This is a linkpost for https://www.youtube.com/watch?v=jGQN0TVCtMo

This is a linkpost for https://www.youtube.com/watch?v=jGQN0TVCtMo

Mathematical Circuits in Neural Networks

5the gears to ascension

2Sean Osier

3Algon

2Sean Osier

1Walid_AlMasri

New Comment

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.

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.

(Also posted on the EA Forum)This is one of my final projects for theColumbia 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 projecthere.SummaryIn this project, I:

What follows is a brief introduction to this work. For full details, please see:

MotivationOlah et al. make three claims about the fundamental interpretability of neural networks:

They demonstrate these claims in the context of image models:

Features / Circuits:Universality:This work demonstrates the same concepts apply in the space of neural networks modeling basic mathematical functions.

ResultsSpecifically, 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:

Minimum Network: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.

Full DetailsFor full details, please see the PDF presentation in the GitHub repo or watch the full video walkthrough: