In contrast with random uniform instances, industrial SAT instances of large size are solvable today by state-of-the-art algorithms. It is believed that this is the consequence of the non-random structure of the distribution of variables into clauses. In order to produce benchmark instances resembling those of real-world formulas with a given structure, generative models have… Continue reading Real-like MAX-SAT Instances and the Landscape Structure Across the Phase Transition
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AI Studies Survey
AI is a rapidly emerging field that has opened up new vistas of innovation and creativity. From intelligent systems to self-driving cars, AI has transformed the way we live and work. While AI is often studied as a subfield of computer science, it has grown so rapidly that it now encompasses many other fields. The… Continue reading AI Studies Survey
The Silent (R)evolution of SAT
THE PROPOSITIONAL SATISFIABILITY problem (SAT) was the first to be shown NP-complete by Cook and Levin. SAT remained the embodiment of theoretical worst-case hardness. However, in stark contrast to its theoretical hardness, SAT has emerged as a central target problem for efficiently solving a wide variety of computational problems. SAT solving technology has continuously advanced since a breakthrough around the millennium, which catapulted practical SAT solving ahead by orders of magnitudes. Today, the many flavors of SAT technology can be found in all areas of technological innovation.
Algorithms for manifold learning
The technical report presents popular methods for mapping data into a low-dimensional manifold (nonlinear dimensionality reduction). Specifically, it presents Isomap, Locally Linear Embedding, Laplacian Eigenmaps, Semidefinite Embedding and variants of those.
Geometric data analysis based on manifold learning with applications for image understanding
The conference paper gives in the first section a brief and easy understandable introduction into the basics of Riemannian geometry. Furthermore, it gives a review of classical methods for mapping data into a low-dimensional manifold / nonlinear dimensionality reduction like Local Linear Embedding (LLE), Isometric Feature Mapping (ISOMAP) and Local Riemannian Manifold Learning (LRML).
Terse notes on Riemannian geometry
The technical report gives a compact introduction into the basic definitions and theorems of Riemannian geometry, Lie groups & Lie algebras and symmetric spaces. Key concepts like smooth manifolds, tangent spaces, geodesics as well as the exponential map and logarithm map are presented.