Darby Brillon
Optimal transport algorithms implemented include: multiple variations of the Sinkhorn algorithm solving entropic optimal transport, OT flow matching, and multimarginal Schrödinger bridge matching. Implementing Douglas-Rachford (DR) algorithm to solve discrete dynamic optimal transport using the proximal operator.
Reproduced results from Erdogan et al.'s "An Information-Theoretic Perspective on LLM Tokenizers" paper. Evaluated how tokenizer training scale, tokenizer family, and training/test domain mismatch affect compression and empirical k-gram entropy. Expanded on paper to include Liu et al.'s SuperBPE tokenizer in evaluation. Link for full report.
Built a convolutional neural network using to classify MNIST digits with 2 hidden layers and 2 convolution layers. All model architecture built from scratch; TensorFlow used only for dataset import.
Designed a 4-stage cube solver using group theory and graph search algorithms (BFS, DFS, pruning tables). Solves any scramble in 13.94s avg with 31.36 moves avg. Coded in Python and Java; currently adapting to C++. No libraries used.
Developed a Python stock analysis bot leveraging DCF, DDM, Black-Scholes, and other mathematical valuation models. Built a historical back testing engine to evaluate strategy performance. Currently expanding to support both discrete and continuous quantitative models. Integrating RNN architecture to connect publicly available data with industry trends and market behavior.
Investigation into the mathematics behind Google's PageRank algorithm. Rigorously proved Markov Chain theorems as results from stochastic linear algebra