Exploring Modular Arithmetic in Neural Networks

How do we figure out whether interpretability is doing its job? One way is to see if it helps us prove things about models that we care about knowing. In this episode, I speak with Jason Gross about his agenda to benchmark interpretability in this way, and his exploration of the intersection of proofs and modern machine learning.

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Transcript: https://axrp.net/episode/2025/03/28/episode-40-jason-gross-compact-proofs-interpretability.html

Topics we discuss, and timestamps:

0:00:40 - Why compact proofs

0:07:25 - Compact Proofs of Model Performance via Mechanistic Interpretability

0:14:19 - What compact proofs look like

0:32:43 - Structureless noise, and why proofs

0:48:23 - What we've learned about compact proofs in general

0:59:02 - Generalizing 'symmetry'

1:11:24 - Grading mechanistic interpretability

1:43:34 - What helps compact proofs

1:51:08 - The limits of compact proofs

2:07:33 - Guaranteed safe AI, and AI for guaranteed safety

2:27:44 - Jason and Rajashree's start-up

2:34:19 - Following Jason's work

Links to Jason:

Github: https://github.com/jasongross

Website: https://jasongross.github.io

Alignment Forum: https://www.alignmentforum.org/users/jason-gross

Links to work we discuss:

Compact Proofs of Model Performance via Mechanistic Interpretability: https://arxiv.org/abs/2406.11779

Unifying and Verifying Mechanistic Interpretability: A Case Study with Group Operations: https://arxiv.org/abs/2410.07476

Modular addition without black-boxes: Compressing explanations of MLPs that compute numerical integration: https://arxiv.org/abs/2412.03773

Stage-Wise Model Diffing: https://transformer-circuits.pub/2024/model-diffing/index.html

Causal Scrubbing: a method for rigorously testing interpretability hypotheses: https://www.lesswrong.com/posts/JvZhhzycHu2Yd57RN/causal-scrubbing-a-method-for-rigorously-testing

Interpretability in Parameter Space: Minimizing Mechanistic Description Length with Attribution-based Parameter Decomposition (aka the Apollo paper on APD): https://arxiv.org/abs/2501.14926

Towards Guaranteed Safe AI: https://www2.eecs.berkeley.edu/Pubs/TechRpts/2024/EECS-2024-45.pdf

Episode art by Hamish Doodles: hamishdoodles.com