Infrastructure-as-Code (IaC), an important component of cloud computing, allows the definition of cloud infrastructure in high-level programs.

The key challenge of multi-view indoor 3D object detection is to infer accurate geometry information from images for precise 3D detection. Previous method relies on NeRF for geometry reasoning.

In many machine learning tasks, data is inherently sequential.

Large language models (LLMs) are of paramount importance in today's technological landscape.

Prior known algorithms for both these settings have strong inherent limitations, making them impractical for real-world scenarios.

However, it seems that including the dimension of time remains challenging.

We introduce Non-Euc lidean-MDS (Neuc-MDS), an extension of classical Multidimensional Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is to generalize the standard inner product to symmetric bilinear forms to utilize the negative eigenvalues of dissimilarity Gram matrices. Neuc-MDS efficiently optimizes the choice of (both positive and negative) eigenvalues of the dissimilarity Gram matrix to reduce STRESS, the sum of squared pairwise error. We provide an in-depth error analysis and proofs of the optimality in minimizing lower bounds of STRESS. We demonstrate Neuc-MDS's ability to address limitations of classical MDS raised by prior research, and test it on various synthetic and real-world datasets in comparison with both linear and non-linear dimension reduction methods.