We review state-of-the-art formal methods applied to the emerging field of the verification of
machine learning systems. Formal methods can provide rigorous correctness guarantees on …

Given the variety of numerical errors that can occur, floating-point programs are difficult to
write, test and debug. One common practice employed by developers without an advanced …

Rigorous estimation of maximum floating-point round-off errors is an important capability
central to many formal verification tools. Unfortunately, available techniques for this task …

The aggressive optimization of floating-point computations is an important problem in high-
performance computing. Unfortunately, floating-point instruction sets have complicated …

Writing accurate numerical software is hard because of many sources of unavoidable
uncertainties, including finite numerical precision of implementations. We present a …

Programs using floating-point arithmetic are prone to accuracy problems caused by
rounding and catastrophic cancellation. These phenomena provoke bugs that are …

We define several abstract semantics for the static analysis of finite precision computations,
that bound not only the ranges of values taken by numerical variables of a program, but also …

It is well-known that floating-point exceptions can be disastrous and writing exception-free
numerical programs is very difficult. Thus, it is important to automatically detect such errors …

Roundoff errors cannot be avoided when implementing numerical programs with finite
precision. The ability to reason about rounding is especially important if one wants to …

Memory system reliability is a serious and growing concern in modern servers. Existing
chipkill-level memory protection mechanisms suffer from several drawbacks. They activate a …