machine learning. We show that one could leverage the interpolation-like conditions satisfied by such models to obtain…
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
This paper studies a bandit optimization problem where the goal is to maximize a function $f(x)$ over $T$ periods for some unknown strongly concave function $f$. We consider a new pairwise comparison oracle, where the decision-maker chooses…
Floating-point computations are quickly finding their way in the design of safety- and mission-critical systems, despite the fact that designing floating-point algorithms is significantly more difficult than designing integer algorithms.…
When studying the dynamics of incompressible fluids in bounded domains the only available data often provide average flow rate conditions on portions of the domain's boundary. In engineering applications a common practice to complete these…
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…
In recent years, Large Language Models such as GPT-3 showed remarkable capabilities in performing NLP tasks in the zero and few shot settings. On the other hand, the experiments highlighted the difficulty of GPT-3 in carrying out tasks that…
Several recent works address the impact of inexact oracles in the convergence analysis of modern first-order optimization techniques, e.g. Bregman Proximal Gradient and Prox-Linear methods as well as their accelerated variants, extending…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…