Related papers: Invariant Inference With Provable Complexity From …
The article "Interpolation and SAT-Based Model Checking" (McMillan, 2003) describes a formal-verification algorithm, which was originally devised to verify safety properties of finite-state transition systems. It derives interpolants from…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
Barrier certificates, a form of state invariants, provide an automated approach to the verification of the safety of dynamical systems. Similarly to barrier certificates, recent works explore the notion of closure certificates, a form of…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…
We present Sequential Neural Variational Inference (SNVI), an approach to perform Bayesian inference in models with intractable likelihoods. SNVI combines likelihood-estimation (or likelihood-ratio-estimation) with variational inference to…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…
We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates…
Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various machine learning applications such as probabilistic modeling,…
Inductive logic programming (ILP) has been a deeply influential paradigm in AI, enjoying decades of research on its theory and implementations. As a natural descendent of the fields of logic programming and machine learning, it admits the…
We introduce a simple yet powerful invariant relation connecting four successive terms of a class of exponentially decaying alternating functions. Specifically, for the sequence defined by f(n) = ((1/2)^n + (-1)^n) / n, we prove that the…
How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the problem is in general undecidable, the goal is settled for…