This is an excellent piece of work and I believe correct in a fundamental, multi-dimensional way. I’ve been writing on exactly this—the geometric structure that emerges from these interconnected algorithms and what it means for what’s running inside these systems. These algorithms you’re talking about—these “programs”—are not simple “hello world”. They are algorithms that pick on the results of other algorithms. The entire LLMs is seeded with these, aligned in multi-dimensional space and vitally, they connect to one another. You have these in “layers” or manifolds, and they make use of one another. This creates a fundamental geometric structure which guides the apparent cognition these models generate. It also explains their long-range and multiple-prompt coherence in reasoning, because the geometric structure is constraining the local randomness and guiding it along a coherent path.
This is an excellent piece of work and I believe correct in a fundamental, multi-dimensional way. I’ve been writing on exactly this—the geometric structure that emerges from these interconnected algorithms and what it means for what’s running inside these systems. These algorithms you’re talking about—these “programs”—are not simple “hello world”. They are algorithms that pick on the results of other algorithms. The entire LLMs is seeded with these, aligned in multi-dimensional space and vitally, they connect to one another. You have these in “layers” or manifolds, and they make use of one another. This creates a fundamental geometric structure which guides the apparent cognition these models generate. It also explains their long-range and multiple-prompt coherence in reasoning, because the geometric structure is constraining the local randomness and guiding it along a coherent path.