Scientific Theory of a Black-Box: A Life Cycle-Scale XAI Framework Based on Constructive Empiricism

TL;DR

The paper proposes Scientific Theory of a Black-Box (SToBB), a life-cycle-spanning, auditable artefact that consolidates explanatory information for a fixed black-box using Constructive Empiricism as its epistemic foundation. It operationalizes CE into concrete design obligations—empirical adequacy, updateable acceptance, and pragmatic transparency—and defines five constituents (Observation base, Hypothesis class, Algorithmic components, Adequate surrogate, Documentation) with interfaces to derive explanations. A proof-of-concept, CoBoT, demonstrates how a rule-based surrogate built from an online observation stream can remain empirically adequate as new data arrive while preserving traceability and auditability. The work frames explainability as a shared, reusable reference across stakeholders, supporting governance, auditing, and cross-context analyses, and outlines future work to expand hypothesis classes, auxiliary measures, and interface design.

Abstract

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.

Figures (4)

• Figure 1: Diagnostic information on the current surrogate model. Left axis ("Ratios"): Compression is defined as the gain $1-\frac{\#boxes}{\#samples}$; success rate is the fraction of samples that did not trigger an update. Right axis ("Counts"): #Feature Sets denotes the number of unique feature sets/distinct subspaces; #singletons and #boxes count the number of singleton and the total boxes, respectively. After processing all available $4\,177$ samples, the surrogate comprises less than 20 boxes. Across all observations, $187$ updates were performed.
• Figure 2: Evolution of the axis-aligned bounding boxes contained in the boxsystem for subapace $I=\{2,6\}$. Each individual image shows the same boxystem after different updates. Updates number [1, 7, 16, 19, 25, 27 (final)]. Colors encode classes.
• Figure 3: 2d UMAP embedding of the 4 177 observed samples in the CoBoT-SToBB. Colors indicate feature sets from $\mathcal{I}^{3\uparrow}$, marker style indicates class label.
• Figure : Local Explanation