Math is a language and language can be simple and more sophisticated. Based on Faraday's discovery of electromagnetism, Maxwell came up with Maxwell equations, the vector calculus language to describe it, but when we elevate to 4D and leverage tensor and differential geometry to describe the same, we got more beautiful statement. From Reumi's world, … Continue reading Understanding Electromagnetism via Field Tensor and Exterior Derivative

If you truly understand a theory, you can code it up and run it. So is my approach to truly understanding q, k and v in transformer's attention mechanism. in Previous blog, using "the cat chased the mouse" as an example the math is illustrated in details. Now apply it in codes (from Andrej Kaparthy): … Continue reading True Understanding of Query, Key and Value in Transformer’s Attention Mechanism

MCP protocol provides a possibility to connect massive amount of API functionalities. It could behave like apps in app store and could be big thing next! So I'd like to dig into 1. browse existing, interesting MCP servers an use them; 2. create a simple MCP server myself; 3. think and make a unique service … Continue reading MCP Server is Like App Store Apps?

OpenAI just released in face of fierce competition in the market. When generating model responses, you can extend model capabilities using built-in tools. These tools help models access additional context and information from the web or your files. The example below uses the web search tool to use the latest information from the web to generate a model … Continue reading Web Search, File Search and Computer Use Released by OpenAI

Manus become a big hype, and in a few day, anus posted open-source codes replicating manus, so let me dive into manus codes to see how to build a multi0agent cool app leveraging AI! The Anus AI agent architecture combines the best aspects of OpenManus and OWL while introducing unique features that address limitations in … Continue reading How to Build a Multi-Agent Cool App Levering AI

If I measure three points in a space with three temperature, it's easy and straightforward to interpolate every point in this triangle so I have a smooth view approximately. We can use simple weighting schema depending on distance to each of the three points. It's exactly the same logic to be applied when elevate to … Continue reading Discrete Differential Geometry: Interpolation and Discretization

Here are the examples of exterior derivative computations for 0-forms, 1-forms, and 2-forms provided by deepseek: Note exterior derivative of the 1-form looks like Green's theorem. Let me try to deduce the exterior derivative of 1-form: This is the stunning beauty of MATH!

In calculus, we learn that the derivative measures change. But in a deeper mathematical sense, differentiation acts as the opposite of taking a boundary. This idea is best understood using the language of differential forms and chains. At its core, differentiation isn't just about slopes—it's about how things flow across a space. And just as … Continue reading Derivative is the Opposite of the Boundary

To thoroughly grasp the concept of a gradient, one needs to think deeply. First, we must understand that the gradient represents the steepest slope, which can be illustrated with an analogy like standing at a position on a mountain. However, while analogies can be helpful, they are often not rigorous enough. Mathematics, on the other … Continue reading Is Gradient a Vector or 1-Form?

Differential Forms is a beauty! Multivariable calculus can be greatly simplified and generalized when applying differential forms.