Related papers: Formally Certified Approximate Model Counting
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission…
Satisfiability Modulo Counting (SMC) is a recently proposed general language to reason about problems integrating statistical and symbolic Artificial Intelligence. An SMC problem is an extended SAT problem in which the truth values of a few…
Propositional model counting is a fundamental problem in artificial intelligence with a wide variety of applications, such as probabilistic inference, decision making under uncertainty, and probabilistic databases. Consequently, the problem…
One approach to probabilistic inference involves counting the number of models of a given Boolean formula. Here, we are interested in inferences involving higher-order objects, i.e., functions. We study the following task: Given a Boolean…
Artificial Neural Networks (ANNs) are being deployed for an increasing number of safety-critical applications, including autonomous cars and medical diagnosis. However, concerns about their reliability have been raised due to their…
In safety-critical applications that rely on the solution of an optimization problem, the certification of the optimization algorithm is of vital importance. Certification and suboptimality results are available for a wide range of…
We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and…
Quantitative model checkers for Markov Decision Processes typically use finite-precision arithmetic. If all the coefficients in the process are rational numbers, then the model checking results are rational, and so they can be computed…
Integer programming (IP) is an important and challenging problem. Approximate methods have shown promising performance on both effectiveness and efficiency for solving the IP problem. However, we observed that a large fraction of variables…
We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…
Model Predictive Control (MPC) offers rigorous safety and performance guarantees but is computationally intensive. Approximate MPC (AMPC) aims to circumvent this drawback by learning a computationally cheaper surrogate policy. Common…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
We introduce a sampling framework to support approximate computing with estimated error bounds in Spark. Our framework allows sampling to be performed at the beginning of a sequence of multiple transformations ending in an aggregation…
Counterfactual explanations (CFE) are being widely used to explain algorithmic decisions, especially in consequential decision-making contexts (e.g., loan approval or pretrial bail). In this context, CFEs aim to provide individuals affected…
Prior methods for retrieval of nearest neighbors in high dimensions are fast and approximate--providing probabilistic guarantees of returning the correct answer--or slow and exact performing an exhaustive search. We present Certified…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
Verification of higher-order probabilistic programs is a challenging problem. We present a verification method that supports several quantitative properties of higher-order probabilistic programs. Usually, extending verification methods to…
Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…