arXiv subjects

Hans-Werner Wiesbrock

Publications and source records attributed to Hans-Werner Wiesbrock.

5 recordsLinked to original sources

arXiv2026

Probabilistic Modelling of Operational Design Domains, A New Approach for Testing AI Systems

The conventional testing process quickly fails when applied to ML-based systems such as obstacle detection in vehicles: if an obstacle is not detected in a test, classical bug fixing is impossible and an AI system will always retain shortcomings. Test results can therefore only be interpreted statistically, which in turn requires test sets that are not only complete with respect to the operational design domain (ODD) of the system, but also representative of it. To this end, we introduce probabilistically extended ontologies (PEONs): ontologies describing the ODD, augmented with a probability distribution over the partitioning they induce. Instead of unmaintainable conditional probability tables, only marginal distributions and functionally described dependencies need to be specified; algorithms based on couplings and optimal transport complete this specification to a Bayesian network. From a PEON we derive the sampling of representative test cases, rigorous end-of-test criteria for given quality targets and significance levels, and methods for re-evaluating existing test results and for assessing the balance of training data. We demonstrate the practical modelling of a complex ODD using the example of automatic train operation.

cs.LG↗

arXiv2024

Outline of an Independent Systematic Blackbox Test for ML-based Systems

This article proposes a test procedure that can be used to test ML models and ML-based systems independently of the actual training process. In this way, the typical quality statements such as accuracy and precision of these models and system can be verified independently, taking into account their black box character and the immanent stochastic properties of ML models and their training data. The article presents first results from a set of test experiments and suggest extensions to existing test methods reflecting the stochastic nature of ML models and ML-based systems.

cs.LG↗

arXiv1998

Weak Hopf Algebras and Reducible Jones Inclusions of Depth 2. I: From Crossed products to Jones towers

We apply the theory of finite dimensional weak C^*-Hopf algebras A as developed by G. Böhm, F. Nill and K. Szlachányi to study reducible inclusion triples of von-Neumann algebras N \subset M \subset (M\cros\A). Here M is an A-module algebra, N is the fixed point algebra and \M\cros\A is the crossed product extension. ``Weak'' means that the coproduct Δon A is non-unital, requiring various modifications of the standard definitions for (co-)actions and crossed products. We show that acting with normalized positive and nondegenerate left integrals l\in\A gives rise to faithful conditional expectations E_l: M-->N, where under certain regularity conditions this correspondence is one-to-one. Associated with such left integrals we construct ``Jones projections'' e_l\in\A obeying the Jones relations as an identity in M\cros\A. Finally, we prove that N\subset M always has finite index and depth 2 and that the basic Jones construction is given by the ideal M_1:=M e_l M \subset M\cros\A, where under appropriate conditions M_1 = M\cros\A. In a subsequent paper we will show that converseley any reducible finite index and depth-2 Jones tower of von-Neumann factors (with finite dimensional centers) arises in this way.

math.QA↗

arXiv1997

Extensions of Conformal Nets and Superselection Structures

Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Moebius group. We infer from this that every conformal net is normal and conormal, namely the local von Neumann algebra associated with an interval coincides with its double relative commutant inside the local von Neumann algebra associated with any larger interval. The net and the dual net give together rise to an infinite dimensional symmetry group, of which we study a class of positive energy irreducible representations. We mention how superselsection sectors extend to the dual net and we illustrate by examples how, in general, this process generates solitonic sectors. We describe the free theories associated with the lowest weight n representations of PSL(2,R), showing that they violate 3-regularity for n>2. When n>1, we obtain examples of non Moebius-covariant sectors of a 3-regular (non 4-regular) net.

hep-th↗

arXiv1994

A Comment on Jones Inclusions with infinite Index

Given an irreducible inclusion of infinite von-Neumann-algebras $\cn \subset \cm$ together with a conditional expectation $ E : \cm \rightarrow \cm $ such that the inclusion has depth 2, we show quite explicitely how $\cn $ can be viewed as the fixed point algebra of $\cm$ w.r.t. an outer action of a compact Kac-algebra acting on $\cm$. This gives an alternative proof, under this special setting of a more general result of M. Enock and R. Nest, [E-N], see also S. Yamagami, [Ya2].

hep-th↗