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Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers. While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g.,…

Probabilistic circuits (PCs) have gained prominence in recent years as a versatile framework for discussing probabilistic models that support tractable queries and are yet expressive enough to model complex probability distributions.…

Approximate Membership Query structures (AMQs) rely on randomisation for time- and space-efficiency, while introducing a possibility of false positive and false negative answers. Correctness proofs of such structures involve subtle…

We study the enumeration of answers to Unions of Conjunctive Queries (UCQs) with optimal time guarantees. More precisely, we wish to identify the queries that can be solved with linear preprocessing time and constant delay. Despite the…

In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we…

In many real-world scenarios, it is crucial to be able to reliably and efficiently reason under uncertainty while capturing complex relationships in data. Probabilistic circuits (PCs), a prominent family of tractable probabilistic models,…

Designing effective quantum circuits remains a central challenge in quantum computing, as circuit structure strongly influences expressivity, trainability, and hardware feasibility. Current approaches, whether using manually designed…

The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…

Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular…

Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal…

Trajectory prediction models that can infer both finite future trajectories and their associated uncertainties of the target vehicles in an online setting (e.g., real-world application scenarios) is crucial for ensuring the safe and robust…

An uncertain database is defined as a relational database in which primary keys need not be satisfied. A repair (or possible world) of such database is obtained by selecting a maximal number of tuples without ever selecting two distinct…

The past decade has seen a significant interest in learning tractable probabilistic representations. Arithmetic circuits (ACs) were among the first proposed tractable representations, with some subsequent representations being instances of…

Tsetlin Machines (TMs) have emerged as a compelling alternative to conventional deep learning methods, offering notable advantages such as smaller memory footprint, faster inference, fault-tolerant properties, and interpretability. Although…

We present LINQ, the first join protocol with linear complexity (in both running time and communication) under the secure multi-party computation model (MPC). It can also be extended to support all free-connex queries, a large class of…

Consistency-based methods have emerged as an effective approach to uncertainty quantification (UQ) in large language models. These methods typically rely on several generations obtained via multinomial sampling, measuring their agreement…

Bayesian structure learning allows one to capture uncertainty over the causal directed acyclic graph (DAG) responsible for generating given data. In this work, we present Tractable Uncertainty for STructure learning (TRUST), a framework for…

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model once, new probabilistic queries can be answered at test time…

In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…