arXiv subjects

Moritz Lang

Publications and source records attributed to Moritz Lang.

4 recordsLinked to original sources

arXiv2025

Explainable Information Retrieval in the Audit Domain

Conversational agents such as Microsoft Copilot and Google Gemini assist users with complex search tasks but often generate misleading or fabricated references. This undermines trust, particularly in high-stakes domains such as medicine and finance. Explainable information retrieval (XIR) aims to address this by making search results more transparent and interpretable. While most XIR research is domain-agnostic, this paper focuses on auditing -- a critical yet underexplored area. We argue that XIR systems can support auditors in completing their complex task. We outline key challenges and future research directions to advance XIR in this domain.

cs.IR↗

arXiv2021

The Mechanism of Scale-Invariance

A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input transformations forms a Lie group, the most prominent examples being scale-invariant ($u\mapsto e^pu$, $p\in\mathbb{R}$) and translational-invariant ($u\mapsto pu$) systems, the latter comprising linear systems with transfer function zeros at the origin. Here, we derive a necessary and sufficient normal form for invariant systems and, by analyzing this normal form, provide a complete characterization of the mechanism by which invariance can be achieved. In this normal form, all invariant systems (i) estimate the applied input transformation by means of an integral feedback, and (ii) then apply the inverse of this estimate to the input before processing it in any other way. We demonstrate our results based on three examples: a scale-invariant "feed-forward loop", a bistable switch, and a system resembling the core of the mammalian circadian network.

math.DS↗

arXiv2019

Sandpile monomorphisms and limits

We introduce a tiling problem between bounded open convex polyforms $\hat{P}\subset\mathbb{R}^2$ with directed and uniquely colored edges. If there exists a tiling of the polyform $\hat{P}_2$ by $\hat{P}_1$, we show that one can construct a monomorphism from the sandpile group $G_{\Gamma_1}=\mathbb{Z}^{\Gamma_1}/\Delta(\mathbb{Z}^{\Gamma_1})$ on the domain (graph) $\Gamma_1=\hat{P}_1\cap\mathbb{Z}^2$ to the respective group on $\Gamma_2=\hat{P}_2\cap\mathbb{Z}^2$. We provide several examples of infinite series of such tilings with polyforms converging to $\mathbb{R}^2$, and thus the first definition of scaling-limits for the sandpile group on the plane. Additional results include an exact sequence relating sandpile configurations to harmonic functions, an alternative formula for the order of the sandpile group based on a basis for the module of integer-valued harmonic functions, and three examples of how to prove the existence of (cyclic) subgroups for infinite families of sandpile groups by constructing appropriate integer-valued harmonic functions. The main open question concerns if the scaling-limits of the sandpile group for different sequences of polyforms converging to $\mathbb{R}^2$ are isomorphic.

math-ph↗

arXiv2018

Harmonic dynamics of the Abelian sandpile

The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit is subject of extensive collaborative research. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second and third order harmonics resemble smooth stretchings, respectively translations, of the identity, while the ones induced by fourth order harmonics resemble magnifications and rotations. Starting with order three, the dynamics pass through extended regions of seemingly random configurations which spontaneously reassemble into accentuated patterns. We show that the space of harmonic functions projects to the extended analogue of the sandpile group, thus providing a set of universal coordinates identifying configurations between different domains. Since the original sandpile group is a subgroup of the extended one, this directly implies that it admits a natural renormalization. Furthermore, we show that the harmonic fields can be induced by simple Markov processes, and that the corresponding stochastic dynamics show remarkable robustness over hundreds of periods. Finally, we encode information into seemingly random configurations, and decode this information with an algorithm requiring minimal prior knowledge. Our results suggest that harmonic fields might split the sandpile group into sub-sets showing different critical coefficients, and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain.

math-ph↗