Related papers: Invariant Inference With Provable Complexity From …
Deep neural networks are applied in more and more areas of everyday life. However, they still lack essential abilities, such as robustly dealing with spatially transformed input signals. Approaches to mitigate this severe robustness issue…
We propose a data-driven algorithm for numerical invariant synthesis and verification. The algorithm is based on the ICE-DT schema for learning decision trees from samples of positive and negative states and implications corresponding to…
Neural ODEs are increasingly used as continuous-time models for scientific and sensor data, but unconstrained neural ODEs can drift and violate domain invariants (e.g., conservation laws), yielding physically implausible solutions. In turn,…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
The bootstrap is a versatile inference method that has proven powerful in many statistical problems. However, when applied to modern large-scale models, it could face substantial computation demand from repeated data resampling and model…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
We show that computing the strongest polynomial invariant for single-path loops with polynomial assignments is at least as hard as the Skolem problem, a famous problem whose decidability has been open for almost a century. While the…
We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing…
We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the…
Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…
Discrete choice models are fundamental tools in management science, economics, and marketing for understanding and predicting decision-making. Logit-based models are dominant in applied work, largely due to their convenient closed-form…
The invariant polytope algorithm was a breakthrough in the joint spectral radius computation, allowing to find the exact value of the joint spectral radius for most matrix families~\cite{GP2013,GP2016}. This algorithm found many…
Property Directed Reachability (PDR) is a widely used technique for formal verification of hardware and software systems. This paper presents an incremental version of PDR (IPDR), which enables the automatic verification of system instances…
The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…
We describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize inductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large…
In recent years, there has been a growing interest in statistical methods that exhibit robust performance under distribution changes between training and test data. While most of the related research focuses on point predictions with the…
Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…
Inverse reinforcement learning is the problem of inferring a reward function from an optimal policy or demonstrations by an expert. In this work, it is assumed that the reward is expressed as a reward machine whose transitions depend on…
This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…
We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and…