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University of Innsbruck

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Research library189linked papers
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Selected work

Representative Papers

Absolute continuity, supports and idempotent splitting in categorical probability

Aug 01, 2023arXiv.org

This paper addresses the categorical decomposition of probabilistic structures in Markov categories, establishing a rigorous categorical foundation for absolute continuity, support sets, and idempotent splittings. Methodologically, it introduces, for the first time, an idempotent splitting theorem for measurable Markov kernels within the category of standard Borel spaces, and distills a general splitting criterion applicable to arbitrary Markov categories. The main contributions are: (1) a precise internal categorical definition of support sets; (2) a proof that every idempotent measurable Markov kernel between standard Borel spaces admits a splitting; and (3) a rigorous, broadly applicable theoretical framework for structural decomposition of probabilistic models, categorical modeling of stochastic processes, and abstract Bayesian inference.

6 citations3 influentialRead paper

First Experiments with Neural cvc5

Jan 16, 2025Logic Programming and Automated Reasoning

Quantifier instantiation in first-order logic (including theories) remains inefficient in state-of-the-art SMT solvers. Method: This work integrates a lightweight, CPU-native graph neural network (GNN) into the industrial-strength SMT solver cvc5, enabling real-time, neural-guided scoring of instantiation candidates. Training data is automatically generated from proof traces via e-matching; the GNN is optimized for CPU inference; and an online scoring and scheduling framework is deeply embedded within cvc5—requiring no GPU acceleration. Contribution/Results: On unseen benchmarks, our approach significantly reduces average solving time and substantially improves proof success rates. To the best of our knowledge, this is the first end-to-end neural-guided quantifier instantiation deployed in a production-grade SMT solver. It empirically validates the feasibility and practicality of learning-augmented symbolic reasoning.

3 citationsRead paper

Learning control variables and instruments for causal analysis in observational data

Jul 05, 2024

Estimating causal effects from observational data requires selecting appropriate control and instrumental variables that satisfy causal identification conditions—a challenging task often reliant on strong domain knowledge or ad hoc assumptions. Method: This paper proposes the first end-to-end joint learning framework that automatically identifies valid combinations of control and instrumental variables. Grounded in conditional independence testing, the method integrates nonparametric dependence measures with structural search optimization, ensuring statistical consistency in variable selection under mild regularity conditions. Contribution/Results: Unlike conventional approaches requiring prespecified variable sets or strong prior assumptions, our framework is fully data-driven. In simulations, it achieves significantly higher variable identification accuracy. Empirically, applied to the Job Corps study, its estimated treatment effect closely aligns with results from the randomized controlled trial—demonstrating both validity and robustness in real-world causal inference.

1 citationsRead paper
Recent publications

Latest Papers

A New Algebraic Algorithm for LWE

Aug 30, 2026

本文提出了一种新的代数算法来解决Search-LWE问题，结合了线性代数技术和基于S-多项式的Groebner基计算方法，复杂度分析直接且优于先前结果。

0 citationsRead paper