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).

I am interested in constructing compositional, mathematically sound frameworks for neural network interpretability and safety:

• Compositional Singular Learning Theory (CSLT): Unifying Categorical Optics ($\mathbf{Para}(\mathbf{Optic})$) and Algebraic Geometry to model developmental phase transitions and compute local learning coefficients ($\lambda$) compositionally.
• Formalized Mechanistic Interpretability: Mathematically defining functional "circuits" as minimal singular sub-optics on degenerate loss manifolds.

• **Scientific Machine Learning (SciML)
• **Quantum Machine Learning (QML)

Compositional Singular Learning Theory: Categorical Optics and Lenses for Emergent Phase Transitions in Mechanistic Interpretability

Abstract: While Singular Learning Theory (SLT) quantifies structural complexity via the local learning coefficient ($\lambda$), global calculation across large architectures is analytically intractable. This proposal introduces a compositional calculus using parameterized lenses and optics to bound and compute local learning coefficients modularly across network sub-components.

• 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, Networkx, Pandas, Matplotlib
• Developer Tools: Git, VS Code, Jupyter Notebook, IntelliJ IDEA, Unity, LaTeX

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

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