(Also posted on the EA Forum)
This is one of my final projects for the Columbia EA Summer 2022 Project Based AI Safety Reading Group (special thanks to facilitators Rohan Subramini and Gabe Mukobi). If you're curious you can find my other project here.
In this project, I:
What follows is a brief introduction to this work. For full details, please see:
Olah et al. make three claims about the fundamental interpretability of neural networks:
They demonstrate these claims in the context of image models:
Features / Circuits:
This work demonstrates the same concepts apply in the space of neural networks modeling basic mathematical functions.
Specifically, I show that the optimal network for calculating the minimum of two arbitrary numbers is fully constructed from smaller "features" and "circuits" used across even simpler mathematical functions. Along the way, I explore:
I also demonstrate that each of these theoretical results hold in practice. The code for these experiments can be found on the GitHub page for this project.
For full details, please see the PDF presentation in the GitHub repo or watch the full video walkthrough:
representation theory is a related topic - representing other math using linear algebra. see, eg, https://www.youtube.com/watch?v=jPx5sW6Bl-M - the wikipedia page is also an okay intro.
Interesting, I'll definitely look into that! Sounds quite related.
For the identity function, wouldn't regularisation would push the non-zero weights towards unity?
Thanks for the comment! I didn't get around to testing that, but that's one of the exact things I had in mind for my "Next Steps" #3 on training regimens that more reliably produce optimal, interpretable models.