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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.

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

7 October 2026·7395 words·35 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