Jul 2022 – Sep 2024 · 2 yrs 2 mos · Bengaluru, Karnataka, India

• A novel meta-algorithm to solve Unsupervised Learning Tasks
• We developed and analyzed (in the smoothed setting) a novel meta algorithm Vector Space Decomposition which can solve a variety of unsupervised learning problems with a decomposition flavor, viz. Subspace Clustering, Mixtures of Gaussians, Tensor Decompositions etc.
• For the application of Subspace Clustering, we provided a complete analysis of the quality and robustness of the algorithm, by bounding singular values of relevant matrices using a novel recursive technique. Our paper was published in ITCS 2024.
• Analyzing Gradient Flow on Self-Attention of Transformers via Linear Neural Networks
• For the study of convergence of gradient descent on transformers, we looked at the simplified setting of transformers with one linear attention layer which solve histogram-problems.
• We showed that such models can be reduced to a two-layer linear network where one layer is diagonal, for which we provided a complete analysis of gradient flow, bypassing the initialization or width assumptions which are typical of such problems.
• A Novel First Principle Based Approach to Concept Learning
• Explored a novel theory of concept learning by exploiting the Subspace Conjecture of semantics. As a preliminary test, we developed a novel neighborhood based shape identification algorithm which could achieve character recognition with arbitrary scripts.
• Using plotly developed an interactive application which furnishes the relevant neighborhood information catalog as a function of the input pixels of any arbitrary character.

Aug 2021 – May 2022 · 9 mos

• Exposited the existing results relating the squared norm of a matrix to the squared norm of its real and imaginary parts for the class of Schatten p-norms. I also resolved a standing question in this subject for p in the interval (1, 2).

Jan 2020 – Dec 2021 · 1 yr 11 mos

• Matrix Analysis
• Algorithm Design and Analysis
• Linear Algebra
• Discrete Maths
• Worked over four semesters with responsibilities including conducting discussion and problem-solving sessions, curating reading materials, and designing and grading assignments, quizzes and projects.

Jun 2021 – Jun 2022 · 1 yr · Haryana, India

• Conducted a comprehensive study and security analysis of FALCON, a NIST finalist signature scheme. Prepared a thorough report of the mathematical structures and algorithms used in the lattice-based cryptographic constructions leading to FALCON.