Sebastian F. Walter

Hamza Gardi, Sebastian F. Walter, Christoph S. Garbe

This paper presents a technique for finding the surface normal of an object from a set of images obtained under different lighting positions. The method presented is based on the principles of Photometric Stereo (PS) combined with Optimum Experimental Design (OED) and Parameter Estimation (PE). Unclear by the approach of photometric stereo, and many models based thereon, is how to position the light sources. So far, this is done by using heuristic approaches this leads to suboptimal and non-data driven positioning of the light sources. But what if the optimal positions of the light sources are calculated for photometric stereo? To this end, in this contribution, the effect of positioning the light sources on the quality of the normal vector for PS is evaluated. Furthermore, a new approach in this direction is derived and formulated. For the calculation of the surface normal of a Lambertian surface, the approach based on calibrated photometric stereo; for the estimation the optimal position of the light sources the approach is premised on parameter estimation and optimum experimental design. The approach is tested using synthetic and real-data. Based on results it can be seen that the surface normal estimated with the new method is more detailed than with conventional methods.

Sebastian F. Walter, Lutz Lehmann, René Lamour

We address the task of higher-order derivative evaluation of computer programs that contain QR decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate Taylor polynomial arithmetic and matrix calculus in the (combined) forward/reverse mode of Algorithmic Differentiation (AD). Explicit algorithms are derived and presented in an accessible form. The approach is illustrated via examples.

Sebastian Walter, Hannah Bast

We propose a new approach for generating SPARQL queries on RDF knowledge graphs from natural language questions or keyword queries, using a large language model. Our approach does not require fine-tuning. Instead, it uses the language model to explore the knowledge graph by strategically executing SPARQL queries and searching for relevant IRIs and literals. We evaluate our approach on a variety of benchmarks (for knowledge graphs of different kinds and sizes) and language models (of different scales and types, commercial as well as open-source) and compare it with existing approaches. On Wikidata we reach state-of-the-art results on multiple benchmarks, despite the zero-shot setting. On Freebase we come close to the best few-shot methods. On other, less commonly evaluated knowledge graphs and benchmarks our approach also performs well overall. We conduct several additional studies, like comparing different ways of searching the graphs, incorporating a feedback mechanism, or making use of few-shot examples.

S. F. Walter, L. Lehmann

We derive algorithms for higher order derivative computation of the rectangular $QR$ and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and reverse mode of algorithmic differentiation (AD) using univariate Taylor propagation of matrices (UTPM). Linear algebra functions are regarded as elementary functions and not as algorithms. The presented algorithms are implemented in the BSD licensed AD tool \texttt{ALGOPY}. Numerical tests show that the UTPM algorithms derived in this paper produce results close to machine precision accuracy. The theory developed in this paper is applied to compute the gradient of an objective function motivated from optimum experimental design: $\nabla_x Φ(C(J(F(x,y))))$, where $Φ= \{λ_1 : λ_1 C\}$, $C = (J^T J)^{-1}$, $J = \frac{\dd F}{\dd y}$ and $F = F(x,y)$.