Related papers: Learning the Boundary of Inductive Invariants

Often in language and other areas of cognition, whether two components of an object are identical or not determines if it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…

The problem of finding boundary conditions for fastening of a ring membrane, which are inaccessible for direct observation from the natural frequencies of its flexural oscillations, is considered. Two theorems on the uniqueness of this…

Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and ARMA time series have been…

In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance…

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…

The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…

In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters,…

Automatic verification of concurrent programs faces state explosion due to the exponential possible interleavings of its sequential components coupled with large or infinite state spaces. An alternative is deductive verification, where…

When function approximation is deployed in reinforcement learning (RL), the same problem may be formulated in different ways, often by treating a pre-processing step as a part of the environment or as part of the agent. As a consequence,…

The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…

We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm…

We introduce some notions of invariant elementary definability which extend the notions of first-order order-invariant definability, and, more generally, definability invariant with respect to arbitrary numerical relations. In particular,…

This paper investigates reinforcement learning with constraints, which are indispensable in safety-critical environments. To drive the constraint violation monotonically decrease, we take the constraints as Lyapunov functions and impose new…

Precondition inference is a non-trivial problem with important applications in program analysis and verification. We present a novel iterative method for automatically deriving preconditions for the safety and unsafety of programs. Each…

This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…

Learning meaningful representations that maintain the content necessary for a particular task while filtering away detrimental variations is a problem of great interest in machine learning. In this paper, we tackle the problem of learning…

We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…

In this contribution, we show how to incorporate prior knowledge to a deep neural network architecture in a principled manner. We enforce feature space invariances using a novel layer based on invariant integration. This allows us to…

3D anomaly detection (AD) is prominent but difficult due to lacking a unified theoretical foundation for preprocessing design. We establish the Fence Theorem, formalizing preprocessing as a dual-objective semantic isolator: (1) mitigating…

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…