Gunnar Carlsson

• Gunnar CarlssonApr 21, 2025, 6:20 PM

  5 points

  0

  in reply to: Davidmanheim’s comment on: Im­prov­ing CNNs with Klein Net­works: A Topolog­i­cal Ap­proach to AI

  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.

Im­prov­ing CNNs with Klein Net­works: A Topolog­i­cal Ap­proach to AI

From Loops to Klein Bot­tles: Un­cov­er­ing Hid­den Topol­ogy in High Di­men­sional Data

Geom­e­try of Fea­tures in Mechanis­tic Interpretability

• Gunnar CarlssonMar 10, 2025, 8:29 PM

  2 points

  1

  in reply to: Martin Vlach’s comment on: Topolog­i­cal Data Anal­y­sis and Mechanis­tic Interpretability

  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

  https://​​www.google.com/​​books/​​edition/​​Basic_Topology/​​NJbuBwAAQBAJ?hl=en&gbpv=1&printsec=frontcover

Topolog­i­cal Data Anal­y­sis and Mechanis­tic Interpretability