Provable unlearning in topic modeling and downstream tasks

Machine unlearning algorithms are increasingly important as legal concerns arise around the provenance of training data, but verifying the success of unlearning is often difficult. Provable guarantees for unlearning are often limited to supervised learning settings. In this paper, we provide the first theoretical guarantees for unlearning in the pre-training and fine-tuning paradigm by studying topic models, simple bag-of-words language models that can be adapted to solve downstream tasks like retrieval and classification. First, we design a provably effective unlearning algorithm for topic models that incurs a computational overhead independent of the size of the original dataset. Our analysis additionally quantifies the deletion capacity of the model -- i.e., the number of examples that can be unlearned without incurring a significant cost in model performance. Finally, we formally extend our analyses to account for adaptation to a given downstream task. In particular, we design an efficient algorithm to perform unlearning after fine-tuning the topic model via a linear head. Notably, we show that it is easier to unlearn pre-training data from models that have been fine-tuned to a particular task, and one can unlearn this data without modifying the base model.

Transformers Provably Learn Sparse Token Selection While Fully-Connected Nets Cannot

The transformer architecture has prevailed in various deep learning settings due to its exceptional capabilities to select and compose structural information. Motivated by these capabilities, Sanford et al. proposed the sparse token selection task, in which transformers excel while fully-connected networks (FCNs) fail in the worst case. Building upon that, we strengthen the FCN lower bound to an average-case setting and establish an algorithmic separation of transformers over FCNs. Specifically, a one-layer transformer trained with gradient descent provably learns the sparse token selection task and, surprisingly, exhibits strong out-of-distribution length generalization. We provide empirical simulations to justify our theoretical findings.