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Provable unlearning in topic modeling and downstream tasks

Stanley Wei, Sadhika Malladi, Sanjeev Arora, Amartya Sanyal

TL;DR

This work establishes the first provable unlearning guarantees for the pre-training and fine-tuning pipeline using topic models. It develops a base unlearning algorithm with deletion capacity $m_U = \tilde{\mathcal{O}}(m/(r^2\sqrt{nr}))$ and extends the analysis to downstream tasks, showing a capacity of $\tilde{\Omega}(mq/(r\sqrt{nr}))$ when a linear head solves the downstream task, with $q \in [1/r,1]$. Crucially, it demonstrates that unlearning pre-training data from a fine-tuned model can be easier and even possible without modifying the base ${A}$, and that realistic settings (releasing $B = A w$) enable efficient unlearning with runtimes faster than retraining. The results leverage anchor-word-based learning, the Gaussian mechanism for indistinguishability under $(\epsilon,\delta)$-unlearning, and careful analyses of deletion capacity and downstream task dependence, providing a principled path toward scalable, compliant unlearning in large pre-trained models.

Abstract

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.

Provable unlearning in topic modeling and downstream tasks

TL;DR

This work establishes the first provable unlearning guarantees for the pre-training and fine-tuning pipeline using topic models. It develops a base unlearning algorithm with deletion capacity and extends the analysis to downstream tasks, showing a capacity of when a linear head solves the downstream task, with . Crucially, it demonstrates that unlearning pre-training data from a fine-tuned model can be easier and even possible without modifying the base , and that realistic settings (releasing ) enable efficient unlearning with runtimes faster than retraining. The results leverage anchor-word-based learning, the Gaussian mechanism for indistinguishability under -unlearning, and careful analyses of deletion capacity and downstream task dependence, providing a principled path toward scalable, compliant unlearning in large pre-trained models.

Abstract

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.

Paper Structure

This paper contains 28 sections, 55 theorems, 123 equations, 1 table, 6 algorithms.

Table of Contents

  1. Introduction
  2. Overview of Results
  3. Topic Models
  4. Problem Description
  5. Downstream Adaptation
  6. Unlearning
  7. Learning and Unlearning Topic Models
  8. Notation.
  9. Learning Algorithm and Guarantees
  10. Unlearning Algorithm and Guarantees
  11. Unlearning with respect to a Downstream Task
  12. Naive Setting
  13. Realistic Setting
  14. Proof sketch.
  15. Related Works
  16. ...and 13 more sections

Key Result

Lemma 1

Let $f$ be an arbitrary $d$-dimensional function, and define its $\ell_2$-sensitivity to be $\Delta_2 f := \max\limits_{\text{adjacent }x, y} \|f(x) - f(y)\|_2$. Then, for $c^2 > 2\log \frac{1.25}{\delta}$, the Gaussian mechanism with parameter $\sigma\geq c\Delta_2 f/\epsilon$ is $(\epsilon,\delta)

Theorems & Definitions (89)

  • Definition 1: Topic Classification Task
  • Definition 2: $\tau$-Head Tuning
  • Definition 3: $(\epsilon,\delta)$-indistinguishable models, dwork2014algorithmic
  • Definition 4: Utility-preserving $({\epsilon},\delta)$-Unlearning with Deletion Capacity
  • Lemma 1: Gaussian Mechanism, dwork2014algorithmic
  • Theorem 1: Learning Guarantee
  • Definition 5
  • Lemma 2: Approximation Guarantee on Anchor Words
  • Lemma 3
  • Theorem 2: Utility-Preserving Unlearning on the Base Model
  • ...and 79 more