below is a collection of notes from various coursework and self-study. course notes are taken either live during lecture or during my free-time, so they are very prone to mistakes. feel free to reach out with any questions or corrections.

writing

• A Condensation Crossover In Softmax Attention
  analyzing a condensation crossover scale in a toy self-attention model
• Towards a Non-Stationary Dynamic Mean Field Theory for Low-Rank Recurrent Neural Networks
  testing if a low-rank Jacobian outlier proxy predicts stability in driven networks

courses

• MATH 553: Partial Differential Equations [wip]
  wave equation, heat equation, laplace equation, smooth/weak solutions, power series, harmonics, distribution theory, fourier transforms, green's functions, potential theory
• Information Geometry For Neuroscience
  fischer information, statistical manifolds, neural coding, gradient learning, feature learning, neural population models
• ECE 598RE: Dynamical Systems & Neural Networks [wip]
  stability, lyapunov theory, rnns, sgd, neural differential equations, neuron dynamics, mean-field theory, random dynamical systems
• ECE 598IS: High-Dimensional Statistics [wip]
  decision theory, information inequalities, le cam's and fano's methods, random matrix theory, spectral estimators, stochastic block models, graph embeddings, laplacian eigenmaps, johnson-lindenstrauss, pca
• CS 540: Deep Learning Theory [wip]
  approximations, optimizations, ntk regime, rademacher complexity, clarke differentials, gradient flows, margins, generalization
• MATH 595: Representation Theory & Quantum Information
  schur-weyl duality, werner states, covariant channels, de finetti theorems, quantum types, spectrum estimation, cloning, source compression
• MATH 466: Applied Random Processes
  discrete/continuous-time markov chains, recurrence, invariant distributions, kolmogorov equations, martingales, brownian motion, queueing, mcmc, population models
• MATH 447: Real Variables
  metric spaces, compactness, connectedness, uniform continuity, \(C(K)\) completeness, dini's theorem, differentiation, integration, fundamental theorem, power series