Related papers: Abstract Interpretation with Infinitesimals: Towar…
Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…
We propose a framework to analyze stability for a class of linear non-autonomous hybrid systems, where the continuous evolution of solutions is governed by an ordinary differential equation and the instantaneous changes are governed by a…
Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to…
Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…
We give thread-modular non-relational value analyses as abstractions of a local trace semantics. The semantics as well as the analyses are formulated by means of global invariants and side-effecting constraint systems. We show that a…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
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…
Finite abstractions (a.k.a. symbolic models) offer an effective scheme for approximating the complex continuous-space systems with simpler models in the discrete-space domain. A crucial aspect, however, is to establish a formal relation…
It was previously shown that control-flow refinement can be achieved by a program specializer incorporating property-based abstraction, to improve termination and complexity analysis tools. We now show that this purpose-built specializer…
Abstract interpretation techniques can be made more precise by distinguishing paths inside loops, at the expense of possibly exponential complexity. SMT-solving techniques and sparse representations of paths and sets of paths avoid this…
Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
Despite many advances that enable the application of model checking techniques to the verification of large systems, the state-explosion problem remains the main challenge for scalability. Compositional verification addresses this challenge…
The objective of this proposal is to bridge the gap between Deep Learning (DL) and System Dynamics (SD) by developing an interpretable neural system dynamics framework. While DL excels at learning complex models and making accurate…
In [ABM07], Abdulla et al. introduced the concept of decisiveness, an interesting tool for lifting good properties of finite Markov chains to denumerable ones. Later, this concept was extended to more general stochastic transition systems…
We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality,…
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…
The strength of a dynamic language is also its weakness: run-time flexibility comes at the cost of compile-time predictability. Many of the hallmarks of dynamic languages such as closures, continuations, various forms of reflection, and a…
Abstract interpretation offers a powerful toolset for static analysis, tackling precision, complexity and state-explosion issues. In the literature, state partitioning abstractions based on (bi)simulation and property-preserving state…
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…