I don't know why the definition of tensor is so mysterious: tensor is something transform like a tensor. Sho Takatori also pointed out the absurdity and illuminate it with Einstein index notation in real calculus computation. Nevertheless, it's still quite complicated, that's why genius Einstein had to come in and provide a notation for generations … Continue reading Master tensor calculus using Einstein index notation by Sho Takatori

The key to success is marketing and promotion rather than just having the best product. Here’s why: 1. The Best Product Doesn’t Always Win Many great products or services fail simply because nobody knows about them. Meanwhile, inferior products can dominate the market due to superior marketing (think of brands like Coca-Cola vs. generic sodas). … Continue reading Marketing is Key

The key traits that an exceptional mathematician or physicist possesses include the ability to identify abstract similarities and commonalities between seemingly disparate objects. The concept of the "square root of geometry" in the context of describing spinors and supersymmetry serves as an exemplary illustration of this skill. However these explanation from chatGPT is not intuitive. … Continue reading Understanding Square Root of Geometry: Lie Algebra to Spinor

Here is a simple example applying it: Magnetic Field at the Center of a Circular Loop

If we apply Noether's theorem in field, given certain epislon to make symmetry: ...

dual vector is like the differential forms, providing the field in background that makes it possible to measure a physical quantity. according to reumi's

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