Sorry, did not make the notion of deformation precise. The idea is that stretching and compressing cannot include attaching one part to another, or tearing it. The mathematical term is that of a “homeomorphism” , which is a one to one, onto, and continuous map. The precise statement is that the figure 8 is not homeomorphic to zero. A good place to look is
Gunnar Carlsson
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- Gunnar Carlsson 10 Mar 2025 20:29 UTC2 points1in reply to: Martin Vlach’s comment on: Topological Data Analysis and Mechanistic Interpretability
Thanks for you comment! My feeling is that the inclusion of “understood” features, as described in this post, will contribute to our understanding of what goes on inside the machines, and therefore allow us to guide and control them better. I am expecting that it will be very important to the application of LLMs as well. So, yes, it may accelerate some things, but it will also add to the degree of controllability that is available to us. I think singluar learning theory is a great direction to move in, and will move us further in the interpretability direction. Not everything in the world is smooth.