Incoming PhD applicant with a strong foundation in Applied Mathematics and Computer Science.

My core objective is to pursue doctoral research in Technical AI Safety, leveraging Applied Category Theory (ACT) and Singular Learning Theory (SLT).

• The question: how does degeneracy behave when neural network components are composed?
• The measure: the learning coefficient from singular learning theory, which captures how much of a parameter space is effectively in use.
• The gap: it can only be computed for whole models, in isolated cases, never assembled from parts.
• The application: whether compositional degeneracy predicts where learned features and circuit descriptions stay stable.
• The tools: algebraic geometry, singular learning theory, applied category theory.

• M.S. in Computer Science (Machine Learning Specialization): Georgia Institute of Technology
• M.Sc. Mathematics & B.E. Computer Science: BITS Pilani

• Languages: C/C++, Python, Julia, MATLAB, Java, C#, SQL
• ML & Scientific: PyTorch, Flower, NumPy, Scikit-learn, Qiskit, Pymc, Turing, Networkx, Pandas, Matplotlib
• Developer Tools: Git, VS Code, Jupyter Notebook, IntelliJ IDEA, Unity, LaTeX

• Bayesian Estimation of Differential Equations (SEIR Model): Github Link
  • Description: This project demonstrates the parameter estimation of the SEIR (Susceptible, Exposed, Infected, Recovered) model using Bayesian inference. The goal of this project is to solve the “inverse problem” of parameter estimation: utilizing noisy observational data to determine non-measurable model parameters with quantified uncertainty.
  • Tech Stack: Turing.jl (Probabilistic Programming), OrdinaryDiffEq.jl (Differential Equations), StatsPlots.jl (Data Visualization)
• JuliaTopOpt/SimpleTopOpt.jl Contributions: Github Link
  • Description: The contributions involve translating complex MATLAB-based topology optimization models (3D, stress, and buckling) into Julia using established academic literature and benchmarking the computational efficiency of the newly developed Julia implementations against their MATLAB counterparts.
  • Tech Stack: SparseArrays.jl, LinearAlgebra.jl, Makie.jl/GLMakie.jl for 3D visualization, Roots.jl, Match.jl, Images.jl, JLD.jl, TimerOutputs.jl, MATLAB.jl for cross-validation, Test.jl

I am actively seeking PhD positions and research co-supervision in Applied Category Theory, SLT, and Technical AI Safety.

• Personal Website: utkarshyashvardhan11.github.io
• Email: uyashvardhan3@gatech.edu
• LinkedIn: linkedin.com/in/utkarshyashvardhan11