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Caihao Cui

Caihao Cui

Knowledge Grounds Action; Learning Nurtures Virtue.

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

Optimization in Machine Learning: From Gradient Descent to Boosting, Neural Networks, and MAP

7 October 2026·7458 words·36 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 2026·40414 words·190 mins

An abstract depiction of a figure being simultaneously elevated onto a pedestal by some hands, while other hands pull it down, symbolizing the dual process of 'god-making' and 'god-destroying' in public perception.

Creating Gods Gives Hope, Destroying Them Gives Self-Esteem: Behind the "Deification" and "Reversal" of Public Figures

2 September 2026·3710 words·18 mins

An abstract depiction of an AI agent interacting with various enterprise systems, illustrating a robust runtime framework (harness) that ensures secure and reliable modification of business states through permission validation, state management, and fault recovery.

When AI Agents Begin Modifying Business State: The Need for a Runtime Framework Beyond the Model

31 August 2026·3659 words·18 mins

A vibrant, intricate network of gears and planned pathways representing research investment and infrastructure, contrasted with a single, brightly illuminated, unpredictable lightning bolt striking in an unexpected direction, symbolizing an original scientific breakthrough that cannot be scheduled or pre-planned. The background subtly suggests a vast, yet partially obscured, landscape of long-term exploration.

Scientific Research: Investment Can Be Planned, But Breakthroughs Cannot Be Scheduled — A Discussion Inspired by Two Fields Medals

30 August 2026·4029 words·9 mins