Related papers: Correctness Kernels of Abstract Interpretations
We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced…
The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification…
We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using…
Most methods for neural network verification focus on bounding the image, i.e., set of outputs for a given input set. This can be used to, for example, check the robustness of neural network predictions to bounded perturbations of an input.…
A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…
The Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it difficult to solve using pure machine…
This article presents a new numerical abstract domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on Difference-Bound Matrices and allows us to represent invariants of the form…
Systems of fixpoint equations over complete lattices, consisting of (mixed) least and greatest fixpoint equations, allow one to express a number of verification tasks such as model-checking of various kinds of specification logics or the…
Neural networks are hypothesized to implement interpretable causal mechanisms, yet verifying this requires finding a causal abstraction -- a simpler, high-level Structural Causal Model (SCM) faithful to the network under interventions.…
This paper presents an abstraction-refinement method to synthesize control inputs for a discrete-time piecewise linear system. The controlled system behavior satisfies a finite-word linear-time temporal objective while incurring minimal…
In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the…
Abstraction (in its various forms) is a powerful established technique in model-checking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an…
While abstraction is a classic tool of verification to scale it up, it is not used very often for verifying neural networks. However, it can help with the still open task of scaling existing algorithms to state-of-the-art network…
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…
We explore denotational interpreters: denotational semantics that produce coinductive traces of a corresponding small-step operational semantics. By parameterising our denotational interpreter over the semantic domain and then varying it,…
Abstract Meaning Representation (AMR) parsing aims to extract an abstract semantic graph from a given sentence. The sequence-to-sequence approaches, which linearize the semantic graph into a sequence of nodes and edges and generate the…
Do large language models (LLMs) genuinely understand abstract concepts, or merely manipulate them as statistical patterns? We introduce an abstraction-grounding framework that decomposes conceptual understanding into three capacities:…
Concept bottleneck models (CBMs) have emerged as critical tools in domains where interpretability is paramount. These models rely on predefined textual descriptions, referred to as concepts, to inform their decision-making process and offer…
Neural abstractions have been recently introduced as formal approximations of complex, nonlinear dynamical models. They comprise a neural ODE and a certified upper bound on the error between the abstract neural network and the concrete…
Kernel-phase is a data analysis method based on a generalization of the notion of closure-phase invented in the context of interferometry, but that applies to well corrected diffraction dominated images produced by an arbitrary aperture.…