I wonder; is this essentially why LLM tech is useful for certain Fields-medal level problems? i.e. because the LLM search construct has no barrier between sub-fields; nor between distant ones? Only multiple likely paths?
In context of packing problem, it's a bit meta to me...
An LLM contains a k-dimensional packing of known knowledge. This packing is highly inefficient because it has holes and unbridged dimensions. By injecting random seed (prompts) into the LLM probability space, it gets perturbed. Sometimes this perturbation fills a hole in the packing and/or connects two adjacent units in way nobody thought of before because it wasn't fashionable any more, or wasn't top of mind. Thus new knowledge is created within the same k-dimensional box through a novel joining-of of existing know-how.
From the article:
> Klartag had broken open a central problem in the world of lattices and sphere packing after just a few months of study and a few weeks of proof writing. “It feels almost unfair,” he said. But that’s often how mathematics works: Sometimes all a sticky problem needs is a few fresh ideas, and venturing outside one’s immediate field can be rewarding. Klartag’s familiarity with convex geometry, usually a separate area of study, turned out to be just what the problem required. “This idea was at the top of my mind because of my work,” he said. “It was obvious to me that this was something I could try.”
In context of packing problem, it's a bit meta to me...
An LLM contains a k-dimensional packing of known knowledge. This packing is highly inefficient because it has holes and unbridged dimensions. By injecting random seed (prompts) into the LLM probability space, it gets perturbed. Sometimes this perturbation fills a hole in the packing and/or connects two adjacent units in way nobody thought of before because it wasn't fashionable any more, or wasn't top of mind. Thus new knowledge is created within the same k-dimensional box through a novel joining-of of existing know-how.
From the article:
> Klartag had broken open a central problem in the world of lattices and sphere packing after just a few months of study and a few weeks of proof writing. “It feels almost unfair,” he said. But that’s often how mathematics works: Sometimes all a sticky problem needs is a few fresh ideas, and venturing outside one’s immediate field can be rewarding. Klartag’s familiarity with convex geometry, usually a separate area of study, turned out to be just what the problem required. “This idea was at the top of my mind because of my work,” he said. “It was obvious to me that this was something I could try.”