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We provide new tools for worst-case performance analysis of the gradient (or steepest descent) method of Cauchy for smooth strongly convex functions, and Newton's method for self-concordant functions, including the case of inexact search…

We present a mathematical model: dynamical systems over finite sets (DSF), and we show that Boolean and discrete genetic models are special cases of DFS. In this paper, we prove that a function defined over finite sets with different number…

Dependency quantified Boolean formulas (DQBF) is a logic admitting existential quantification over Boolean functions, which allows us to elegantly state synthesis problems in verification such as the search for invariants, programs, or…

Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC,…

In this work, we are concerned with the worst case complexity analysis of "a posteriori" methods for unconstrained multi-objective optimization problems where objective function values can only be obtained by querying a black box. We…

Real-world data in health, economics, and environmental sciences are often collected across heterogeneous domains (such as hospitals, regions, or time periods). In such settings, distributional shifts can make standard PCA unreliable, in…

In this article we treat a notion of continuity for a multi-valued function F and we compute the descriptive set-theoretic complexity of the set of all x for which F is continuous at x. We give conditions under which the latter set is…

Interpretable deep learning is a fundamental building block towards safer AI, especially when the deployment possibilities of deep learning-based computer-aided medical diagnostic systems are so eminent. However, without a computational…

Abstraction is a commonly used process to represent some low-level system by a more coarse specification with the goal to omit unnecessary details while preserving important aspects. While recent work on abstraction in the situation…

We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal…

We consider the problem of synthesizing provably non-overflowing integer arithmetic expressions or Boolean relations among integer arithmetic expressions. First we use a numerical abstract domain to infer numerical properties among program…

We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…

The reliability of Neural Networks has gained significant attention, prompting efforts to develop SW-based hardening techniques for safety-critical scenarios. However, evaluating hardening techniques using application-level fault injection…

A degree-$d$ polynomial $p$ in $n$ variables over a field $\F$ is {\em equidistributed} if it takes on each of its $|\F|$ values close to equally often, and {\em biased} otherwise. We say that $p$ has a {\em low rank} if it can be expressed…

Some aspects of the result of applying unit resolution on a CNF formula can be formalized as functions with domain a set of partial truth assignments. We are interested in two ways for computing such functions, depending on whether the…

We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…

Counterfactual Explanations are becoming a de-facto standard in post-hoc interpretable machine learning. For a given classifier and an instance classified in an undesired class, its counterfactual explanation corresponds to small…

A polymorphic analysis is an analysis whose input and output contain parameters which serve as placeholders for information that is unknown before analysis but provided after analysis. In this paper, we present a polymorphic groundness…

Many of the successes of machine learning are based on minimizing an averaged loss function. However, it is well-known that this paradigm suffers from robustness issues that hinder its applicability in safety-critical domains. These issues…

Minimum Bayes risk (MBR) decoding is a decision rule of text generation, which selects the hypothesis that maximizes the expected utility and robustly generates higher-quality texts than maximum a posteriori (MAP) decoding. However, it…