Paul Jason Mello

About Me

Hi, I'm Paul! A PhD student at the University of Nevada, Reno researching the deep mathematical foundations of deep learning. My research interests bridge topics like information theory, category theory, and manifold methods to understand and improve how neural networks learn. Recently I have completed work in building a deep learning framework from categorical first principles and studying delayed generalization through manifold geometry.

For collaborations or questions, feel free to reach out via my email or socials.

Blogs

• [ESN Research] Echo State Networks [November 1, 2025]
• [LTCN Research] Liquid Time-Constant Networks [June 2, 2025]
• • [SNN Research] Sheaf Neural Networks [May 19, 2025]
  • [Thoughts On] Tweedie's Formula [May 16, 2025]
  • [Noise Research] Perturbation Driven Generalization [May 5, 2025]

Projects

• [Category Theory] Categorical Deep Learning [April 1, 2026]
• [Fourier Research] Fourier Transforms [January 12, 2026]
• • [ESN Implementation] Echo State Networks [November 1, 2025]
  • [Attention Research] Transformer Attention Bench [October 29, 2025]
  • [Matrix Research] Random Matrix Theory [August 29, 2025]

Publications

• [Master's Thesis] An Exploration of Information Processing in Diffusion Models [August 16, 2024]
• [IEEE Publication] Multi-Resolution Diffusion for Privacy-Sensitive Recommender Systems [April 12, 2024]

Education

• PhD in Computer Science and Engineering - University of Nevada, Reno Fall 2024 - Present
• MSc in Artificial Intelligence - San José State University Fall 2021 - Spring 2024
• BSc in Computer Science - California State University, Sacramento Fall 2016 - Spring 2021
  • Minors: Mathematics, Philosophy