Related papers: Learning the Boundary of Inductive Invariants

Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…

While reinforcement learning algorithms provide automated acquisition of optimal policies, practical application of such methods requires a number of design decisions, such as manually designing reward functions that not only define the…

The manifold hypothesis (real world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high dimensional problems that are common in domains such as…

We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree…

Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…

The performance of machine learning models can be impacted by changes in data over time. A promising approach to address this challenge is invariant learning, with a particular focus on a method known as invariant risk minimization (IRM).…

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference…

We present a systematic method for exactly enforcing Dirichlet, Neumann, and Robin type conditions on general quadrilateral domains with arbitrary curved boundaries. Our method is built upon exact mappings between general quadrilateral…

Let $Z \subseteq \proj{n}$ be a fat points scheme, and let $d(Z)$ be the minimum distance of the linear code constructed from $Z$. We show that $d(Z)$ imposes constraints (i.e., upper bounds) on some specific shifts in the graded minimal…

This paper focuses on finding reinforcement learning policies for control systems with hard state and action constraints. Despite its success in many domains, reinforcement learning is challenging to apply to problems with hard constraints,…

We propose a novel way to incorporate expert knowledge into the training of deep neural networks. Many approaches encode domain constraints directly into the network architecture, requiring non-trivial or domain-specific engineering. In…

It is well known that complete prior ignorance is not compatible with learning, at least in a coherent theory of (epistemic) uncertainty. What is less widely known, is that there is a state similar to full ignorance, that Walley calls…

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background…

An artificial intelligence (AI) model can be viewed as a function that maps inputs to outputs in high-dimensional spaces. Once designed and well trained, the AI model is applied for inference. However, even optimized AI models can produce…

In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural…

Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits…

Traditional reinforcement learning agents learn from experience, past or present, gained through interaction with their environment. Our approach synthesizes experience, without requiring an agent to interact with their environment, by…

We design learning algorithms for synthesizing invariants using Horn implication counterexamples (Horn-ICE), extending the ICE-learning model. In particular, we describe a decision-tree learning algorithm that learns from Horn-ICE samples,…

We study the reachability problem for one-counter automata in which transitions can carry disequality tests. A disequality test is a guard that prohibits a specified counter value. This reachability problem has been known to be NP-hard and…