Compact Proofs of Model Performance via Mechanistic Interpretability

In this work, we propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance. We prototype this approach by formally proving lower bounds on the accuracy of 151 small transformers trained on a Max-of-$K$ task. We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models. Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding. Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds. We confirm these connections by qualitatively examining a subset of our proofs. Finally, we identify compounding structureless noise as a key challenge for using mechanistic interpretability to generate compact proofs on model performance.

Provable Guarantees for Model Performance via Mechanistic Interpretability

In this work, we propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance. We prototype this approach by formally proving lower bounds on the accuracy of 151 small transformers trained on a Max-of-$K$ task. We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models. Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding. Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds. We confirm these connections by qualitatively examining a subset of our proofs. Finally, we identify compounding structureless noise as a key challenge for using mechanistic interpretability to generate compact proofs on model performance.

Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data

The proliferation of generative models, combined with pretraining on web-scale data, raises a timely question: what happens when these models are trained on their own generated outputs? Recent investigations into model-data feedback loops discovered that such loops can lead to model collapse, a phenomenon where performance progressively degrades with each model-fitting iteration until the latest model becomes useless. However, several recent papers studying model collapse assumed that new data replace old data over time rather than assuming data accumulate over time. In this paper, we compare these two settings and show that accumulating data prevents model collapse. We begin by studying an analytically tractable setup in which a sequence of linear models are fit to the previous models' predictions. Previous work showed if data are replaced, the test error increases linearly with the number of model-fitting iterations; we extend this result by proving that if data instead accumulate, the test error has a finite upper bound independent of the number of iterations. We next empirically test whether accumulating data similarly prevents model collapse by pretraining sequences of language models on text corpora. We confirm that replacing data does indeed cause model collapse, then demonstrate that accumulating data prevents model collapse; these results hold across a range of model sizes, architectures and hyperparameters. We further show that similar results hold for other deep generative models on real data: diffusion models for molecule generation and variational autoencoders for image generation. Our work provides consistent theoretical and empirical evidence that data accumulation mitigates model collapse.