I am curious in general how mathematics can fundamentally guide the direction of development of computer science most effectively.📈
About
I am Tiantian (Crystal) Zhang. My training combines computer science, optimization, and financial engineering: I completed a B.A. in Computer Science through Columbia University, and I will begin the M.S. in Financial Engineering program at Columbia Engineering / IEOR in Fall 2026.💙
Tiantian (Crystal) Zhang
I work on operations research(portfolio optimization), theorectical computer science(complexity), machine learning theory, diffusion model(generative probabilistic graphical models theory), maybe future (game theory, econ & cs, llm post training).
0. First linear attention inspired from Daniel Hsu's course projectarxiv link without beta tuning .
blog link>
1. LLM's theory need humanity, physics and optimization guidance. seminar notes
2. Learning Theory （in Machine Learning）development？ - momo's answerzhihu , 199 upvote
3. How to self- help confusion as a phd beginner, zhihu's article, 500+ stars.
4. I lead a LLM theory seminar with my research and industry friends.course webpagepaper reading and discussion with over 100 participants.
Research
My work moves between theoretical models, algorithm design, and empirical benchmarks where decision quality is the actual object of interest.
Deep decision optimization and predict-then-optimize methods that train models with awareness of the downstream objective, including SPO/SPO+ style baselines and shortest-path or portfolio decision benchmarks.
Reward-guided post-training methods that view each prompt as a finite decision problem over candidate responses, moving beyond purely pairwise fitting toward decision-distribution updates.
Sleeping experts, rank-induced distributions, mirror descent, and sequential decision problems where availability, ranking, and uncertainty shape the learner’s regret.
My goal is to connect mathematically grounded learning objectives with algorithms that remain useful in realistic, uncertain decision.
Selected work
I am fortunate to have recieved guidance and help from brilliant faculty and postdocs.🦁
A reward-guided decision-distribution approach for LLM preference optimization. The public benchmark is deliberately narrow and preliminary: it compares DDO-RM with DPO on a held-out preference split and frames scaling to larger candidate sets and stronger model families as the next step.
A rank-faithful mirror descent algorithm for sleeping experts under partial availability, using a rank-induced Plackett–Luce parameterization. This project grew from a Machine Learning Theory course project; I am grateful for Prof. Daniel Hsu’s instruction and feedback on the problem area.
An active DDO direction comparing decision-aware training updates with SPO/SPO+ style baselines on downstream optimization benchmarks.
Placeholder for the dynamic prediction-to-decision project from the Boke Technology internship. The planned wording keeps it as an unpublished manuscript and leaves the arXiv / paper link empty until it is public.
A combinatorial optimization project studying extension-complexity lower bounds through polynomial and geometric methods over finite fields, connecting slack-matrix structure with communication-complexity style arguments.
Earlier projects studied causal constraints for robust generalization and rectified-flow ideas for generative learning and transport-based sampling.
Education
Cross-section training.
Incoming M.S. in Financial Engineering, Columbia Engineering / IEOR.
B.A. in Computer Science
Convex Optimization, Statistical Learning, Advanced Algorithms, Theory of Large Language Models, Combinatorial Optimization, Reinforcement Learning in LLMs, and Machine Learning Theory.
Dean’s List, Computer Science Honor Society, Women in Computer Science, William Lowell Putnam Mathematical Competition 2024, and Chinese Mathematics Competition first prize with full marks in 2017.
Experience
I am interested in decision pipelines where prediction, uncertainty, and optimization must be designed together.
Portfolio optimization research on dynamic prediction + decision systems, including multi-horizon prediction models and downstream mean–variance style objectives. The related manuscript is in preparation and should remain a placeholder until public.
Machine learning research for FX options, predictive analysis, and noisy market data workflows.
People
I am again fortunate to have recieved guidance from brilliant faculty and postdocs.🦁
I am also the founder and president of columbia quant llm club.
I feel fortunate to have worked with Prof. Adam Elmachtoub, Prof. Yuri Faenza , Prof. Kede Ma, Prof. Qiang Liu,and Dr. Yong Lin,on projects spanning decision focused learning, discrete optimization, robust learning, generative learning and LLM / reward-model questions.
I am grateful for Prof. Daniel Hsu’s instruction and feedback on the sleeping-experts direction, and his sequence of machine learning theory. I am especially grateful for Prof. Kede Ma, where he opens the gateway to magic research through nine month academic training(full time research assistant).
