Related papers: Synthesizing Backward Error Bounds, Backward
A stochastic Forward-Backward algorithm with a constant step is studied. At each time step, this algorithm involves an independent copy of a couple of random maximal monotone operators. Defining a mean operator as a selection integral, the…
Automatic software generation based on some specification is known as program synthesis. Most existing approaches formulate program synthesis as a search problem with discrete parameters. In this paper, we present a novel formulation of…
The notion of refinement plays an important role in software engineering. It is the basis of a stepwise development methodology in which the correctness of a system can be established by proving, or computing, that a system refines its…
Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing…
As the complexity of software systems rises, methods for explaining their behaviour are becoming ever-more important. When a system fails, it is critical to determine which of its components are responsible for this failure. Within the…
We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method…
We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{argument stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which…
We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
Integration of Ordinary Differential Equations (ODEs) using Backward Difference formula (BDF) methods with p backward steps achieves order p accuracy if specific conditions are met. This work extends the composition technique with complex…
Recursive self-modification is increasingly central in AutoML, neural architecture search, and adaptive optimization, yet no existing framework ensures that such changes are made safely. Godel machines offer a principled safeguard by…
The goal of program synthesis is to automatically generate programs in a particular language from corresponding specifications, e.g. input-output behavior. Many current approaches achieve impressive results after training on randomly…
We present a new framework and associated synthesis algorithms for program synthesis over noisy data, i.e., data that may contain incorrect/corrupted input-output examples. This framework is based on an extension of finite tree automata…
Several recent papers have introduced a periodic verification mechanism to detect silent errors in iterative solvers. Chen [PPoPP'13, pp. 167--176] has shown how to combine such a verification mechanism (a stability test checking the…
To implement important quality attributes of software such as architectural security tactics, developers incorporate API of software frameworks, as building blocks, to avoid re-inventing the wheel and improve their productivity. However,…
The Forward-Forward algorithm has evolved in machine learning research, tackling more complex tasks that mimic real-life applications. In the last years, it has been improved by several techniques to perform better than its original…
Program synthesis has seen many new applications in recent years, in large part thanks to the introduction of SyGuS. However, no existing SyGuS solvers have support for synthesizing recursive functions. We introduce an multi-phase algorithm…
Forward stagewise regression follows a very simple strategy for constructing a sequence of sparse regression estimates: it starts with all coefficients equal to zero, and iteratively updates the coefficient (by a small amount $\epsilon$) of…
Traditional code instruction data synthesis methods suffer from limited diversity and poor logic. We introduce Infinite-Instruct, an automated framework for synthesizing high-quality question-answer pairs, designed to enhance the code…
The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem.…