Eike Stadtländer

Sebastian Müller, Vanessa Toborek, Eike Stadtländer et al.

Explainable AI (XAI) offers a growing number of algorithms that aim to answer specific questions about black-box models. What is missing is a principled way to consolidate explanatory information about a fixed black-box model into a persistent, auditable artefact, that accompanies the black-box throughout its life cycle. We address this gap by introducing the notion of a scientific theory of a black (SToBB). Grounded in Constructive Empiricism, a SToBB fulfils three obligations: (i) empirical adequacy with respect to all available observations of black-box behaviour, (ii) adaptability via explicit update commitments that restore adequacy when new observations arrive, and (iii) auditability through transparent documentation of assumptions, construction choices, and update behaviour. We operationalise these obligations as a general framework that specifies an extensible observation base, a traceable hypothesis class, algorithmic components for construction and revision, and documentation sufficient for third-party assessment. Explanations for concrete stakeholder needs are then obtained by querying the maintained record through interfaces, rather than by producing isolated method outputs. As a proof of concept, we instantiate a complete SToBB for a neural-network classifier on a tabular task and introduce the Constructive Box Theoriser (CoBoT) algorithm, an online procedure that constructs and maintains an empirically adequate rule-based surrogate as observations accumulate. Together, these contributions position SToBBs as a life cycle-scale, inspectable point of reference that supports consistent, reusable analyses and systematic external scrutiny.

Eike Stadtländer, Tamás Horváth, Stefan Wrobel

One of the central problems studied in the theory of machine learning is the question of whether, for a given class of hypotheses, it is possible to efficiently find a {consistent} hypothesis, i.e., which has zero training error. While problems involving {\em convex} hypotheses have been extensively studied, the question of whether efficient learning is possible for non-convex hypotheses composed of possibly several disconnected regions is still less understood. Although it has been shown quite a while ago that efficient learning of weakly convex hypotheses, a parameterized relaxation of convex hypotheses, is possible for the special case of Boolean functions, the question of whether this idea can be developed into a generic paradigm has not been studied yet. In this paper, we provide a positive answer and show that the consistent hypothesis finding problem can indeed be solved in polynomial time for a broad class of weakly convex hypotheses over metric spaces. To this end, we propose a general domain-independent algorithm for finding consistent weakly convex hypotheses and prove sufficient conditions for its efficiency that characterize the corresponding hypothesis classes. To illustrate our general algorithm and its properties, we discuss several non-trivial learning examples to demonstrate how it can be used to efficiently solve the corresponding consistent hypothesis finding problem. Without the weak convexity constraint, these problems are known to be computationally intractable. We then proceed to show that the general idea of our algorithm can even be extended to the case of extensional weakly convex hypotheses, as it naturally arise, e.g., when performing vertex classification in graphs. We prove that using our extended algorithm, the problem can be solved in polynomial time provided the distances in the domain can be computed efficiently.