Raghavendra Sridharamurthy

Nishanth Upadhyaya, Raghavendra Sridharamurthy

In this article, we introduce 'Internalized Self-Correction' (InSeC) for large language models (LLMs). While many approaches exist for self-reflection at inference time, we propose a novel method that combines ideas from negative sampling, self-reflection during training, and inference time. InSeC allows LLMs to correct themselves by introducing mistakes and their corresponding corrections during training, thereby converting the learning process into a true supervised learning task with both positive and negative examples. This approach can be extended to improve instruction following and correct hallucinations or incorrect sentences generated by LLMs.

Somenath Das, Raghavendra Sridharamurthy, Vijay Natarajan

We introduce time-varying extremum graph (TVEG), a topological structure to support visualization and analysis of a time-varying scalar field. The extremum graph is a substructure of the Morse-Smale complex. It captures the adjacency relationship between cells in the Morse decomposition of a scalar field. We define the TVEG as a time-varying extension of the extremum graph and demonstrate how it captures salient feature tracks within a dynamic scalar field. We formulate the construction of the TVEG as an optimization problem and describe an algorithm for computing the graph. We also demonstrate the capabilities of \TVEG towards identification and exploration of topological events such as deletion, generation, split, and merge within a dynamic scalar field via comprehensive case studies including a viscous fingers and a 3D von Kármán vortex street dataset.

Lin Yan, Talha Bin Masood, Raghavendra Sridharamurthy et al.

In topological data analysis and visualization, topological descriptors such as persistence diagrams, merge trees, contour trees, Reeb graphs, and Morse-Smale complexes play an essential role in capturing the shape of scalar field data. We present a state-of-the-art report on scalar field comparison using topological descriptors. We provide a taxonomy of existing approaches based on visualization tasks associated with three categories of data: single fields, time-varying fields, and ensembles. These tasks include symmetry detection, periodicity detection, key event/feature detection, feature tracking, clustering, and structure statistics. Our main contributions include the formulation of a set of desirable mathematical and computational properties of comparative measures, and the classification of visualization tasks and applications that are enabled by these measures.