20230715 Shifting the Lens: Perhaps We Need to See AI and Neural Networks Beyond the Constraints of Coordinates and Formulas

Why do we persist in expressing AI and neural networks through coordinates and seemingly complex formulas? The whole truth is that we don’t need to map every detail into coordinates. AI and deep learning are inching closer to replicating the real world. However, traditional coordinate systems and symbolized formulas represent abstractions within set boundaries - they only offer a piece of the truth.

Such partial truth has created a chasm between academia ensconced in their ivory towers and the industrial world. But why does industry favor AI and deep learning? Because they’re built on the premise of the whole truth, and the industry thrives on this foundation.

It’s time we ask ourselves, who is closer to the truth? If it’s the industry, then we need to broaden our perspective and step away from the distortions created by ‘coordinates’. Only by doing so, can we better understand AI and deep learning, bringing us closer to that alluring truth. This, in turn, will allow us to depict the truth more authentically and create greater value for the industrial world.

With this in mind, I want to share an article I recently came across: “For the use of exterior form in daily physics, an introduction without coordinate frame” by Raphael Ducatez. The author introduces the concept of exterior form in physics from a new, global perspective, which I believe is invaluable.

What caught my attention was the concept of ‘k-form’ - defined as an object that can be integrated on a k-dimensional submanifold. This bypasses the need for specific coordinate systems and allows us to contemplate integration on any k-dimensional submanifold, a luxury not restricted to just three-dimensional space or other specific spatial dimensions. This approach offers us a global view, independent of any specific coordinate system, enhancing our understanding of integral calculus.

Moreover, the idea of a ‘coordinate-free’ description provides a holistic perspective, adaptable to any space and coordinate system. This is fascinating because it challenges the confines of a specific coordinate system and allows us to perceive the world from diverse angles. We can choose to adopt specific coordinate systems when required - almost like shifting from a bird’s eye view to a worm’s eye view.

In conclusion, Ducatez’s global perspective has broadened my horizons, and I believe it carries immense value in understanding and describing the fundamental structures in physics. I eagerly anticipate more such exploratory research and applications in the future.

Remember, AI is not just about crunching numbers in a complex formula or within a set of coordinates. It’s about understanding the essence of intelligence and learning, and then capturing this understanding in the most truthful way possible. This way, we can add more value to the industrial world and bring the academia closer to it.

Reference:

  1. Ducatez, R. For the use of exterior form in daily physics, an introduction without coordinate frame. Preprint at http://arxiv.org/abs/2307.06597 (2023).

2023.7.13 xiaowen kang.