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
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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
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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