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Caihao Cui

Caihao Cui

Knowledge Grounds Action; Learning Nurtures Virtue.

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$Proof fragments stream rapidly toward the center while researchers inspect, connect, and interpret them on the other side$

If Only AI Understands the Proof: When Machines Take Over Deduction and Code

31 October 2026·3547 words·17 mins

A dark-blue retail network in which two warehouses, several stores, and a central fulfillment node are connected by teal guarded paths, amber probability flows, and violet graph relationships.

Retail Demand Forecasting with Graph Neural Networks: Mathematical Principles, Controlled Experiments, and Production Boundaries

24 October 2026·Updated: 30 October 2026·11549 words·55 mins

An illustration depicting a progression from a simple, isolated decision tree to a dense, interconnected forest of trees, symbolizing the evolution and complexity of ensemble tree models in machine learning.

From a Single Tree to a Forest: Mathematical Principles, Algorithmic Evolution, and Engineering Practices of Tree Models

17 October 2026·18578 words·38 mins

Gradient descent, Newton's method, and BFGS following different trajectories toward the minimum of an elliptical quadratic objective.

What Are Machine Learning Models Really Optimizing? From Gradient Descent to Large Language Models

7 October 2026·Updated: 11 October 2026·7808 words·37 mins

Cartoon illustration of retail demand forecasting, seasonal cycles, and inventory planning

Retail Demand Forecasting with Prophet: From Model Fundamentals to Engineering Practice

1 October 2026·Updated: 11 October 2026·40470 words·81 mins