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Achievement: Pair ExtraordinaireAchievement: Arctic Code Vault Contributor

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nathan-albin/README.md

Hi, I'm Nathan Albin

Applied mathematician and research engineer working at the intersection of optimization, machine learning, and numerical methods. I write both code and proofs.

I build scientific software and study the mathematics underneath modern AI: automatic differentiation, graph neural networks, convex optimization, and the numerical-precision questions that decide whether an algorithm actually returns the right answer.

What I work on

  • Machine learning from first principles: reverse-mode autodiff engines and graph neural networks built from scratch, and neural ODEs for nonlinear system identification.
  • Convex optimization and graph theory: network modulus, spectral graph theory, and exact/rational-arithmetic solvers that return provably correct answers with no floating-point error.
  • Numerical methods and HPC: high-order spectral (Fourier-continuation) PDE solvers and MPI-parallel scientific computing on SLURM clusters.
  • Formal methods: actively learning Lean 4, and leading a seminar series introducing it to my research group.

Toolkit

Python (NumPy, SciPy, PyTorch, TensorFlow) · Julia · Lean 4 · C/C++ · Fortran · SQL · Git · Linux · high-performance computing (MPI, SLURM, GPU)

Elsewhere

  • Book: Mathematics of Networks: Modulus Theory and Convex Optimization (Chapman & Hall/CRC, 2025)
  • Google Scholar: full publication list, roughly 48 peer-reviewed papers
  • LinkedIn

I'm always glad to connect with people working on AI/ML research, scientific machine learning, optimization, and formal verification.

Pinned Loading

  1. discrete-modulus discrete-modulus Public

    Reference implementations of discrete modulus algorithms, with an accompanying book.

    Python

  2. lean-modulus lean-modulus Public

    Lean 4 formalizations of results from my research on graphs, networks, and the modulus of families of objects.

    Lean

  3. quant-reasoning quant-reasoning Public

    Does int8/int4 quantization hurt LLM math reasoning more than perplexity? A controlled Qwen2.5-7B study (vLLM + GSM8K + MATH-500) suggesting perplexity may be an unreliable proxy for more complex r…

    Python

  4. coulomb-explosion coulomb-explosion Public

    High-performance C++20 simulator for molecular Coulomb explosions — SIMD-vectorized, cache-aware engine (~27× over scalar) generating ML training sets to invert momentum measurements back to molecu…

    C++

  5. mass-spring-neural-ode mass-spring-neural-ode Public

    Jupyter notebook assignment for undergraduate ODEs class. Uses a neural ODE to learn a nonlinear damping response from real experimental data.

    Jupyter Notebook