Related papers: Automatic Verification of Floating-Point Accumulat…
We introduce data structures and algorithms to count numerical inaccuracies arising from usage of floating numbers described in IEEE 754. Here we describe how to estimate precision for some collection of functions most commonly used for…
Test instability in a floating-point program occurs when the control flow of the program diverges from its ideal execution assuming real arithmetic. This phenomenon is caused by the presence of round-off errors that affect the evaluation of…
We present a scheme to automatically set the precision of floating point variables in an application. We design a framework that profiles applications to measure undesirable numerical behavior at the floating point operation level. We use…
In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…
Given a combinatorial decomposition for a counting problem, we resort to the simple scheme of approximating large numbers by floating-point representations in order to obtain efficient Fully Polynomial Time Approximation Schemes (FPTASes)…
Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…
Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning…
This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to…
Automatic passenger counting (APC) in public transport has been introduced in the 1970s and has been rapidly emerging in recent years. APC systems, like all other measurement devices, are susceptible to error, which is treated as random…
In recent years, Deep Neural Networks (DNN) based methods have achieved remarkable performance in a wide range of tasks and have been among the most powerful and widely used techniques in computer vision. However, DNN-based methods are both…
We present the first formal verification of approximation algorithms for NP-complete optimization problems: vertex cover, independent set, set cover, center selection, load balancing, and bin packing. We uncover incompletenesses in existing…
As we reach the limit of Moore's Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate Computing (AC), which relies on the ability of applications to tolerate some error in the results to…
Proper representation of data in graphical visualizations becomes challenging when high accuracy in data types is required, especially in those situations where the difference between double-precision floating-point and single-precision…
Neural networks offer high-accuracy solutions to a range of problems, but are costly to run in production systems because of computational and memory requirements during a forward pass. Given a trained network, we propose a techique called…
The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O(|At(P)|size(P))…
Floating-point program errors can lead to severe consequences, particularly in critical domains such as military applications. Only a small subset of inputs may induce substantial floating-point errors, prompting researchers to develop…
Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…
Automated techniques for rigorous floating-point round-off error analysis are important in areas including formal verification of correctness and precision tuning. Existing tools and techniques, while providing tight bounds, fail to analyze…
Neural network verification aims at providing formal guarantees on the output of trained neural networks, to ensure their robustness against adversarial examples and enable their deployment in safety-critical applications. This paper…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…